1 O que é o ggplot

O ggplot é uma função da linguagem R, do package ggplot2, usado para a construção de gráficos e lidar com dados estatísticos. Nele, é possíve criar diferentes tipos de gráficos, com diferentes configurações, para diferentes tipos de demandas.

1.1 Usar o ggplot ou os plot normais?

Se você já usa o R há algum tempo, e precisou criar gráficos, você já deve saber, mas se você começou agora nesse mundo, saiba que é possível criar gráficos apenas com o R, sem precisar de um package extra. Essas são as funções como plot(), boxplot() e hist().

1.2 A praticidade do ggplot

Por mais que os plots normais sejam mais fáceis de aprender, e relativamente mais rápidos, são muito rígidos e poucos práticos para configurá-los. No dia-a-dia das pesquisas, análises e relatórios, onde se está todo dia com diferentes tipos de dados, situações, exigências e demandas singulares, tanto para as análises quanto para expor esses resultados de diferentes maneiras a um público, como a apresentação de um seminário, uma banca avaliadora ou até uma empresa que contratou seus serviços, ter uma ferramenta como o ggplot, que permite que seja possível criar uma maior gama de diferentes tipos de gráficos, pode acabar sendo a diferença entre um gráfico informativo, prático e que economize tempo e dinheiro para entender um resultado e tomar uma decisão, e um gráfico ilegível e pouco entendível, gerando conflitos de interpretações, perda de tempo, de dinheiro, e até correndo o risco de tomar uma decisão errada. Tendo entendido o valor de se dedicar a entender e dominar o ggplot, vamos agora sim dar os primeiros passos.

2 Primeiros passos

2.1 Packages exigidos

library(tidyverse)

Foi carregado o package tidyverse, que, aumaticamente, carrega o package ggplot2.

2.2 Carregando a base de dados

SW<-starwars
SW
## # A tibble: 87 × 14
##    name        height  mass hair_…¹ skin_…² eye_c…³ birth…⁴ sex   gender homew…⁵
##    <chr>        <int> <dbl> <chr>   <chr>   <chr>     <dbl> <chr> <chr>  <chr>  
##  1 Luke Skywa…    172    77 blond   fair    blue       19   male  mascu… Tatooi…
##  2 C-3PO          167    75 <NA>    gold    yellow    112   none  mascu… Tatooi…
##  3 R2-D2           96    32 <NA>    white,… red        33   none  mascu… Naboo  
##  4 Darth Vader    202   136 none    white   yellow     41.9 male  mascu… Tatooi…
##  5 Leia Organa    150    49 brown   light   brown      19   fema… femin… Aldera…
##  6 Owen Lars      178   120 brown,… light   blue       52   male  mascu… Tatooi…
##  7 Beru White…    165    75 brown   light   blue       47   fema… femin… Tatooi…
##  8 R5-D4           97    32 <NA>    white,… red        NA   none  mascu… Tatooi…
##  9 Biggs Dark…    183    84 black   light   brown      24   male  mascu… Tatooi…
## 10 Obi-Wan Ke…    182    77 auburn… fair    blue-g…    57   male  mascu… Stewjon
## # … with 77 more rows, 4 more variables: species <chr>, films <list>,
## #   vehicles <list>, starships <list>, and abbreviated variable names
## #   ¹​hair_color, ²​skin_color, ³​eye_color, ⁴​birth_year, ⁵​homeworld

Essa é uma base de dados já pronta do package ggplot2, sem ser necessário carregá-la externamente. Basta apenas chama-la por “starwars”. É uma base de dados de diversos personagens da franquia Star Wars, com dados como altura, peso, gênero, sexo, etc. Há outras bases no ggplot2, que também podem ser utilizadas. É aconselhado sempre ler antes sua base de dados, para saber os tipos de dados que está lidando, como irá ser feito as análises, o gráfico, etc. Para ser mais fácil, essa base de dados foi atribuída ao objeto SW. Não apenas o package ggplot2, mas o próprio R possui bases de dddados já carregadas que você pode acessar, como a base de dados iris.

2.3 Criando o tema

windowsFonts(TimesNewRoman = windowsFont("Times New Roman"))

tema<-theme(text=element_text(family="TimesNewRoman"),
            title=element_text(color="black",size=15),
            axis.text = element_text(color="black",size=10),
            axis.title = element_text(color="black",size=10),
            panel.grid=element_line(color="grey75",linetype = "dashed",size=.8),
            axis.line=element_blank(),
            plot.background=element_rect(fill="white",color="white"),
            panel.background=element_rect(fill="white"),
            panel.border = element_rect(colour = "black", fill = NA,size=0.59),
            legend.key= element_rect(color="white",fill="white"))
## Warning: The `size` argument of `element_rect()` is deprecated as of ggplot2 3.4.0.
## ℹ Please use the `linewidth` argument instead.
## Warning: The `size` argument of `element_line()` is deprecated as of ggplot2 3.4.0.
## ℹ Please use the `linewidth` argument instead.

Os gráficos podem ser personalizados em relação à sua estetítica, escolhendo as cores do fundo, dos valores e das linhas de grade. Usa-se a função theme() para isso, e atribuiu o tema criado ao objeto tema. Será abordado com mais detalhes sobre isso no capítulo 17.

2.4 Especifcando os eixos

SW %>%
  ggplot(aes(height,mass))+
  tema

Foi adicionada a função %\>% (pipe) à frente da base de dados SW. Essa é uma função do package tidyr, e serve para informar que comandos serão usados em sequência. Nesse caso, foi utilizado para indicar que que os dados utilizados no ggplot serão da base de dados SW. Alternativamente, dentro de ggplot(), é possível usar o comando data=, para indicar a base de dados que será utilizada. Logo abaixo, fez-se a construção do ggplot, onde uma das primeiras coisas ao se fazer no ggplot é especificar os eixos a serem usados. Para isso, usa-se a função aes() (aesthetically), que é a função que lida com a estética do gráfico, para indicar os eixos. O primeiro termo que você utilizar em aes() sempre será o eixo X, e o segundo, o eixo Y. Nestes, estarão variáveis da própria base de dados.

2.5 Comandos color=, fill=, alpha= e label=

SW %>%
  ggplot(aes(x=eye_color,y=mass))+
  geom_boxplot(color="black",fill="green")+
  geom_label(aes(label=name),size=2,alpha=0.2)+
  tema
## Warning: Removed 28 rows containing non-finite values (`stat_boxplot()`).
## Warning: Removed 28 rows containing missing values (`geom_label()`).

SW %>%
  ggplot(aes(x=eye_color,y=mass))+
  geom_boxplot(color="black",fill="green")+
  geom_text(aes(label=name),size=2.5,alpha=1)+
  tema
## Warning: Removed 28 rows containing non-finite values (`stat_boxplot()`).
## Warning: Removed 28 rows containing missing values (`geom_text()`).

4 dos principais comandos que controlam as estéticas dos gráficos no ggplot são:

  • color: controla a cor de contorno que será utilizada;

  • fill: controla a cor de preenchimento que será utilizada;

  • alpha: controla a transparência do objeto do gráfico, onde varia de 0 (valor mínimo) até 1 (valor máximo);

  • label: controla os rótulos, caso use o comando geom_label() (primeiro gráfico), ou textos, caso use o comando geom_text() (segundo gráfico), que serão utilizados. Neste caso, tanto nos comandos geom_label() quanto geom_text() usaram o um label=variável escolhida da base de dados dentro de um aes().

O R usa um sistema de cores bastante vasto. É possível selecionar a cor colocando o nome da cor em inglês entre aspas (como na imagem abaixo), ou utilizando o sistema Color-Hex, que consiste em um # seguido por código com 6 caractéres. Os gráfico utilizados foram do tipo boxplot, que será melhor abordado no capítulo 13.

As diversas tonalidades e paletas de cores que o R permite para o color= e o fill=. Ao serem urilizadas, devem estre entre aspas.

2.6 Especificando os títulos dos eixos, do gráfico, das legendas e notas de roda-pé

SW %>%
  ggplot(aes(height,mass))+
  labs(title="gráfico",
       x="eixo x",
       y="eixo y",
       caption ="nota de roda-pé")+
  tema

Mais ainda, é possível selecionar como estarão o título e os eixos, através da função labs():

  • title: adiciona o título ao gráfico;

  • x: adiciona e altera o título do eixo X;

  • y: adiciona e altera o título do eixo y;

  • caption: adiciona uma nota de roda-pé.

Além destes comandos básicos, todos aqueles que inseridos dentro do comando aes() podem ser adicionados e alterados no comando labs(). exemplos são os comandos color=, fill=, alpha= e label=. Se algum desses comandos for utilizado dentro do comando aes(), serão atribuidos à estas variáveis da base de dados, e para alterar o título destas nas legendas, basta apenas usar o mesmo comando em labs(), e atribuir o título que deseja. Exemplo:

SW %>%
  ggplot(aes(x=height,y=mass,color=sex,fill=gender,alpha=birth_year,label=name))+
  geom_point()+
  geom_label(size=0.5)+
  labs(title="exemplo",
       x="altura",
       y="massa",
       color="sexo do personagem",
       fill="gênero do personagem",
       alpha="ano de nascimento do personagem",
       label="nome do personagem")+
  tema
## Warning: Removed 28 rows containing missing values (`geom_point()`).
## Warning: Removed 28 rows containing missing values (`geom_label()`).

3 Gráfico de histograma

3.1 Quando usar

O hisograma é utilizado para criar uma distribuição de frequências, quando deseja-se divdir um conjunto de variáveis em intervalos (eixo X), e quantos dados cada um desses conjuntos possuem (eixo Y). Exemplo: da base de dados starwars, a maioria dos personagens possuem qual altura? É o que será feito agora.

3.2 Packages exigidos

library(tidyverse)

3.3 Carregando a base de dados

SW<-starwars
SW
## # A tibble: 87 × 14
##    name        height  mass hair_…¹ skin_…² eye_c…³ birth…⁴ sex   gender homew…⁵
##    <chr>        <int> <dbl> <chr>   <chr>   <chr>     <dbl> <chr> <chr>  <chr>  
##  1 Luke Skywa…    172    77 blond   fair    blue       19   male  mascu… Tatooi…
##  2 C-3PO          167    75 <NA>    gold    yellow    112   none  mascu… Tatooi…
##  3 R2-D2           96    32 <NA>    white,… red        33   none  mascu… Naboo  
##  4 Darth Vader    202   136 none    white   yellow     41.9 male  mascu… Tatooi…
##  5 Leia Organa    150    49 brown   light   brown      19   fema… femin… Aldera…
##  6 Owen Lars      178   120 brown,… light   blue       52   male  mascu… Tatooi…
##  7 Beru White…    165    75 brown   light   blue       47   fema… femin… Tatooi…
##  8 R5-D4           97    32 <NA>    white,… red        NA   none  mascu… Tatooi…
##  9 Biggs Dark…    183    84 black   light   brown      24   male  mascu… Tatooi…
## 10 Obi-Wan Ke…    182    77 auburn… fair    blue-g…    57   male  mascu… Stewjon
## # … with 77 more rows, 4 more variables: species <chr>, films <list>,
## #   vehicles <list>, starships <list>, and abbreviated variable names
## #   ¹​hair_color, ²​skin_color, ³​eye_color, ⁴​birth_year, ⁵​homeworld

3.4 Criando o gráfico

SW %>%
  ggplot(aes(height))+
  geom_histogram()+
  tema
## Warning: Removed 6 rows containing non-finite values (`stat_bin()`).

Após especificar os eixos, é preciso especificar o tipo de gráfico a ser feito. Para isso, se usa um + após a primeira linha do ggplot, para especificar os próximos passos a serem feitos. Para fazer um histograma, Se usa a função geom_histogram. Como os histogramas são gráficos de variáveis únicas, se usará apenas a variável height.

3.5 Colorindo o contorno das barras

SW %>%
  ggplot(aes(height))+
  geom_histogram(color="black")+
  tema
## Warning: Removed 6 rows containing non-finite values (`stat_bin()`).

Com a função color="black" em geom_histogram, é possível criar linhas de borda que dividem e diferenciem as barras. As coresna linguagem R são escritas em inglês e em aspas, ou através de códigos do sistema de cores Color Hex.

3.6 Colorindo as barras

SW %>%
  ggplot(aes(height))+
  geom_histogram(fill="green",color="black")+
  tema
## Warning: Removed 6 rows containing non-finite values (`stat_bin()`).

Com a função fill="green", é possível especificar o preenchimento das barras no histograma, que nesse caso, serão verdes. É possível também escolher outras cores.

4 Gráfico de densidade

4.1 Quando usar

O gráfico de densidade é utilizado quando se deseja criar um resultado parecido ao de um histograma, mas sem dividir os valores em categorias de intervalo: não cria barras, mas sim uma linha que traça um caminho, sendo a sua altura equivalente à quantidade de repetições que aquele intervalo possui. No gráfico de densidade, o eixo X é contínuo, sem criar intervalores, sendo a gráficação representada por uma linha. Exemplo: da base de dados starwars, a maioria dos personagens possuem qual altura, mas de uma forma contínua? É o que será feito agora.

4.2 Packages exigidos

library(tidyverse)

4.3 Carregando a base de dados

SW<-starwars
SW
## # A tibble: 87 × 14
##    name        height  mass hair_…¹ skin_…² eye_c…³ birth…⁴ sex   gender homew…⁵
##    <chr>        <int> <dbl> <chr>   <chr>   <chr>     <dbl> <chr> <chr>  <chr>  
##  1 Luke Skywa…    172    77 blond   fair    blue       19   male  mascu… Tatooi…
##  2 C-3PO          167    75 <NA>    gold    yellow    112   none  mascu… Tatooi…
##  3 R2-D2           96    32 <NA>    white,… red        33   none  mascu… Naboo  
##  4 Darth Vader    202   136 none    white   yellow     41.9 male  mascu… Tatooi…
##  5 Leia Organa    150    49 brown   light   brown      19   fema… femin… Aldera…
##  6 Owen Lars      178   120 brown,… light   blue       52   male  mascu… Tatooi…
##  7 Beru White…    165    75 brown   light   blue       47   fema… femin… Tatooi…
##  8 R5-D4           97    32 <NA>    white,… red        NA   none  mascu… Tatooi…
##  9 Biggs Dark…    183    84 black   light   brown      24   male  mascu… Tatooi…
## 10 Obi-Wan Ke…    182    77 auburn… fair    blue-g…    57   male  mascu… Stewjon
## # … with 77 more rows, 4 more variables: species <chr>, films <list>,
## #   vehicles <list>, starships <list>, and abbreviated variable names
## #   ¹​hair_color, ²​skin_color, ³​eye_color, ⁴​birth_year, ⁵​homeworld

4.4 Criando o gráfico

SW %>%
  ggplot(aes(x=height))+
  geom_density(size=1)+
  labs(title="densidade das alturas dos personagens de Starwars",
       x="densidade dos dados",
       y="altura")+
  tema
## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.
## Warning: Removed 6 rows containing non-finite values (`stat_density()`).

Agora o gráfico de densidade será o feito. Ele é utilizado para entender em que espaço ou período mais os dados se concentram. Neste caso, foi feito um gráfico de densidade para entender qual é a altura da maioria dos personagens da base de dados SW. Como é possível observar no gráfico, a maioria dos personagens possui uma altura entre 1,5-1,8m.

4.5 Separando por cores em relação ao sexo dos personagens

SW %>%
  ggplot(aes(height,color=sex))+
  geom_density(size=1)+
  labs(title="densidade das alturas dos personagens de Starwars, 
baseado pelo sexo",
       x="densidade dos dados",
       y="altura",
       color="sexo")+
  tema
## Warning: Removed 6 rows containing non-finite values (`stat_density()`).
## Warning: Groups with fewer than two data points have been dropped.
## Warning in max(ids, na.rm = TRUE): nenhum argumento não faltante para max;
## retornando -Inf

No gráfico anterior, todos os personagens estavam em uma mesma linha de densidade, sem nenhuma descriminação por características deles. Agora, foram feitas linhas para os personagens em função do seu sexo, da variável sex da base de dados. Nesse caso, como se adicionará uma estética para diferenciar a altura baseado na variável sexo dos personagens, então se adicionaá color=sex na função aes(). Isso significa que as cores das linhas devem ser diferenciadas em relação ao sexo dos personagens. COmo é possível observar, quando é descriminado pelo sexo, os siferentes sexos possuem diferentes densidades nos seus dados.

5 Gráficos de dispersão

5.1 Quando usar

O gráfico de dispersão é utilizado para interpretar como determinados dados são distribuídos em relação à uma variável contínua (eixo X) sobre outra variável contínua (eixo Y). É muito utilizado quando se deseja entender como um fator influenciando outro gera um perfil de comportamento em dados resultantes das interações dos fatores, como em estudos de regressão, que será explicado no capítulo 12. Exemplo: da base de dados starwars, personagens mais mais altos são mais pesados (possuem maior massa)?

5.2 Packages exigidos

library(tidyverse)

5.3 Carregando base de dados

SW<-starwars
SW
## # A tibble: 87 × 14
##    name        height  mass hair_…¹ skin_…² eye_c…³ birth…⁴ sex   gender homew…⁵
##    <chr>        <int> <dbl> <chr>   <chr>   <chr>     <dbl> <chr> <chr>  <chr>  
##  1 Luke Skywa…    172    77 blond   fair    blue       19   male  mascu… Tatooi…
##  2 C-3PO          167    75 <NA>    gold    yellow    112   none  mascu… Tatooi…
##  3 R2-D2           96    32 <NA>    white,… red        33   none  mascu… Naboo  
##  4 Darth Vader    202   136 none    white   yellow     41.9 male  mascu… Tatooi…
##  5 Leia Organa    150    49 brown   light   brown      19   fema… femin… Aldera…
##  6 Owen Lars      178   120 brown,… light   blue       52   male  mascu… Tatooi…
##  7 Beru White…    165    75 brown   light   blue       47   fema… femin… Tatooi…
##  8 R5-D4           97    32 <NA>    white,… red        NA   none  mascu… Tatooi…
##  9 Biggs Dark…    183    84 black   light   brown      24   male  mascu… Tatooi…
## 10 Obi-Wan Ke…    182    77 auburn… fair    blue-g…    57   male  mascu… Stewjon
## # … with 77 more rows, 4 more variables: species <chr>, films <list>,
## #   vehicles <list>, starships <list>, and abbreviated variable names
## #   ¹​hair_color, ²​skin_color, ³​eye_color, ⁴​birth_year, ⁵​homeworld

5.4 Pergunta: Personagens mais altos tem maior peso?

SW %>%
  ggplot(aes(height,mass))+
  geom_point(color="darkgoldenrod4",fill="yellow",shape=21,size=4)+
  labs(title="Alturas dos personagens de Starwars em relação à massa",
       x="altura",
       y="massa")+
  tema
## Warning: Removed 28 rows containing missing values (`geom_point()`).

Como esse gráfico criado tem o intuíto de responder onde os pontos de realção das variáveis de massa (mass) e altura (altura) se estabelecem, com a função geom_point() é possível criar um gráfico de dispersão, através de pontos. Para isso, é preciso especificar as variáveis do eixo X e o eixo Y em aes(). Contudo, há um ponto muito alto, com um valor de massa > 1000, que compromete a interpretação. Para contornar isso, os dados devem ser filtrados.

5.5 filtrando os pontos discrepantes

SW %>%
  filter(mass<1000) %>%
  ggplot(aes(height,mass))+
  labs(title="Alturas dos personagens de Starwars em relação à massa",
       x="altura",
       y="massa")+
  geom_point(color="darkgoldenrod4",fill="yellow",shape=21,size=4)+
  tema

Como havia um ponto solitário com um valor muito alto > 1000, a interpretação do gráfico ficou comprometida. Para resolver isso, usa-se a função filter(), do package dplyr, onde esta faz um filtro dos tipo de dados que serão inseridos, e com base no que esses dados serão filtrados. Como deseja-se filtrar um ponto de massa muito alto, que gerou um aoutlier, é feito filter(mass<1000), para especificar que só devem entrar dados de massa com valores abaixo de 1000.

5.6 Criando uma linha de tendência linear

SW %>%
  filter(mass<1000) %>%
  ggplot(aes(height,mass))+
  labs(title="Alturas dos personagens de Starwars em relação à massa",
       x="altura",
       y="massa")+
  geom_point(color="darkgoldenrod4",fill="yellow",shape=21,size=4)+
  geom_smooth(method="lm",color="red")+
  tema

Agora, como se deseja saber qual é a tendência dos dados, para então responder a pergunta anteriormente feita, com a função geom_smooth() é possível criar uma linha de tendência, para então interpretar melhor como os valores se distribuem no gráfico. Com o argumento lm, cria-se uma linha de tendência linear. Com esses resultados, é possivel dizer que existe uma tendência de um personagem da base da dados ter mais massa quanto mais alto ser.

5.7 Modelo polinomial

SW %>%
  filter(mass<1000) %>%
  ggplot(aes(height,mass))+
  labs(title="Alturas dos personagens de Starwars em relação à massa",
       x="altura",
       y="massa")+
  geom_point(color="darkgoldenrod4",fill="yellow",shape=21,size=4)+
  geom_smooth(method="loess",color="red")+
  tema

Além da linha de tendência linear, também épossível criar outras linhas de tendência. Com o argumento method="loess", cria-se uma linha de tendência polinomial, mostrando que a linha segue de outra forma a distribuição dos dados.

5.8 Usando os dois métodos

SW %>%
  filter(mass<1000) %>%
  ggplot(aes(height,mass))+
  labs(title="Alturas dos personagens de Starwars em relação à massa",
       x="altura",
       y="massa")+
  geom_point(color="darkgoldenrod4",fill="yellow",shape=21,size=4)+
  geom_smooth(method="loess",color="red")+
  geom_smooth(method="lm",color="red")+
  tema

É possivel criar duas linhas antes feitas, ao mesmo tempo, apenas usando duas vezes a função geom_smoth(). Contudo, por serem da mesma cor, isso acaba prejudicando a interpretação. Para resolver isso, então é necessário defenciá-las, como por cores.

5.9 Diferenciando as linhas por cores

SW %>%
  filter(mass<1000) %>%
  ggplot(aes(height,mass))+
  labs(title="Alturas dos personagens de Starwars em relação à massa",
       x="altura",
       y="massa")+
  geom_point(color="darkgoldenrod4",fill="yellow",shape=21,size=4)+
  geom_smooth(method="loess",color="sienna1")+
  geom_smooth(method="lm",color="royalblue1")+
  tema

Usando o comando color= em cada geom_smoth(), é possível então fazer uma melhor interpretação das tendências, selecionando uma cor específica para cada tipo de linha.

5.10 Diferenciando os tipos de dados por cor. Pergunta: como é a tendência de cada sexo?

SW %>%
  filter(mass<1000) %>%
  ggplot(aes(height,mass,color=sex,fill=sex))+
  labs(title="Alturas dos personagens de Starwars em relação à massa,
baseado pelo sexo",
       x="altura",
       y="massa",
       color="sexo",
       fill="sexo")+
  geom_point(color="black",shape=21,size=4)+
  geom_smooth(method="lm",aes())+
  tema

Neste caso, como o objetivo é entender essa mesma relação, mas para cada um dos sexos dos personagens, será feito uma descriminação, baseada nessa característica. Para poder difernciar os dados por cores e fazer cada um ter sua linha de tendência, usa-se o argumento color=sex e fill=sex em aes(), para especificar que se deseja fazer uma diferenciação baseada no sexo dos personagens. Com esses dados, é possil ver que o sexo feminino é que teve a menor tendência.

5.11 Adicionar linhas horizontais e verticais

SW %>%
  filter(mass<1000) %>%
  ggplot(aes(height,mass))+
  labs(title="Alturas dos personagens de Starwars em relação à massa",
       x="altura",
       y="massa")+
  geom_point(color="darkgoldenrod4",fill="yellow",shape=21,size=4)+
  geom_hline(yintercept = 80)+
  geom_vline(xintercept=125)+
  tema

Caso fosse preferíveel separar os dados por setores, é também possível, traçando linhas que cortam o gráfico. Com a função geom_hline(), é possível traçar uma linha horizontal que corta o gráfico, especificando o ponto do eixo Y que a linha passará, através do argumento yintercept=. O mesmo vale para criar uma linha vertical, usando a função geom_vline(), com o argumento xintercept=. Os pontos que as linhas passarão serão os valores dos elementos yintercept= e xintercept=.

5.12 Definindo o tipo da linha

SW %>%
  filter(mass<1000) %>%
  ggplot(aes(height,mass))+
  labs(title="Alturas dos personagens de Starwars em relação à massa",
       x="densidade dos dados",
       y="altura")+
  geom_point(color="darkgoldenrod4",fill="yellow",shape=21,size=4)+
  geom_hline(yintercept = 80,linetype="dashed")+
  geom_vline(xintercept=125,linetype="dotted")+
  tema

Também é possível definir o tipo de linha pela função linetype=. O tipo de linha deve estar entre aspas, e em inglês.

5.13 Definindo a cor da linha

SW %>%
  filter(mass<1000) %>%
  ggplot(aes(height,mass))+
  labs(title="Alturas dos personagens de Starwars em relação à massa",
       x="densidade dos dados",
       y="altura")+
  geom_point(color="darkgoldenrod4",fill="yellow",shape=21,size=4)+
  geom_hline(yintercept = 80,linetype="dashed")+
  geom_vline(xintercept=125,linetype="dotted",color="red")+
  tema

Também é possível definir a cor da linha, pelo elemento color=.

6 Gráficos de barras/colunas

6.1 Quando usar

O gráfico de barras é utilizado quando o objetivo é entender o quanto de unidades amostrais, contágens ou repetições uma variável qualitativa possui dentro de uma base de dados. Um exemplo é o quanto de observações são feitas para três espécies diferentes em algum local de estudo. Nesse gráfico, no eixo X ficam as variável qualitativas, e no eixo Y as variáveis quantitativas. É bastante semelhante ao gráfico de histograma e de sensidade, mas a diferença é que este usa, obrigatoriamente, dados qualitativos no eixo X. Exemplo: na base de dados starwars, qual é a cor de olho que a maioria dos personagens possuem?

6.2 Packages exigidos

library(tidyverse)

6.3 Carregando base de dados

SW<-starwars
SW
## # A tibble: 87 × 14
##    name        height  mass hair_…¹ skin_…² eye_c…³ birth…⁴ sex   gender homew…⁵
##    <chr>        <int> <dbl> <chr>   <chr>   <chr>     <dbl> <chr> <chr>  <chr>  
##  1 Luke Skywa…    172    77 blond   fair    blue       19   male  mascu… Tatooi…
##  2 C-3PO          167    75 <NA>    gold    yellow    112   none  mascu… Tatooi…
##  3 R2-D2           96    32 <NA>    white,… red        33   none  mascu… Naboo  
##  4 Darth Vader    202   136 none    white   yellow     41.9 male  mascu… Tatooi…
##  5 Leia Organa    150    49 brown   light   brown      19   fema… femin… Aldera…
##  6 Owen Lars      178   120 brown,… light   blue       52   male  mascu… Tatooi…
##  7 Beru White…    165    75 brown   light   blue       47   fema… femin… Tatooi…
##  8 R5-D4           97    32 <NA>    white,… red        NA   none  mascu… Tatooi…
##  9 Biggs Dark…    183    84 black   light   brown      24   male  mascu… Tatooi…
## 10 Obi-Wan Ke…    182    77 auburn… fair    blue-g…    57   male  mascu… Stewjon
## # … with 77 more rows, 4 more variables: species <chr>, films <list>,
## #   vehicles <list>, starships <list>, and abbreviated variable names
## #   ¹​hair_color, ²​skin_color, ³​eye_color, ⁴​birth_year, ⁵​homeworld

6.4 Criando o gráfico

SW %>%
  ggplot(aes(eye_color,mass))+
  geom_bar(stat = "identity")+
  labs(title="Número de personagens por cores de olho",
       x="cor do olho",
       y="massa")+
  tema
## Warning: Removed 28 rows containing missing values (`position_stack()`).

Nesse caso, foi graficado a massa de cada personagem baseado em sua cor de olho. Para isso, dentro do peimeiro aes(), foi adicionado uma variável qualitativa (cor do olho) ao eixo X e uma variável quantitativa (massa) ao eixo Y. Para usar o gráfico de barras, foi usada a função geom_bar().

6.5 Gráfico baseado na quantidade de personagens pela cor de olho

SW %>%
  group_by(eye_color) %>%
  summarise(
    contagem = n()
  ) %>%
  ggplot(aes(eye_color,contagem))+
  geom_bar(stat = "identity")+
  labs(title="Número de personagens por cores de olho",
       x="cor do olho",
       y="n° de ocorrência")+
  tema

Alternativamente ao modo do gráfico anterior, é possível criar gráfico com a altura das barras baseado no número de unidades amostrais de uma variável qualitativa, como o número de personagens por cada cor de olho. Uma forma de fazer isso é a base de dados possuir uma variável quantitativa com esses dados. Outro forma, é manipular os dados para criar essa contagem. No gráfico acima, foi feito isso, com a função group_by(), onde foram criados grupos baseado na cor dos olhos dos personagens, e a função summarise(), para a fazer a contagem destes dados e atribuido ao objeto contagem, para que fosse possível adicionar ao ggplot.

6.6 Envertendo os eixos

SW %>%
  group_by(eye_color) %>%
  summarise(
    contagem = n()
  ) %>%
  ggplot(aes(eye_color,contagem))+
  geom_bar(stat = "identity")+
  labs(title="Número de personagens por cores de olho",
       x="cor do olho",
       y="n° de ocorrência")+
  coord_flip()+
  tema

Para que seja mais fácil de observar os nomes no eixo X, é poossível inveter a posição dos eixos, atraves da função coord_flip().

6.7 Personalizando por cores

SW %>%
    group_by(eye_color) %>%
    summarise(
      contagem = n()
    ) %>%
    ggplot(aes(eye_color,contagem))+
    geom_bar(stat = "identity",fill="lightblue",color="black")+
  labs(title="Número de personagens por cores de olho",
       x="cor do olho",
       y="n° de ocorrência")+
    coord_flip()+
  tema

Mais ainda, é possível adicionar uma cor de contorno e preenchimento para as barras.

6.8 Adicionar rótulos

SW %>%
    group_by(eye_color) %>%
    summarise(
      contagem = n()
    ) %>%
    ggplot(aes(eye_color,contagem,label=contagem))+
    geom_bar(stat = "identity",fill="lightblue",color="black")+
  labs(title="Número de personagens por cores de olho",
       x="cor do olho",
       y="n° de ocorrência")+
    coord_flip()+
    geom_label()+
  tema

Para ser mais visível de interpretar os valores de cada grupo, também é possível adicionar rótulos às barras, estes contendo os seus valores, com a função geom_label().

6.9 Personalizando os rótulos

SW %>%
    group_by(eye_color) %>%
    summarise(
      contagem = n()
    ) %>%
    ggplot(aes(eye_color,contagem,label=contagem))+
    geom_bar(stat = "identity",fill="green",color="black",alpha=0.5)+
  labs(title="Número de personagens por cores de olho",
       x="cor do olho",
       y="n° de ocorrência")+
    coord_flip()+
    geom_label(size=3,fill="green")+
    coord_flip()+
  tema

Os rótulos também podem sua estética editada, sendo que size= altera o tamanho, fill= altera o preenchimento e alpha= altera a transparência.

6.10 Grupos múltiplos: agrupar por cor de olho e sexo

SW %>%
    group_by(eye_color,sex) %>%
    summarise(
      contagem = n()
    ) %>%
    ggplot(aes(eye_color,contagem,fill=sex))+
    geom_bar(stat = "identity", color="black")+
  labs(title="Número de personagens por cores de olho,
em relação ao sexo",
       x="cor do olho",
       y="n° de ocorrência",
       fill="sexo")+
    coord_flip()+
  tema

É possível também agrupar as barras em relação à porcentagem de uma variável da base de dados. Nesse caso, agrupando pelo sexo dos personagnes, dentro da função aes(), se adiciona a variável fill=sex.

6.11 Detalhes em brown, blue e black, barras lado a lado, com label

 SW %>%
    filter(eye_color %in% c("brown","blue","black")) %>%
    group_by(eye_color,sex) %>%
    summarise(
      contagem = n()
    ) %>%
    ggplot(aes(eye_color,contagem,fill=sex, label=contagem))+
    geom_bar(stat = "identity",position = "dodge",color="black", alpha=0.5)+
  labs(title="Número de personagens por cores de olho,
em relação ao sexo e 3 cores de olho específicas",
       x="cor do olho",
       y="n° de ocorrência",
       fill="sexo")+
    geom_label(position = position_dodge(width = 1))+
  tema

Para separar apenas os olhos de cor marrom (brown), azul (blue) e preto (black), usa-se a função filter(), com o comando %in%, para a variável eye_color, especificando quais as cores de olho a serem selecionadas. Na função group_by(), se adicionará as variáveis eye_color e sex para especificar que se formaram grupos baseados na quantidade de indivíduos com uma cor de olho por determinado sexo, e então, a função summarise().

7 Gráficos de barras de erro

7.1 Quando usar

Esse gráfico pode ser utilizado em duas principais situações: quando se deseja entender o erro ou a incerteza dos dados trabalhados em uma análise ou quando os valores dos objetos de uma variável qualitativa possuem valores mínimos e máximos diferentes. No primeiro caso, quanto menor a barra de erro, menor a incerteza dos dados. Exemplo: na base dados starwars, numa análise do genêro dos personagens, qual gênero possui uma maior incerteza sobre os dados das suas alturas?

7.2 Packages exigidos

library(tidyverse)

7.3 Carregando os dados

SW<-starwars
SW
## # A tibble: 87 × 14
##    name        height  mass hair_…¹ skin_…² eye_c…³ birth…⁴ sex   gender homew…⁵
##    <chr>        <int> <dbl> <chr>   <chr>   <chr>     <dbl> <chr> <chr>  <chr>  
##  1 Luke Skywa…    172    77 blond   fair    blue       19   male  mascu… Tatooi…
##  2 C-3PO          167    75 <NA>    gold    yellow    112   none  mascu… Tatooi…
##  3 R2-D2           96    32 <NA>    white,… red        33   none  mascu… Naboo  
##  4 Darth Vader    202   136 none    white   yellow     41.9 male  mascu… Tatooi…
##  5 Leia Organa    150    49 brown   light   brown      19   fema… femin… Aldera…
##  6 Owen Lars      178   120 brown,… light   blue       52   male  mascu… Tatooi…
##  7 Beru White…    165    75 brown   light   blue       47   fema… femin… Tatooi…
##  8 R5-D4           97    32 <NA>    white,… red        NA   none  mascu… Tatooi…
##  9 Biggs Dark…    183    84 black   light   brown      24   male  mascu… Tatooi…
## 10 Obi-Wan Ke…    182    77 auburn… fair    blue-g…    57   male  mascu… Stewjon
## # … with 77 more rows, 4 more variables: species <chr>, films <list>,
## #   vehicles <list>, starships <list>, and abbreviated variable names
## #   ¹​hair_color, ²​skin_color, ³​eye_color, ⁴​birth_year, ⁵​homeworld

7.4 Calcular o desvio padrão da altura entre os gêneros

médias<-SW %>%
  filter(!is.na(height)) %>%
  group_by(gender) %>%
  summarise(
    media = mean(height),
    limite_superior = mean(height) + sd(height),
    limite_inferior = mean(height) - sd(height)
  )
médias 
## # A tibble: 3 × 4
##   gender    media limite_superior limite_inferior
##   <chr>     <dbl>           <dbl>           <dbl>
## 1 feminine   165.            188.            141.
## 2 masculine  177.            214.            139.
## 3 <NA>       181.            184.            178.

Para a criação de um gráfico de desvio padrão, é necessário antes calcular a média, o limite superior e o limite inferior de uma variável da bse de dados. Nesse caso, procura-se saber da altura (height) em relação aos gêneros dos personagens. Para isso, é usado a função filter(), adicionando a função !is.na para retirar os valores nulos (NA) da altura. Logo em seguida, é feito o group_by() para a variável gênero (gender), o summarise(), para calcular a média, o limite superior e o limite inferior. Tudo isso então é atribuído ao objeto médias.

7.5 Criando o gráfico de barras de erro

médias %>%
  ggplot(aes(x=gender,y=media))+
  labs(title="média da altura dos personagens em relação ao gênero",
       x="gênero",
       y="média")+
  geom_bar(stat="identity",color="black")+
  geom_errorbar(aes(ymin = limite_inferior, ymax =  limite_superior), width = 0.2)+
  tema

Nesse caso, não se usará a base de dados SW, mas sim a base de dados médias. Para criar o gráfico de erro, será usado tanto a função geom_bar(), para criar as barras das médias em relação ao gênero, quanto a função geom_errorbar(), parar criar as barras de erro. Dentro de geom_errorbar(), na função aes(), é especificado o limite inferior (ymin), o limite superior (ymin) e a alarbura das barras de erro width=..

7.6 Criando o gráfico com pontos nos lugares das médias

médias %>%
  ggplot(aes(x=gender,y=media))+
  labs(title="média da altura dos personagens em relação ao gênero",
       x="gênero",
       y="média")+
  geom_pointrange(color="black",fill="gray",shape=21,size=1,
                  aes(ymin = limite_inferior, ymax =  limite_superior))+
  tema

É possível também substituir as barras, colocando pontos nos valores das médias, usando a função geom_pointrange().

7.7 Difernciando por cores

médias %>%
  ggplot(aes(x=gender,y=media,fill=gender))+
  labs(title="média da altura dos personagens em relação ao gênero,
em relação so gênero",
       x="gênero",
       y="média",
fill="gênero")+
  geom_pointrange(color="black",shape=21,size=1,
                  aes(ymin = limite_inferior, ymax =  limite_superior))+
  tema

Para diferenciar as linhas e as médias em função do gênero, é adicionado a função color=gender na função aes().

7.8 Exemplo de experimento

dados<-data.frame(
  metricas<-c("m1","m2","m3","m4","m5"),
  limite_inferior<-c(-3.5,-2.5,1,4,8),
  limite_superior<-c(1,1.5,3,7,10),
  significativo<-c("não","não","sim","sim","sim")
)
dados %>%
  ggplot(aes(metricas, color= significativo))+
  geom_errorbar(size=1,aes(ymin = limite_inferior, ymax =  limite_superior),width=0.2)+
  geom_hline(yintercept = 0,linetype="dotted",color="black")+
  tema

Esse foi um experimento usando dados criados, para averiguar se o erro padrão dos elementos (m1, m2, m3, m4, m5). Para isso, dentro da função aes() se adicionou color=significativo, para separar os elementos ccom relção a essa variável. Como o erro padrão só é significativo com valores de limite superior e limite inferior forem acima de 0, então pode-se traçar uma linha horizontal no ponto 0 para melhor interpretar, pela função geom_hline().

7.9 Alterando as métricas nos eixos

dados %>%
  ggplot(aes(metricas, color= significativo))+
  geom_errorbar(size=1,aes(ymin = limite_inferior, ymax =  limite_superior),width=0.2)+
  geom_hline(yintercept = 0,linetype="dotted",color="black")+
  theme_light()+
  coord_flip()+
  tema

7.9.0.0.1 Também é possível alterar a posição dos eixos, pela função coord_flip().

8 Gráfico de linhas

8.1 Quando usar

Bem semelhante ao gráfico de dispersão, esse gráfico é utilizado quando se deseja entender o comportamento dos dados resultantes da interação de uma variável contínua (eixo X) com outra variável contínua (eixo Y). Mas ao invés de de usar pontos dispersos pelo gráfico, é utilizado uma ou mais linhas, sendo mais esse modelo de gráfico mais utilizado para tratar com séries temporais. Exemplo: utilizando a base de dados economics, como foi a taxa de desemprego dos Estados Unidos ao longo das décadas recentes?

8.2 Packages exigidos

library(tidyverse)
library(gapminder)

8.3 Carregando base de dados

Ecs<-economics
Ecs
## # A tibble: 574 × 6
##    date         pce    pop psavert uempmed unemploy
##    <date>     <dbl>  <dbl>   <dbl>   <dbl>    <dbl>
##  1 1967-07-01  507. 198712    12.6     4.5     2944
##  2 1967-08-01  510. 198911    12.6     4.7     2945
##  3 1967-09-01  516. 199113    11.9     4.6     2958
##  4 1967-10-01  512. 199311    12.9     4.9     3143
##  5 1967-11-01  517. 199498    12.8     4.7     3066
##  6 1967-12-01  525. 199657    11.8     4.8     3018
##  7 1968-01-01  531. 199808    11.7     5.1     2878
##  8 1968-02-01  534. 199920    12.3     4.5     3001
##  9 1968-03-01  544. 200056    11.7     4.1     2877
## 10 1968-04-01  544  200208    12.3     4.6     2709
## # … with 564 more rows

Nesse caso, não será usado a base de dados starwars, mas sim a base de dados economics. Essa base de dados também é do package ggplot, que apresenta dados de séries econômicas da história dos Estados Unidos.

8.4 Criando o gráfico

Ecs%>%
  ggplot(aes(date,unemploy))+
  labs(title="desemprego nos Estados Unidos entre 1970-2015",
       x="data",
       y="desemprego")+
  geom_line(size=1)+
  tema

Para criar um gráfico de linhas, usa-se a função geom_line(). Na função aes(), usar-se as variáveis de datas (date) para o eixo X e de desempregados/1000 (unemploy).

8.5 Definir a escala das datas

Ecs%>%
  ggplot(aes(date,unemploy))+
  labs(title="desemprego nos Estados Unidos entre 1990-2000",
       x="data",
       y="desemprego")+
  geom_line(size=1)+
  scale_x_date(limits = c(as.Date("1990-01-01"),as.Date("1999-12-31")))+
  tema
## Warning: Removed 454 rows containing missing values (`geom_line()`).

Em alguns casos, é desejável analisar um período específico, também é possível fazer um recorte de um período específico de tempo. Usa-se a função scale_x_date(), onde se definem as datas, já que avariável date é feita dados temporais, e está no eixo X. Se define da data inical e a final onde se deseja avaliar, onde a ordem da data é ano-mês-dia.

8.6 Gráficos de linhas com pontos

Gap<-gapminder
Gap
## # A tibble: 1,704 × 6
##    country     continent  year lifeExp      pop gdpPercap
##    <fct>       <fct>     <int>   <dbl>    <int>     <dbl>
##  1 Afghanistan Asia       1952    28.8  8425333      779.
##  2 Afghanistan Asia       1957    30.3  9240934      821.
##  3 Afghanistan Asia       1962    32.0 10267083      853.
##  4 Afghanistan Asia       1967    34.0 11537966      836.
##  5 Afghanistan Asia       1972    36.1 13079460      740.
##  6 Afghanistan Asia       1977    38.4 14880372      786.
##  7 Afghanistan Asia       1982    39.9 12881816      978.
##  8 Afghanistan Asia       1987    40.8 13867957      852.
##  9 Afghanistan Asia       1992    41.7 16317921      649.
## 10 Afghanistan Asia       1997    41.8 22227415      635.
## # … with 1,694 more rows
Gap%>%
  filter(country=="Brazil") %>%
  ggplot(aes(year,pop))+
  labs(title="População brasileira entre 1955-2015",
       x="data",
       y="população")+
  geom_line(size=0.7)+
  geom_point(color="black",fill="yellow",shape=21,size=3.5)+
  tema

Para criar pontos nas linhas, semelhante ao que o Excel produz, é necessário usar a função gapminder, carregando uma base de dados da população de diversos lugares do mundo, desde a década de 1950. Usa-se a função filter() para selecionar o Brasil, e então usa-se as funções geom_line() e geom_point().

8.7 Gráfico com múltiplas linhas

Gap%>%
  filter(country %in% c("Brazil","Uruguay","Argentina")) %>%
  ggplot(aes(year,pop,color=country,fill=country))+
  labs(title="População da Argentina, Brasil e Uruguai entre 1955-2015",
       x="data",
       y="população",
       color="país",
       fill="país")+
  geom_line()+
  geom_point(color="black",shape=21,size=3)+
  tema

Para analisar mais de um tipo de dado ao mesmo tempo, como entender o crescimento populacional de diferentes lugares numa mesma escala de tempo. Com a função filter(), é possível selecionar mais de um país por vez, através da função country %in% c(), e a função color=country em aes() para poder diferenciar os países através de cores diferentes.

8.8 Criando uma escala de cor

Ecs%>%
  ggplot(aes(date,unemploy,color=pop))+
  labs(title="desemprego nos Estados Unidos entre 1970-2015",
       x="data",
       y="desemprego",
       color="população")+
  geom_line(size=1)+
  tema

Como é um gráfico de linha, para selecionar a cor da linha, é selecionado a função color= no comando aes(). Nesse caso, para criar uma cor em função de um gradiente, é usado a variável pop. Por ser uma variável quantitativa contínua, a cor da linha está em um gradiente.

8.8.1 Alterando a cor da escala

Ecs%>%
  ggplot(aes(date,unemploy,color=pop))+
  labs(title="desemprego nos Estados Unidos entre 1970-2015",
       x="data",
       y="desemprego",
       color="população")+
  geom_line(size=1)+
  scale_color_gradient(low="yellow",high="brown")+
  tema

Com a função scale_color_gradient() é possível selecionar um gradiente específico de cores selecionadas. O elemento low= é a cor dos valores mais baixos, e o elemento high= é a cor dos valores mais altos. É aconselhado usar cores claras em low= e cores mais escuras em high=.

8.8.2 Escolhendo uma paleta com mais cores

Ecs%>%
  ggplot(aes(date,unemploy,color=pop))+
  labs(title="desemprego nos Estados Unidos entre 1970-2015",
       x="data",
       y="desemprego",
       color="população")+
  geom_line(size=1)+
  scale_color_gradientn(colours =c("purple4","royalblue","dodgerblue","deepskyblue","mediumspringgreen","springgreen","green","lawngreen","greenyellow","yellow", "gold","darkorange","chocolate1","orangered","red","darkred"),breaks=seq(0,325000,20000))+
  tema

Com o comando scale_color_gradientn(), com o comando interno colours=c(), é possível não apenas escolher um gradiente com mais cores, onde aqui foram usadas 16 cores diferentes, como também definir o intervalo dos valores do gradiente, com o comando interno breaks=seq(), onde o primeiro valor é o valor inicial, o segundo valor é o valor final e o terceiro valor é o intervalo de cada valor.

9 Gráfico de frequência

9.1 Quando usar

Esse gráfico é utilizado quando se deseja identificar o quanto cada variável contribui para formar o todo, e qual variável se faz mais presente. É um tipo de gráfico bastante utilizado para identificar, dentro de um conjunto de eventos ou ações, quem mais apresentou ações, contribuições para formar o conjunto todo, ou seja, frequência, como na contribuição de certos funcionários para um produto. É semelhante ao gráfico de barras, mas nesse, é possível limitar à apenas 1 única barra, ou até criar um gráfico de pizza. Exemplo: da base de dados starwars, qual gênero representa a maioria dos oersonagens? É o que será feito agora.

9.2 Packages exigidos

library(ggplot2)
library(tidyverse)

9.3 Carregando base de dados

SW<-starwars
SW
## # A tibble: 87 × 14
##    name        height  mass hair_…¹ skin_…² eye_c…³ birth…⁴ sex   gender homew…⁵
##    <chr>        <int> <dbl> <chr>   <chr>   <chr>     <dbl> <chr> <chr>  <chr>  
##  1 Luke Skywa…    172    77 blond   fair    blue       19   male  mascu… Tatooi…
##  2 C-3PO          167    75 <NA>    gold    yellow    112   none  mascu… Tatooi…
##  3 R2-D2           96    32 <NA>    white,… red        33   none  mascu… Naboo  
##  4 Darth Vader    202   136 none    white   yellow     41.9 male  mascu… Tatooi…
##  5 Leia Organa    150    49 brown   light   brown      19   fema… femin… Aldera…
##  6 Owen Lars      178   120 brown,… light   blue       52   male  mascu… Tatooi…
##  7 Beru White…    165    75 brown   light   blue       47   fema… femin… Tatooi…
##  8 R5-D4           97    32 <NA>    white,… red        NA   none  mascu… Tatooi…
##  9 Biggs Dark…    183    84 black   light   brown      24   male  mascu… Tatooi…
## 10 Obi-Wan Ke…    182    77 auburn… fair    blue-g…    57   male  mascu… Stewjon
## # … with 77 more rows, 4 more variables: species <chr>, films <list>,
## #   vehicles <list>, starships <list>, and abbreviated variable names
## #   ¹​hair_color, ²​skin_color, ³​eye_color, ⁴​birth_year, ⁵​homeworld

9.4 Criando a freqência de personagens por gênero

gênero<-starwars %>%
  group_by(gender) %>%
  summarise(
    n = n()
  )
gênero
## # A tibble: 3 × 2
##   gender        n
##   <chr>     <int>
## 1 feminine     17
## 2 masculine    66
## 3 <NA>          4

Para facilitar o uso dos dados, foi atribuído ao objeto gênero a frequência dos gêneros da variável gender, através da função group_by() e summarise(), criando assim a variável n, correspondente ao nº de personagens de cada gênero.

9.5 Criando o gráfico

gênero %>%
  ggplot(aes(gender,n,fill=gender,label=n))+
  labs(title="n° de personagens de Stawars por gênero",
       x="gênero",
       y="n° de ocorrência",
       fill="gênero")+
  geom_bar(stat="identity",color="black",alpha=0.5)+
  coord_flip()+
  geom_label(color="black")+
  tema

Com a função geom_bar() para criar barras, com a função stat=identity, e alpha=0.5 para deixar as barras transparente, a função coord_flip para enverter os eixos, a função geom_label() para adicionar rótulos às barras e a função label=n na função aes() para adicinar o valor dos rótulos, foi feito o gráfico de frequência.

9.6 Criando o gráfico com apenas 1 barra

gênero %>%
  ggplot(aes("",n,fill=gender,label=n))+
  labs(title="n° de personagens de Stawars por gênero",
       x=NULL,
       y="n° de ocorrência",
       fill="gênero")+
  geom_bar(stat="identity",color="black",alpha=0.5,width=0.3)+
  coord_flip()+
  geom_label(position = position_stack(vjust=0.5),color="black")+
  theme_void()+
  tema

Removendo a variável gender, alterando a largura da barra com a função width=0.3, usando a função position = position_stack(vjust=0.5) para posicionar corretamente os rótulos e a função theme_void() para remover todos os elementos do fundo, fica apenas as barrras e seus respectivos rótulos.

9.7 Criando o gráfico de pizza

gênero %>%
  ggplot(aes("",n,fill=gender,label=n))+
  labs(title="n° de personagens de Stawars por gênero",
       x=NULL,
       y=NULL,
       fill="gênero")+
  geom_bar(stat="identity",color="black",alpha=0.5,width=0.3)+
  coord_flip()+
  coord_polar(theta="y",start=0)+
  geom_label(position = position_stack(vjust=0.5),color="black")+
  tema

Com a função coord_polar(), é possível criar um gráfico circulas, de pizza, com os mesmos elementos usadoa anteriormente.

10 Gráficos de correlação

10.1 Quando usar

O gráfico de correlação é utilizado para entender relações de porporcionalidade de covariância entre duas variáveis quantitativas contínuas, sendo esta uma relação diretamente proporcional (positiva: à medida que uma variável cresce, a outra crescerá junto) ou inversalmente proporcional (negativa: à medida que uma cresce, outra diminuirá). Exemplo: da base de dados mtcars, o peso dos carros está correlacionado com o nº de galões por milhas? É o que será feito agora.

10.2 Packages exigidos

library(tidyverse)
library(ggcorrplot)

10.3 Carregando base de dados

MC<-mtcars
MC
##                      mpg cyl  disp  hp drat    wt  qsec vs am gear carb
## Mazda RX4           21.0   6 160.0 110 3.90 2.620 16.46  0  1    4    4
## Mazda RX4 Wag       21.0   6 160.0 110 3.90 2.875 17.02  0  1    4    4
## Datsun 710          22.8   4 108.0  93 3.85 2.320 18.61  1  1    4    1
## Hornet 4 Drive      21.4   6 258.0 110 3.08 3.215 19.44  1  0    3    1
## Hornet Sportabout   18.7   8 360.0 175 3.15 3.440 17.02  0  0    3    2
## Valiant             18.1   6 225.0 105 2.76 3.460 20.22  1  0    3    1
## Duster 360          14.3   8 360.0 245 3.21 3.570 15.84  0  0    3    4
## Merc 240D           24.4   4 146.7  62 3.69 3.190 20.00  1  0    4    2
## Merc 230            22.8   4 140.8  95 3.92 3.150 22.90  1  0    4    2
## Merc 280            19.2   6 167.6 123 3.92 3.440 18.30  1  0    4    4
## Merc 280C           17.8   6 167.6 123 3.92 3.440 18.90  1  0    4    4
## Merc 450SE          16.4   8 275.8 180 3.07 4.070 17.40  0  0    3    3
## Merc 450SL          17.3   8 275.8 180 3.07 3.730 17.60  0  0    3    3
## Merc 450SLC         15.2   8 275.8 180 3.07 3.780 18.00  0  0    3    3
## Cadillac Fleetwood  10.4   8 472.0 205 2.93 5.250 17.98  0  0    3    4
## Lincoln Continental 10.4   8 460.0 215 3.00 5.424 17.82  0  0    3    4
## Chrysler Imperial   14.7   8 440.0 230 3.23 5.345 17.42  0  0    3    4
## Fiat 128            32.4   4  78.7  66 4.08 2.200 19.47  1  1    4    1
## Honda Civic         30.4   4  75.7  52 4.93 1.615 18.52  1  1    4    2
## Toyota Corolla      33.9   4  71.1  65 4.22 1.835 19.90  1  1    4    1
## Toyota Corona       21.5   4 120.1  97 3.70 2.465 20.01  1  0    3    1
## Dodge Challenger    15.5   8 318.0 150 2.76 3.520 16.87  0  0    3    2
## AMC Javelin         15.2   8 304.0 150 3.15 3.435 17.30  0  0    3    2
## Camaro Z28          13.3   8 350.0 245 3.73 3.840 15.41  0  0    3    4
## Pontiac Firebird    19.2   8 400.0 175 3.08 3.845 17.05  0  0    3    2
## Fiat X1-9           27.3   4  79.0  66 4.08 1.935 18.90  1  1    4    1
## Porsche 914-2       26.0   4 120.3  91 4.43 2.140 16.70  0  1    5    2
## Lotus Europa        30.4   4  95.1 113 3.77 1.513 16.90  1  1    5    2
## Ford Pantera L      15.8   8 351.0 264 4.22 3.170 14.50  0  1    5    4
## Ferrari Dino        19.7   6 145.0 175 3.62 2.770 15.50  0  1    5    6
## Maserati Bora       15.0   8 301.0 335 3.54 3.570 14.60  0  1    5    8
## Volvo 142E          21.4   4 121.0 109 4.11 2.780 18.60  1  1    4    2

Para esse exemplo, a base de dados usada sera a mtcars, que descreve dados de carros. Dados estes extraídoss de 1974 da Revista de Estadunidense de Tendência de Motores, e então essa base dados atribuída ao objeto MC.

10.4 calculando a métrica de correlação

COR<-cor(MC$wt,MC$mpg)
COR
## [1] -0.8676594

Esse resultado mostra que há uma relação inversalmente proporcional entre as variáveis calculadas da correlação (R=-0.86). próximo de R=1: correlação diretamente proporcional; próximo de R=0: ausência de correlação; próximo de R=-1: correlação inversalmente proporciona.

10.5 Calculando a correlação de várias variáveis da de correlação

CORR<-cor(MC)
CORR
##             mpg        cyl       disp         hp        drat         wt
## mpg   1.0000000 -0.8521620 -0.8475514 -0.7761684  0.68117191 -0.8676594
## cyl  -0.8521620  1.0000000  0.9020329  0.8324475 -0.69993811  0.7824958
## disp -0.8475514  0.9020329  1.0000000  0.7909486 -0.71021393  0.8879799
## hp   -0.7761684  0.8324475  0.7909486  1.0000000 -0.44875912  0.6587479
## drat  0.6811719 -0.6999381 -0.7102139 -0.4487591  1.00000000 -0.7124406
## wt   -0.8676594  0.7824958  0.8879799  0.6587479 -0.71244065  1.0000000
## qsec  0.4186840 -0.5912421 -0.4336979 -0.7082234  0.09120476 -0.1747159
## vs    0.6640389 -0.8108118 -0.7104159 -0.7230967  0.44027846 -0.5549157
## am    0.5998324 -0.5226070 -0.5912270 -0.2432043  0.71271113 -0.6924953
## gear  0.4802848 -0.4926866 -0.5555692 -0.1257043  0.69961013 -0.5832870
## carb -0.5509251  0.5269883  0.3949769  0.7498125 -0.09078980  0.4276059
##             qsec         vs          am       gear        carb
## mpg   0.41868403  0.6640389  0.59983243  0.4802848 -0.55092507
## cyl  -0.59124207 -0.8108118 -0.52260705 -0.4926866  0.52698829
## disp -0.43369788 -0.7104159 -0.59122704 -0.5555692  0.39497686
## hp   -0.70822339 -0.7230967 -0.24320426 -0.1257043  0.74981247
## drat  0.09120476  0.4402785  0.71271113  0.6996101 -0.09078980
## wt   -0.17471588 -0.5549157 -0.69249526 -0.5832870  0.42760594
## qsec  1.00000000  0.7445354 -0.22986086 -0.2126822 -0.65624923
## vs    0.74453544  1.0000000  0.16834512  0.2060233 -0.56960714
## am   -0.22986086  0.1683451  1.00000000  0.7940588  0.05753435
## gear -0.21268223  0.2060233  0.79405876  1.0000000  0.27407284
## carb -0.65624923 -0.5696071  0.05753435  0.2740728  1.00000000

Com a função cor(), é possível calcular o indice de correlação entre as diversas variáveis da base de dados MC.

10.6 Criando um gráfico com as correlações feitas

ggcorrplot(CORR)+
  tema

Criando índices de correlação das variáveis da base de dados mtcars e atribuindo ao objeto CORR, usando a função ggcorplot(), é possível criar um gráfico de correlação das variáveis. Nesse tipo de gráfico, os pontos mais vermelhos representam as maiores correlações diretalmente proporcionais, e os pontos mais azuis representam as maiores correlações inversalmente porporcionais.

10.7 Criando um gráfico com as correlações feitas, mas com círculos

ggcorrplot(
  CORR,
  method="circle"
  )+
  tema

Também é possível usar círculos como os pontos das correlação, através do comando method="circle".

10.8 Ordenamento das variáveis por agrupamento hierarquico

ggcorrplot(
  CORR,
  method="circle",
  hc.order=TRUE
)+
  tema

Também é possível agrupar de maneira hierarquica, para facilitar o entendimento do gráfico em realação às correlações das variáveis, com o comando hc.order=TRUE.

10.9 Gráfico sem espelhamento

ggcorrplot(
  CORR,
  method="circle",
  hc.order=TRUE,
  type="lower"
)+
  tema

Nos gráficos anteriores, eram gráficos espelhados, o que poderia torná-los não apenas redundantes, como também poder comprometer a sua interpretação. Para solucionar essa questão, Com a função type="lower" é possível criar um gráfico mais simples.

10.10 Adicionando o valor da correlação

ggcorrplot(
  CORR,
  method="circle",
  hc.order=TRUE,
  type="lower",
  lab=TRUE
)+
  tema

Para facilitar mais ainda o entendimento, é possível também adicionar os valores aoss pontos da correlação, com a função lab=TRUE.

10.11 Alterando o tamanho da fonte

ggcorrplot(
  CORR,
  method="circle",
  hc.order=TRUE,
  type="lower",
  lab=TRUE,
  lab_size = 3.5
)+
  tema

Em caso do valor ficar desporpociaonal aos tamanhos dos pontos da correlação, também é possível ajustar o tamanho da fonte dos rótulos, com a função lab_size=3.5.

10.12 Deixar em branco as correlações não significativas

ggcorrplot(
  CORR,
  method="circle",
  hc.order=TRUE,
  type="lower",
  lab=TRUE,
  lab_size = 3.5,
  p.mat = cor_pmat(MC),
  insig = "blank"
)+
  tema

Para fins didáticos, em caso de apenas desejar os pontos com valores de correlação significativos, também é possível excluir os valores não significativos (<0.5, >-0.5).

10.13 Alterando o título da legenda

CORR<-cor(MC)
ggcorrplot(
  CORR,
  method="circle",
  hc.order=TRUE,
  type="lower",
  lab=TRUE,
  lab_size = 3,
  p.mat = cor_pmat(MC),
  insig = "blank",
  legend.title="coeficiente de correlação"
)+
  tema

Com a função legend.title=, é possível determinar o título do da legenda do gráfico de correlação.

10.14 Definindo as cores

CORR<-cor(MC)
ggcorrplot(
  CORR,
  method="circle",
  hc.order=TRUE,
  type="lower",
  lab=TRUE,
  lab_size = 3,
  p.mat = cor_pmat(MC),
  insig = "blank",
  legend.title="coeficiente de correlação",
  colors=c("red","yellow","green")
)+
  tema

Com a função colors=c(), é possível escolher as conres. Devem ser escolhidos três cores, com seus nomes em inglês e entre aspas. É aconselhado que a segunda cor seja uma cor que consiga ser transitória entre os extremos.

11 Gráfico de regressão

11.1 Quando usar

Semelhante ao gráfico de correlação, o gráfico de regressão é utilizado quando as análises são feitas com dados com variáveis dependentes e variáveis independentes, quando há sim uma relação de causalidade entre as variáveis, através de uma graficação de dispersão de pontos no gráfico. Nesse caso, o objetivo desse gráfico é mostrar as realações de causa e efeito, através tanto da dispersão dos dados quanto pelo parâmetro R². Exemplo: na base de dados mtcars, o nº de cilindros é ditado pelo nº de galões por milhas?

11.2 Packages exigidos

library(tidyverse)
library(ggpubr)

11.3 Carregando base de dados

MC<-mtcars
MC
##                      mpg cyl  disp  hp drat    wt  qsec vs am gear carb
## Mazda RX4           21.0   6 160.0 110 3.90 2.620 16.46  0  1    4    4
## Mazda RX4 Wag       21.0   6 160.0 110 3.90 2.875 17.02  0  1    4    4
## Datsun 710          22.8   4 108.0  93 3.85 2.320 18.61  1  1    4    1
## Hornet 4 Drive      21.4   6 258.0 110 3.08 3.215 19.44  1  0    3    1
## Hornet Sportabout   18.7   8 360.0 175 3.15 3.440 17.02  0  0    3    2
## Valiant             18.1   6 225.0 105 2.76 3.460 20.22  1  0    3    1
## Duster 360          14.3   8 360.0 245 3.21 3.570 15.84  0  0    3    4
## Merc 240D           24.4   4 146.7  62 3.69 3.190 20.00  1  0    4    2
## Merc 230            22.8   4 140.8  95 3.92 3.150 22.90  1  0    4    2
## Merc 280            19.2   6 167.6 123 3.92 3.440 18.30  1  0    4    4
## Merc 280C           17.8   6 167.6 123 3.92 3.440 18.90  1  0    4    4
## Merc 450SE          16.4   8 275.8 180 3.07 4.070 17.40  0  0    3    3
## Merc 450SL          17.3   8 275.8 180 3.07 3.730 17.60  0  0    3    3
## Merc 450SLC         15.2   8 275.8 180 3.07 3.780 18.00  0  0    3    3
## Cadillac Fleetwood  10.4   8 472.0 205 2.93 5.250 17.98  0  0    3    4
## Lincoln Continental 10.4   8 460.0 215 3.00 5.424 17.82  0  0    3    4
## Chrysler Imperial   14.7   8 440.0 230 3.23 5.345 17.42  0  0    3    4
## Fiat 128            32.4   4  78.7  66 4.08 2.200 19.47  1  1    4    1
## Honda Civic         30.4   4  75.7  52 4.93 1.615 18.52  1  1    4    2
## Toyota Corolla      33.9   4  71.1  65 4.22 1.835 19.90  1  1    4    1
## Toyota Corona       21.5   4 120.1  97 3.70 2.465 20.01  1  0    3    1
## Dodge Challenger    15.5   8 318.0 150 2.76 3.520 16.87  0  0    3    2
## AMC Javelin         15.2   8 304.0 150 3.15 3.435 17.30  0  0    3    2
## Camaro Z28          13.3   8 350.0 245 3.73 3.840 15.41  0  0    3    4
## Pontiac Firebird    19.2   8 400.0 175 3.08 3.845 17.05  0  0    3    2
## Fiat X1-9           27.3   4  79.0  66 4.08 1.935 18.90  1  1    4    1
## Porsche 914-2       26.0   4 120.3  91 4.43 2.140 16.70  0  1    5    2
## Lotus Europa        30.4   4  95.1 113 3.77 1.513 16.90  1  1    5    2
## Ford Pantera L      15.8   8 351.0 264 4.22 3.170 14.50  0  1    5    4
## Ferrari Dino        19.7   6 145.0 175 3.62 2.770 15.50  0  1    5    6
## Maserati Bora       15.0   8 301.0 335 3.54 3.570 14.60  0  1    5    8
## Volvo 142E          21.4   4 121.0 109 4.11 2.780 18.60  1  1    4    2

11.4 Criando gráfico de correlação

MC %>%
  ggplot(aes(carb, mpg))+
  labs(title="relação entre o n° carburadores por nº milhas/galão",
       x="n° de carburadores",
       y="nº milhas/galão")+
  geom_point(color="darkgoldenrod4",fill="yellow",shape=21,size=4)+
  tema

Para criar o gráfico de regressão, primeiro é feito o gráfico de dispersão, usando a função geom_point(), e adicionando às variáveis carb ao eixo X e mpg ao eixo Y, dentro do comando aes().

11.5 Criando a curva de regressão

MC %>%
  ggplot(aes(carb, mpg))+
  labs(title="relação entre o n° carburadores por nº milhas/galão",
       x="n° de carburadores",
       y="nº milhas/galão")+
  geom_point(color="darkgoldenrod4",fill="yellow",shape=21,size=4)+
  geom_smooth(method = "lm", col="red", se=FALSE,formula = "y~x")+
  tema

É então calculada a curva de regressão dos dados, com a função geom_smooth(). É usado o comando method="lm", assim como anteriormente doi feito nos gráficos de dispersão.

11.6 Criando a equação derivada da regressão e o R²

MC %>%
  ggplot(aes(carb, mpg))+
  labs(title="relação entre o n° carburadores por nº milhas/galão",
       x="n° de carburadores",
       y="nº milhas/galão")+
  geom_point(color="darkgoldenrod4",fill="yellow",shape=21,size=4)+
  geom_smooth(method = "lm", col="red", se=FALSE,formula = "y~x")+
  stat_regline_equation(aes(label=paste(..eq.label..,..rr.label..,sep = "~~")),size=5)+
  tema
## Warning: The dot-dot notation (`..eq.label..`) was deprecated in ggplot2 3.4.0.
## ℹ Please use `after_stat(eq.label)` instead.

Para calcular a função geradora da curva e o R2, usa-se a função stat_regline_equation(aes(label=paste(..eq.label..,..rr.label..,sep = "~~"))), Criando assim tanto a função geradora dos dados do gráfico, quanto o . Esses resultados mostram que há uma mínima relação nº de carburadores e o nº de milhas/galão, com a variável independente (eixo X) explicando 30% dos dados observados na variável dependente (eixo Y), sendo esta uma relação inversalmente proporcional.

11.7 Alterando a posição da equação derivada e do R²

MC %>%
  ggplot(aes(carb, mpg))+
  labs(title="relação entre o n° carburadores por nº milhas/galão",
       x="n° de carburadores",
       y="nº milhas/galão")+
  geom_point(color="darkgoldenrod4",fill="yellow",shape=21,size=4)+
  geom_smooth(method = "lm", col="red", se=FALSE,formula = "y~x")+
  stat_regline_equation(aes(label=paste(..eq.label..,..rr.label..,sep = "~~")),size=5,label.x=5,label.y=32.5)+
  tema

Dentro do comando stat_regline_equation(), usando os comandos internos label.x= e label.y=, é possível aterar a posição da equação derivada da requessão e do R², escolhendo os pontos no eixo X e no eixo Y, respctivamente.

12 Gráfico de boxplot

12.1 Quando usar

O gráfico de boxplot é utilizado quando há variáveis qualitativas, em que cada um dos objetos da variável qualitativa apresenta um conjunto de dados, dados esses da variável quantitativa, como em dados de pH em três trechos específicos de um fragmento de mata ao longo dos 12 meses do ano. Nesse gráfico, são criados boxplots, sendo assim, o gráfico de boxplot é um gráfico com uma variável qualitativa (eixo X) e uma varável quantitativa (eixo Y). Exemplo: da base de dados starwars, qual a variação da altura dos personagens em função da cor dos olhos? É o que será feito agora.

12.2 Packages exigidos

library(tidyverse)

12.3 Carregando base de dados

SW<-starwars
SW
## # A tibble: 87 × 14
##    name        height  mass hair_…¹ skin_…² eye_c…³ birth…⁴ sex   gender homew…⁵
##    <chr>        <int> <dbl> <chr>   <chr>   <chr>     <dbl> <chr> <chr>  <chr>  
##  1 Luke Skywa…    172    77 blond   fair    blue       19   male  mascu… Tatooi…
##  2 C-3PO          167    75 <NA>    gold    yellow    112   none  mascu… Tatooi…
##  3 R2-D2           96    32 <NA>    white,… red        33   none  mascu… Naboo  
##  4 Darth Vader    202   136 none    white   yellow     41.9 male  mascu… Tatooi…
##  5 Leia Organa    150    49 brown   light   brown      19   fema… femin… Aldera…
##  6 Owen Lars      178   120 brown,… light   blue       52   male  mascu… Tatooi…
##  7 Beru White…    165    75 brown   light   blue       47   fema… femin… Tatooi…
##  8 R5-D4           97    32 <NA>    white,… red        NA   none  mascu… Tatooi…
##  9 Biggs Dark…    183    84 black   light   brown      24   male  mascu… Tatooi…
## 10 Obi-Wan Ke…    182    77 auburn… fair    blue-g…    57   male  mascu… Stewjon
## # … with 77 more rows, 4 more variables: species <chr>, films <list>,
## #   vehicles <list>, starships <list>, and abbreviated variable names
## #   ¹​hair_color, ²​skin_color, ³​eye_color, ⁴​birth_year, ⁵​homeworld
12.3.0.0.1 Novamente, será trabalhado com a base de dados starwars.

12.4 Criando o boxplot

SW %>%
  ggplot(aes(skin_color, height))+
  labs(title="altura dos persoanagens em relação à cor do olho",
       x="cor da pele",
       y="altura")+
  geom_boxplot(fill="green", color="black")+
  tema
## Warning: Removed 6 rows containing non-finite values (`stat_boxplot()`).

Para criar os boxplot, deve ser ecolhida uma variável qualitativa para o eixo X, como a cor da pele (skin_color), e uma quantitativa para o eixo Y, como a altura (height). Para produzir os boxplots, usa-se a função geom_boxplot(). Porém, são muitos boxplots, prejudicando o a interpretação dos dados.

12.5 Filtrando os tipos de cores de pele que aparecem

SW %>% 
  filter(skin_color %in% c("light","dark","green","fair")) %>% 
  ggplot(aes(skin_color, height))+
  labs(title="altura dos persoanagens em relação à cor do olho",
       x="cor da pele",
       y="altura")+
  geom_boxplot(fill="green", color="black")+
  tema
## Warning: Removed 4 rows containing non-finite values (`stat_boxplot()`).

É possível também selecionar uma cor para cada boxplot. Através do comando fill=skin_color foi possível colorir os boxplots de acordo com seus grupos.

12.6 Selecionando um grupo de cores específicas do preenchimento dos boxplots

SW %>% 
  filter(skin_color %in% c("light","dark","green","fair")) %>% 
  ggplot(aes(skin_color, height,fill=skin_color))+
  labs(title="altura dos persoanagens em relação à cor do olho",
       x="cor do olho",
       y="altura",
       fill="cor da pele")+
  geom_boxplot(color="black")+
  scale_fill_manual(values = c("#5D5D5D","#E5BB91","green1","cyan"))+
  tema
## Warning: Removed 4 rows containing non-finite values (`stat_boxplot()`).

Com a função scale_fill_manual() é possível selecionar uma paleta de cores específicas para os preenchimentos dos boxplots, facilitando a interpretação de cada boxplot.

12.7 Selecionando um grupo de cores específicas da borda dos boxplots

SW %>% 
  filter(skin_color %in% c("light","dark","green","fair")) %>% 
  ggplot(aes(skin_color, height,fill=skin_color,color=skin_color))+
  labs(title="altura dos persoanagens em relação à cor do olho",
       x="cor do olho",
       y="altura",
       fill="cor da pele",
       color="cor da pele")+
  geom_boxplot()+
  scale_fill_manual(values = c("#5D5D5D","#E5BB91","green1","cyan"))+
  scale_color_manual(values = c("red","yellow","darkgreen","blue"))+
  tema
## Warning: Removed 4 rows containing non-finite values (`stat_boxplot()`).

Também é possível escolher as cores da borda de cada boxplot. Para isso, é preciso primeiro especificar à função aes() o comando color=skin_color, para especificar que as cores das bordas variam em função da cor de pele dos personagens. Após, é adicionada a função scale_color_manual(), seguindo os mesmos passos da função scale_fill_manual(), sendo que agora o que será selecionado serão as cores das bordas de cada um dos boxplots. Outro ponto importante é: quando você atribui a fill= e color= o mesmo título, eles acabam se tornando a mesma legenda.

13 Adicionado texto ao gráfico

13.1 Quando usar

Em algumas situações específicas, se faz necessário o uso de textos, com o intúito apontar ou enfatizar informações no gráfico em questão. Um exemplo é quando linhas são traçadas, como com as funções geom_hline() e geom_vline(), em que deseja-se delimitar regiões ou limites dos dados trabalhados, o uso de textos para explicar e apontar estes limites torna-se um recurso útil. Outro bom exemplo é no uso de mapas, onde é possível combinar os textos com labels, criar legendas para as regiões do mapa.

13.2 Packages exigidos

library(tidyverse)

Primeiro, foi carregada o package ggplot2, para conseguir produzir os gráficos ggplot, assim como carregar bases de dados a seres analisadas. Em seguida, foi carregado o package tidyverse, para melhor manipular e trabalhar com os dados utilizados

13.3 Base de dados

resposta<-c(0,0,0.05,0.06,0.1,0.15,0.2,0.37,0.45,0.5,0.68,0.74,0.82,0.95,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0.05,0.09,0.15,0.27,0.39,0.42,0.5,0.62,0.78,0.83,0.91,1,1,1,1,1,1,1,1)

dose<-(rep(c(0,10,20,30,40,50,60,70,80,90,100,110,120,130,140,150,160,170,180,190,200,210,220,230,240,250,260,270,280,290,300),2))

espécies<-(rep(c("sp1","spe2"),each=31))

dados.toxicidade<-data.frame(resposta,dose,espécies)
dados.toxicidade
##    resposta dose espécies
## 1      0.00    0      sp1
## 2      0.00   10      sp1
## 3      0.05   20      sp1
## 4      0.06   30      sp1
## 5      0.10   40      sp1
## 6      0.15   50      sp1
## 7      0.20   60      sp1
## 8      0.37   70      sp1
## 9      0.45   80      sp1
## 10     0.50   90      sp1
## 11     0.68  100      sp1
## 12     0.74  110      sp1
## 13     0.82  120      sp1
## 14     0.95  130      sp1
## 15     1.00  140      sp1
## 16     1.00  150      sp1
## 17     1.00  160      sp1
## 18     1.00  170      sp1
## 19     1.00  180      sp1
## 20     1.00  190      sp1
## 21     1.00  200      sp1
## 22     1.00  210      sp1
## 23     1.00  220      sp1
## 24     1.00  230      sp1
## 25     1.00  240      sp1
## 26     1.00  250      sp1
## 27     1.00  260      sp1
## 28     1.00  270      sp1
## 29     1.00  280      sp1
## 30     1.00  290      sp1
## 31     1.00  300      sp1
## 32     0.00    0     spe2
## 33     0.00   10     spe2
## 34     0.00   20     spe2
## 35     0.00   30     spe2
## 36     0.00   40     spe2
## 37     0.00   50     spe2
## 38     0.00   60     spe2
## 39     0.00   70     spe2
## 40     0.00   80     spe2
## 41     0.00   90     spe2
## 42     0.00  100     spe2
## 43     0.00  110     spe2
## 44     0.05  120     spe2
## 45     0.09  130     spe2
## 46     0.15  140     spe2
## 47     0.27  150     spe2
## 48     0.39  160     spe2
## 49     0.42  170     spe2
## 50     0.50  180     spe2
## 51     0.62  190     spe2
## 52     0.78  200     spe2
## 53     0.83  210     spe2
## 54     0.91  220     spe2
## 55     1.00  230     spe2
## 56     1.00  240     spe2
## 57     1.00  250     spe2
## 58     1.00  260     spe2
## 59     1.00  270     spe2
## 60     1.00  280     spe2
## 61     1.00  290     spe2
## 62     1.00  300     spe2

Para a construção do gráfico, foi criada uma base de dados de toxidade de uma substância na água em função da sua toxicidade (mortalidade) em duas espécies, e atribuído ao objeto dados.toxicidade. Primeiro, foi criada a variável resposta, e atribuído a esta os valores de % de mortalidade de cada espécies às diferentes concentrações da susbtância. Após, foi criada a variável dose, e atribuindo à esta os valores das concentrações testadas para cada espécie. Em seguida, foi criada a variável espécies, e utilizando a função rep(), foram adicionados as espécies testadas, com 15 repetições para ambas. Por último, foi criado o data frame dados.toxicidade, através da função data.frame(), utilizando as variáveis resposta, dose e espécies.

13.4 Criando o gráfico

dados.toxicidade %>% 
  ggplot(aes(dose,resposta,color=espécies))+
  geom_line(size=2)+
  labs(title="respostas das espécies às concentrações da substância",
       x="dose (mg/L)",
       y="mortalidade (%)",
       color="espécies")+
  geom_hline(yintercept=0.5,color="red",linetype="dashed",size=1)+
  geom_vline(xintercept=90,color="darkgreen",size=1)+
  geom_vline(xintercept=180,color="darkred",size=1)+
  scale_x_continuous(breaks=seq(0,300,20))+
  scale_y_continuous(breaks=seq(0,1,0.1))+
  scale_color_manual(values=c("green1","red"),labels=c("espécie 1","espécie 2"))+
  tema

Com os dados da base de dados dados.toxicidade, é possível criar o gráfico. Para se tornar mais didático, será adicionado textos.

13.5 Adicionando texto ao gráfico

dados.toxicidade %>% 
  ggplot(aes(dose,resposta,color=espécies))+
  geom_line(size=2)+
  labs(title="respostas das espécies às concentrações da substância",
       x="dose (mg/L)",
       y="mortalidade (%)",
       color="espécies")+
  geom_hline(yintercept=0.5,color="red",linetype="dashed",size=1)+
  geom_vline(xintercept=90,color="darkgreen",size=1)+
  geom_vline(xintercept=180,color="darkred",size=1)+
  scale_x_continuous(breaks=seq(0,300,20))+
  scale_y_continuous(breaks=seq(0,1,0.1))+
  scale_color_manual(values=c("green1","red"),labels=c("espécie 1","espécie 2"))+
  geom_text(aes(x = 29.5, y = 0.55),
                label = "50% de mortalidade",
            size = 4, 
            color = "red")+
  tema

Usando a função geom_text() é possível adicionar textos ao gráfico. Dentro da função aes():

  • x: posição do eixo X onde o texto se encontrará;

  • y: posição do eixo Y onde o texto se encontrará.

Fora da função aes():

  • size: tamanho da letra;

  • color: cor do texto.

Nesse caso, como é de interesse saber saber a marca onde atingiu 50% de mortalidade, não apenas foi traçada uma linha no ponto 0.5 do eixo Y, como foi aí adicionado o texto.

dados.toxicidade %>% 
  ggplot(aes(dose,resposta,color=espécies))+
  geom_line(size=2)+
  labs(title="respostas das espécies às concentrações da substância",
       x="dose (mg/L)",
       y="mortalidade (%)",
       color="espécies")+
  geom_hline(yintercept=0.5,color="red",linetype="dashed",size=1)+
  geom_vline(xintercept=90,color="darkgreen",size=1)+
  geom_vline(xintercept=180,color="darkred",size=1)+
  scale_x_continuous(breaks=seq(0,300,20))+
  scale_y_continuous(breaks=seq(0,1,0.1))+
  scale_color_manual(values=c("green1","red"),labels=c("espécie 1","espécie 2"))+
  geom_text(aes(x = 29.5, y = 0.55),
                label = "50% de mortalidade",
            size = 4, 
            color = "red")+
  geom_text(aes(x = 85, y = -0.03),
                label = "dose com 50% de letalida",
            size = 3.5, 
            color = "darkgreen")+
  geom_text(aes(x = 190, y = -0.03),
                label = "dose com 50% de letalida",
            size = 3.5, 
            color = "darkred")+
  tema

Além da linha que delimita o ponto de 50% de mortalidade, é possível também marcar o ponto da dose onde causa 50% de letalidade, para ambas as espécies.

14 Salvando o gráfico no dispositivo

14.1 Quando usar

Como muitas vezes aqueles gráficos produzidos irão para algum destino, como alguma atividade, seminário, artigo, relatório ou tese, é preiso que aquele gráfico produzido no ggplot seja exportado. Há duas principais maneiras: manualmente na aba dos plots ou através da função ggsave().

14.2 Exportando a partir da aba de plots

Na região marcada em vermelho é onde começa a exportação, onde o gráfico poderá ser enviado para alguma área do computador do usuário.

Na região marcada em vermelho, há os formatos possíveis a ser exportados os arquivos, como em imagem, PDF ou até copiar, como um simples ctrl+C. A escolha vai do desejo do usuário, mas aqui iremos usar o formato de imagem, marcado em amarelo.

Na região marcada em vermelho é o formato do arquivo que será selecionado para exportar a imagem, sendo os formatos disponíveis para imagem: PNG, JPG, JPEG, TIFF, BMP, Metafile, SVG e EPS. A região marcada em laranja é o diretório, o local do dispositivo onde arquivo será exportado. A região marcada em amarelo é o nome do arquivo que será exportado. A região marcada em verde é a largura da imagem, em azul a altura. A região marcada em roxo é onde salvar e começar a exportar a imagem, em rosa cancelar toda a ação. Porém há um jeito mais simples de salvar o gráfico, a partir da função ggsave(), do package ggplot.

14.3 Salvando o gráfico com a função ggsave

14.3.1 O que é o ggsave

Como já falado antes, a função ggsave() é uma função do package ggplot, que salva o último gráfico plotado para um diretório do dispositivo.

14.3.2 Packages exigidos

library(tidyverse)

14.3.3 Carregando base de dados

SW<-starwars
SW
## # A tibble: 87 × 14
##    name        height  mass hair_…¹ skin_…² eye_c…³ birth…⁴ sex   gender homew…⁵
##    <chr>        <int> <dbl> <chr>   <chr>   <chr>     <dbl> <chr> <chr>  <chr>  
##  1 Luke Skywa…    172    77 blond   fair    blue       19   male  mascu… Tatooi…
##  2 C-3PO          167    75 <NA>    gold    yellow    112   none  mascu… Tatooi…
##  3 R2-D2           96    32 <NA>    white,… red        33   none  mascu… Naboo  
##  4 Darth Vader    202   136 none    white   yellow     41.9 male  mascu… Tatooi…
##  5 Leia Organa    150    49 brown   light   brown      19   fema… femin… Aldera…
##  6 Owen Lars      178   120 brown,… light   blue       52   male  mascu… Tatooi…
##  7 Beru White…    165    75 brown   light   blue       47   fema… femin… Tatooi…
##  8 R5-D4           97    32 <NA>    white,… red        NA   none  mascu… Tatooi…
##  9 Biggs Dark…    183    84 black   light   brown      24   male  mascu… Tatooi…
## 10 Obi-Wan Ke…    182    77 auburn… fair    blue-g…    57   male  mascu… Stewjon
## # … with 77 more rows, 4 more variables: species <chr>, films <list>,
## #   vehicles <list>, starships <list>, and abbreviated variable names
## #   ¹​hair_color, ²​skin_color, ³​eye_color, ⁴​birth_year, ⁵​homeworld

Para fins práticos, será feito com o último gráfico boxplot feito.

14.3.4 Salvando

SW %>% 
  filter(skin_color %in% c("light","dark","green","fair")) %>% 
  ggplot(aes(skin_color, height,fill=skin_color))+
  geom_boxplot(color="black")+
  labs(title = "Altura dos personagens em função da cor de pele",
       x="Cor de pele",
       y="Altura (cm)",
       fill="cor de pele")+
  scale_fill_manual(values = c("#5D5D5D","#E5BB91","green1","cyan"))+
  tema
## Warning: Removed 4 rows containing non-finite values (`stat_boxplot()`).

ggsave(filename = "G:/Meu Drive/R/Gráfico_Export.png")
## Warning: Removed 4 rows containing non-finite values (`stat_boxplot()`).

Com a função filename = "G:/Meu Drive/R/Gráfico_Export.png", é informado dois elementos: 1) o diretório onde o gráfico será exportado (G:/Meu Drive/R/); 2) o nome do arquivo, com o seu formato (Gráfico_Export.png).

14.3.5 Vendo que o gráfico foi exportado para o dispositivo

Como feito no ggsave, o gráfico foi exportado para o diretório selecionado.

14.3.6 Vendo o gráfico então exportado

Como visto, o gráfico foi exportado com sucesso. Também é preciso saber que o ggsave() exporta o último gráfico plotado, independente se a linha de código do ggsave() está abaixo das linhas do ggplot que se deseja exportar. Por isso, antes de exportar seu gráfico, certifique-se que o seu gráfico escolhido foi plotado.

15 Gráficos interativos

Tudo que foi mostrado aqui são gráficos parados, sem nenhum tipo de interação com quem o está fazendo ou o lendo. Porém, há um jeito de tornar os gráficos criados no R interativos, como se fossem um dashboard

15.1 Packages exigidos

library(tidyverse)
library(plotly)
library(htmlwidgets)

Porém, dessa vez, além de dos pacotes básicos já usados, serão também utilizados mais dois novos. O package plotly é usado para criar os gráficos interativos, como um dashboard. Já o package htmlwidgets para salvar os gráficos, com eles continuando por serem interativos.

15.2 Carregando base de dados

SW<-starwars
SW
## # A tibble: 87 × 14
##    name        height  mass hair_…¹ skin_…² eye_c…³ birth…⁴ sex   gender homew…⁵
##    <chr>        <int> <dbl> <chr>   <chr>   <chr>     <dbl> <chr> <chr>  <chr>  
##  1 Luke Skywa…    172    77 blond   fair    blue       19   male  mascu… Tatooi…
##  2 C-3PO          167    75 <NA>    gold    yellow    112   none  mascu… Tatooi…
##  3 R2-D2           96    32 <NA>    white,… red        33   none  mascu… Naboo  
##  4 Darth Vader    202   136 none    white   yellow     41.9 male  mascu… Tatooi…
##  5 Leia Organa    150    49 brown   light   brown      19   fema… femin… Aldera…
##  6 Owen Lars      178   120 brown,… light   blue       52   male  mascu… Tatooi…
##  7 Beru White…    165    75 brown   light   blue       47   fema… femin… Tatooi…
##  8 R5-D4           97    32 <NA>    white,… red        NA   none  mascu… Tatooi…
##  9 Biggs Dark…    183    84 black   light   brown      24   male  mascu… Tatooi…
## 10 Obi-Wan Ke…    182    77 auburn… fair    blue-g…    57   male  mascu… Stewjon
## # … with 77 more rows, 4 more variables: species <chr>, films <list>,
## #   vehicles <list>, starships <list>, and abbreviated variable names
## #   ¹​hair_color, ²​skin_color, ³​eye_color, ⁴​birth_year, ⁵​homeworld

Para esse exemplo, continuará sendo usado a base de dados Starwars.

15.3 Criando o gráfico

Gráfico<-SW %>%
  filter(mass<1000) %>%
  ggplot(aes(height,mass,fill=eye_color))+
  labs(title="relação entre a altura e a massa dos personagens",
       x="altura",
       y="massa",
       color="cor do olho")+
  geom_point(color="black",shape=21,size=4)+
  scale_color_manual(values=c("black","blue","#597DAB","#875E1E","#B2FF00","#FFB727","orange","red","#A9A9A9","white","yellow"))+
  tema
Gráfico

Para o exemplo que será feito com um gráfico interativo, será utilizado um gráfico de pontos. Para ser mais interessante e prático de ser feito com ele, foram feitas duas alterações, em relação ao gráfico de dsipersão, feito anteriormente no começo desse guia: 1) o gráfico é feito avaliando à massa em relação à altura dos personagaens da franquia Star Wars, mas agora os pontos foram coloridos e diferenciados em função da cor do olho dos personagens; 2) para ser prático, todo o script do ggplot foi atribuído ao objeto Gráfico, e então usado no função ggplotly().

15.4 Tornando o gráfico interativo

Inter.Graf<-ggplotly(Gráfico)
Inter.Graf

Para poder salvar o gráfico com o formato interativo posteriormente, foi atribuido ao objeto Inter.Graf. À primeira vista, pode parecer não haver mudado nada, mas ao passar o mouse pelo gráfico, ou clicando em zoom, as diferenças parecem, como neste gráfico acima deste texto mesmo, ou através dp exemplo da imagem abaixo. Como é possível ver, ao passar o mouse por cima dos pontos, é possivel ver os dados do ponto, como a sua altura, a massa e a cor. Na segunda imagem, é possível ver a barra de ferramentas na posição superior Direita. Da esquerda para a direita, respectivamente:

*download do gráfico como png;

*zoom, puxando e arrastando, para dar zoom em uma área específica do gráfico;

  • movimentar e arrastar o gráfico; selecionar pontos específicos com contorno em caixa;

  • selecionar pontos específicos com contorno livre;

  • zoom in, para se “aprofundar” no gráfico;

*zoom out, para se “distanciar” no gráfico;

  • autoescala;

  • resetar área selecionada;

  • mostar os dados de cada ponto por vez e mostrar todos os dados dos pontos selecionados.

15.5 Salvando como gráfico interativo

saveWidget(Inter.Graf,file ="G:/Meu Drive/R/Gráfico.html")

Com a função saveWidget(), do pacote htmlwidget, é possível salvar o gráfico, preservando ele na sua forma interativa. Para isso, é especificado o gráfico, que estava no objeto Inter.Graf, e o local do dispositivo onde o gráfico será salvo (file ="G:/Meu Drive/R/") e o nome do arquivo, no formato html (Gráfico.html).

Como é possível observar, o arquivo foi salvo no formato html e no local informado. É importante verificar se o arquivo está programado para ser aberto com o seu navegador, que neste caso aqui, é o Microsft Edge. Caso não, procure alterar nas configuras, em propriedades, do arquivo.

E como pode ser visto, o arquivo foi aberto no Mirosoft Edge, preservando sua capacidade de ser interativo.

16 Personalizando os temas do ggplot

16.1 O que são os temas do ggplot

Quando criamos um ggplot, ele automaticamente lhe cria um aparência para o plano de fundo, as grades, os nomes dos eixos, valores dos eixos, aparência do título, etc. Isso é o que se chama de tema. Esses temas são feitos através da função theme() e suas variações, como:

  • theme();

  • theme_bw();

  • theme_classic();

  • theme_dark();

  • theme_get();

  • theme_gray();

  • theme_grey();

  • theme_light();

  • theme_linedraw();

  • theme_minimal();

  • theme_replace();

  • theme_set();

  • theme_test();

  • theme_update();

  • theme_void()

Algumas vezes, o tema padrão que o ggplot pode não influenciar na legidibilidade do gráficco, e em outras pode até ajudar. Contudo, há situações que os temas precisam ser alterados, por simples motivos estéticos, ou pelo tema padrão atrapalhar a legidibilidade ou até uma exigência de quem irá avaliar o trabalho. Como é possível personalizar os temas, é uma importante ferramenta para alterar os temas.

16.2 Criando um gráfico para ser modelo da personalização de temas

Antes de começar a personalizar, é importante lembrar que não existem, necessariamente, temas melhores ou temas piores. Existem sim temas mais adequados para diversos fins e necessidades, mas com as possibilidades que serão expostas aqui, existem mais 5.500 possibilidades de temas personalizados. Por isso, lembre-se que cada caso é um caso, e não encare um único tema como um “salvador universal”.

16.2.1 Package exigidos

library(tidyverse)
library(grDevices)

Para começar a criar um gráfico a ser usado para os exemplos, são carregados os packages ggplot2, para criar os gráficos em ggplot, e tidyverse, mas conseguir trabalhar melhor com os dados. Em seguida, foi carregado o package grDevices, para manipular as fontes de texto dos gráficos.

16.2.2 Criando um gráfico exemplo

Ecs<-economics
Ecs
## # A tibble: 574 × 6
##    date         pce    pop psavert uempmed unemploy
##    <date>     <dbl>  <dbl>   <dbl>   <dbl>    <dbl>
##  1 1967-07-01  507. 198712    12.6     4.5     2944
##  2 1967-08-01  510. 198911    12.6     4.7     2945
##  3 1967-09-01  516. 199113    11.9     4.6     2958
##  4 1967-10-01  512. 199311    12.9     4.9     3143
##  5 1967-11-01  517. 199498    12.8     4.7     3066
##  6 1967-12-01  525. 199657    11.8     4.8     3018
##  7 1968-01-01  531. 199808    11.7     5.1     2878
##  8 1968-02-01  534. 199920    12.3     4.5     3001
##  9 1968-03-01  544. 200056    11.7     4.1     2877
## 10 1968-04-01  544  200208    12.3     4.6     2709
## # … with 564 more rows

Para começar, foi carregado a base de dados Economics, e atribuída ao objeto Ecs. Essa base de dados é do package ggplot, que apresenta dados de séries econômicas da história dos Estados Unidos. Ela será usada para construir o gráfico ggplot que será testado as funções de personalização de tema.

exemplo<-Ecs%>%
  ggplot(aes(date,unemploy,color=pop))+
  geom_line(size=1.1)+
  labs(title="Nº de desempregados nos Estados Unidos",
       subtitle=" entre 01/07/1967-01/04/2015", 
       x="Data",
       y="Desemprego",
       color="tamanho populacional",
       caption="dados: Economics")+
  scale_color_gradientn(colours =c("purple4","royalblue","dodgerblue","deepskyblue","mediumspringgreen","springgreen","green","lawngreen","greenyellow","yellow", "gold","darkorange","chocolate1","orangered","red","darkred"),breaks=seq(0,325000,20000))
exemplo

Criado o gráfico, é possível criar os temas personalizados.

16.3 Personalizando

16.3.1 Elemento element_text()

Esse elemento de texto do gráffico, como títulos e legendas. É possível alterar tamanho, forma e cor. Os elementos devem sempre ser seguidos de element_text(). Dentre os diversos elementos de texto, estão:

  • text=: personaliza todo e qualquer texto do gráfico, sendo tílos ou elementos da legenda;
exemplo+
  theme( text  = element_text(color="red"))

  • axis.text=: personaliza todo e qualquer texto os eixos do gráfico;
exemplo+
  theme( axis.text  = element_text(color="red"))

  • axis.text.x=: personaliza o texto do eixo X do gráfico;
exemplo+
  theme( axis.text.x  = element_text(color="red"))

  • axis.text.y=: personaliza o texto do eixo Y do gráfico;
exemplo+
  theme( axis.text.y  = element_text(color="red"))

  • legend.text=: personaliza o texto da legenda do gráfico;
exemplo+
  theme( legend.text  = element_text(color="red"))

  • title=: personaliza apenas os títulos do gráfico;
exemplo+
  theme( title  = element_text(color="red"))

  • legend.title=: personaliza o título da legenda;
exemplo+
  theme( legend.title  =  element_text(color="red"))

  • plot.title=: personaliza o título do gráfico:
exemplo+
  theme( plot.title  =  element_text(color="red"))

  • plot.subtitle=: personaliza o subtítulo do gráfico:
exemplo+
  theme( plot.subtitle  =  element_text(color="red"))

  • plot.caption=: personaliza a nota de roda-pé do gráfico:
exemplo+
  theme( plot.caption  =  element_text(color="red"))

  • plot.tag=: personaliza a marcação do gráfico:
exemplo2<-Ecs%>%
  ggplot(aes(date,unemploy,color=pop))+
  geom_line(size=1.1)+
  labs(title="Nº de desempregados nos Estados Unidos",
       subtitle=" entre 01/07/1967-01/04/2015",
       tag="o tamanho populacional só cresceu", 
       x="Data",
       y="Desemprego",
       color="tamanho populacional",
       caption="dados: Economics")+
  scale_color_gradientn(colours =c("purple4","royalblue","dodgerblue","deepskyblue","mediumspringgreen","springgreen","green","lawngreen","greenyellow","yellow", "gold","darkorange","chocolate1","orangered","red","darkred"),breaks=seq(0,325000,20000))

exemplo2+
  theme( plot.tag  =  element_text(color="red"))

  • axis.title=:personaliza os títulos dos eixos X e Y;
exemplo+
  theme( axis.title  = element_text(color="red"))

  • axis.title.x=: personaliza apenas o título do eixo X;
exemplo+
  theme( axis.title.x  = element_text(color="red"))

  • axis.title.y=: personaliza apenas o título do eixo Y.
exemplo+
  theme( axis.title.y =  element_text(color="red"))

  • Personalizando a fonte:
windowsFonts(TimesNewRoman=windowsFont("Times New Roman"),
                        WideLatin=windowsFont("Wide Latin"),
                        Mistral=windowsFont("Mistral"))

exemplo+
  theme(text=element_text(family = "TimesNewRoman"))

exemplo+
  theme(text=element_text(family = "WideLatin"))

exemplo+
  theme(text=element_text(family = "Mistral"))

Naturalmente, é o ggplot criar seus plots com textos na fonte Arial, mas também é possível alterar a fonte dos textos do plot. Para isso, é usado a função Windownsfonts(), do package grDevices, especificando uma fonte salva no sistema do dispositivo, e atribuindo a um objeto. Após feito, basta apenas usar o comando family= para o objeto criado, dentro do comando text=element_text().

16.3.2 Elemento element_line()

Esse elemento de linhas do gráfico, como as linhas dos eixos e as grades. É possível alterar tamanho, forma e cor. Os elementos devem sempre ser seguidos de element_line(). Dentre os diversos elementos de texto, estão:

  • axis.line=: personaliza as linhas dos eixos X e Y;
exemplo+
  theme( axis.line  = element_line(color="red"))

  • axis.line.x=: personaliza apenas a linha do eixo X;
exemplo+
  theme( axis.line.x  = element_line(color="red"))

  • axis.line.y=: personaliza apenas a linha do eixo Y;
exemplo+
  theme( axis.line.y  = element_line(color="red"))

  • axis.ticks=: personaliza as marcas dos valores dos eixos;
exemplo+
  theme( axis.ticks  = element_line(color="red"))

  • axis.ticks.x=: personaliza as marcas dos valores do eixo X;
exemplo+
  theme( axis.ticks.x  = element_line(color="red"))

  • axis.ticks.y=: personaliza as marcas dos valores do eixo Y;
exemplo+
  theme( axis.ticks.y  = element_line(color="red"))

  • panel.grid=: personaliza as linhas de grade;
exemplo+
  theme( panel.grid  = element_line(color="red"))

  • panel.grid,major=: personaliza as linhas de grade superiores;
exemplo+
  theme( panel.grid.major  = element_line(color="red"))

  • panel.grid,major.x=: personaliza as linhas de grade superiores do eixo X;
exemplo+
  theme( panel.grid.major.x  = element_line(color="red"))

  • panel.grid.major.y=: personaliza as linhas de grade superiores do eixo Y;
exemplo+
  theme( panel.grid.major.y  = element_line(color="red"))

  • panel.grid.minor=: personaliza as linhas de grade inferiores;
exemplo+
  theme( panel.grid.minor  = element_line(color="red"))

  • panel.grid.minor.x=: personaliza as linhas de grade inferiores do eixo X;
exemplo+
  theme( panel.grid.minor.x  = element_line(color="red"))

  • panel.grid.minor.y=: personaliza as linhas de grade inferiores do eixo Y;
exemplo+
  theme( panel.grid.minor.y  = element_line(color="red"))

16.3.3 Elemento element_rect()

Esse elemento do retângulo do controno do gráfico. É possível alterar tamanho, forma e cor. Os elementos devem sempre ser seguidos de element_rect(). Dentre os diversos elementos de texto, estão:

  • legend.background=: personaliza o retângulo que forma-se em volta da legenda. Usando a função fill=, escolhendo uma cor, é possível colorir o preenchimento do retângulo;
exemplo+
  theme( legend.background  = element_rect(color="red",fill="green"))

  • legend.key=: personaliza o retângulo que forma-se em volta de cada elemento da legenda. Nesse caso, foi usado um outro gráfico, usando a base de dadUsando a função fill=, escolhendo uma cor, é possível colorir o preenchimento do retângulo;
SW<-starwars
SW
## # A tibble: 87 × 14
##    name        height  mass hair_…¹ skin_…² eye_c…³ birth…⁴ sex   gender homew…⁵
##    <chr>        <int> <dbl> <chr>   <chr>   <chr>     <dbl> <chr> <chr>  <chr>  
##  1 Luke Skywa…    172    77 blond   fair    blue       19   male  mascu… Tatooi…
##  2 C-3PO          167    75 <NA>    gold    yellow    112   none  mascu… Tatooi…
##  3 R2-D2           96    32 <NA>    white,… red        33   none  mascu… Naboo  
##  4 Darth Vader    202   136 none    white   yellow     41.9 male  mascu… Tatooi…
##  5 Leia Organa    150    49 brown   light   brown      19   fema… femin… Aldera…
##  6 Owen Lars      178   120 brown,… light   blue       52   male  mascu… Tatooi…
##  7 Beru White…    165    75 brown   light   blue       47   fema… femin… Tatooi…
##  8 R5-D4           97    32 <NA>    white,… red        NA   none  mascu… Tatooi…
##  9 Biggs Dark…    183    84 black   light   brown      24   male  mascu… Tatooi…
## 10 Obi-Wan Ke…    182    77 auburn… fair    blue-g…    57   male  mascu… Stewjon
## # … with 77 more rows, 4 more variables: species <chr>, films <list>,
## #   vehicles <list>, starships <list>, and abbreviated variable names
## #   ¹​hair_color, ²​skin_color, ³​eye_color, ⁴​birth_year, ⁵​homeworld
exemplo3<-SW%>%
  ggplot(aes(height,mass,color=eye_color))+
  geom_line(size=1)+
  labs(title="Relação altura em relação à massa dos personagens da franquia de Star Wars",
       x="Altura",
       y="Massa",
       color="cor do olho")

exemplo3+
  theme( legend.key  = element_rect(color="red",fill="green"))
## Warning: Removed 12 rows containing missing values (`geom_line()`).

  • legend.box.background=: personaliza o semi-retângulo que forma-se em volta de cada elemento da legenda;
exemplo+
  theme( legend.box.background  = element_rect(color="red"))

  • panel.background=: personaliza o retângulo que forma-se em volta do gráfico. Com a função fill=, é possível colorir o interior do gráfico;
exemplo+
  theme( panel.background  = element_rect(color="red",fill="green"))

  • plot.background=: personaliza o retângulo que forma-se em volta dde todo o plot. Com a função fill=, é possível colorir o interior do gráfico;
exemplo+
  theme( plot.background  = element_rect(color="red",fill="green",size=1.5))

16.3.4 Elemento element_blank()

Esse elemento elimina os demais elementos do gráfico, apagando-os. Os elementos, como text=, line= ou react devem sempre ser seguidos de element_blank(). Dentre os diversos elementos de texto, estão:

  • text=: apaga todos os elementos de texto do gráfico;
exemplo+
  theme( title  = element_blank())

  • elementos específicos do texto: é possível também apagar um elemento de texto em específico, como o título da legenda, o título do eixo X ou os valores dos eixos, com os comandos para estes mesmos elementos específicos, ensinados antiormente
exemplo+
  theme( legend.title  = element_blank())

exemplo+
  theme( axis.title.x = element_blank())

exemplo+
  theme( axis.text = element_blank())

  • line=: apaga todos os elementos de linha gráfico;
exemplo+
  theme( line  = element_blank())

  • elementos específicos de linha: é possível também apagar um elemento de texto em específico, como as linhas dos valores do eixo X, as linhas dos valores do eixo Y ou as linha dos valores superiores dos eixos, com os comandos para estes mesmos elementos específicos, ensinados antiormente
exemplo+
  theme( axis.ticks.x  = element_blank())

exemplo+
  theme( axis.ticks.y = element_blank())

exemplo+
  theme(  panel.grid.major = element_blank())

  • react=: apaga todos os retângulos;
exemplo3+
  theme( legend.key  = element_blank())
## Warning: Removed 12 rows containing missing values (`geom_line()`).

16.4 Criando um tema

Em muitas situações, é preciso reutilizar aquele mesmo tema, com aquele mesmo estilo para gráficos com finalidades semelhantes. Para evitar ter que escrever tudo de novo, é possível atribuir a configuração de uma tema a um objeto. Porém, antes de criar um novo e tema e atribuir à qualquer gráfico, certifique-se que o gráfico é compatível com as configurações do tema criado, a fim de evitar problemas de plotar.

16.4.1 Criando um objeto com a nova configuração do tema

theme.new<-theme(  text = element_text(color="black",size=12),axis.text=element_text(color="black"),legend.title = element_text(color="black"),panel.grid=element_line(color="gray"),axis.line=element_line(color="black"),panel.background=element_rect(fill="white"),legend.background = element_rect(fill="white"),plot.background=element_rect(fill="#7494a5"))

Tendo criado agora o tema, é possível configurar o gráfico modelo com este tema.

16.4.2 Transformando o gráfico com o tema criado

exemplo+
  theme.new

Adicionando ao ggplot o objeto theme.line, é possível agora configurar o gráfico com o tema criado.

17 Plotando mais de um gráfico ao mesmo tempo

17.1 Quando usar

Há siruações em que diferentes análises semelhantes são feitas. Exemplo é testando o crescimento populacional de 4 espécies num mesmo espaço de tempo. Para facilitar a interpretação e análise nestas situações, uma solução útil é pôr os gráficos todos juntos no mesmo campo de visão. Para isso, os gráficos são plotados de uma única vez.

17.2 Packages exigidos

library(tidyverse)
library(cowplot)

Foi carregado o package ggplot2 para criar os gráficos, assim como para carregar as bases de dados que serão utilizadas. Em seguida, foi carregado o package tidyverse, para melhor trabalahr com os dados que serão utilizados. Por último, foi carregado o package cowplot, para poder ser plotado vários gráficos de uma vez.

17.3 Carregando a base de dados

SW<-starwars
SW
## # A tibble: 87 × 14
##    name        height  mass hair_…¹ skin_…² eye_c…³ birth…⁴ sex   gender homew…⁵
##    <chr>        <int> <dbl> <chr>   <chr>   <chr>     <dbl> <chr> <chr>  <chr>  
##  1 Luke Skywa…    172    77 blond   fair    blue       19   male  mascu… Tatooi…
##  2 C-3PO          167    75 <NA>    gold    yellow    112   none  mascu… Tatooi…
##  3 R2-D2           96    32 <NA>    white,… red        33   none  mascu… Naboo  
##  4 Darth Vader    202   136 none    white   yellow     41.9 male  mascu… Tatooi…
##  5 Leia Organa    150    49 brown   light   brown      19   fema… femin… Aldera…
##  6 Owen Lars      178   120 brown,… light   blue       52   male  mascu… Tatooi…
##  7 Beru White…    165    75 brown   light   blue       47   fema… femin… Tatooi…
##  8 R5-D4           97    32 <NA>    white,… red        NA   none  mascu… Tatooi…
##  9 Biggs Dark…    183    84 black   light   brown      24   male  mascu… Tatooi…
## 10 Obi-Wan Ke…    182    77 auburn… fair    blue-g…    57   male  mascu… Stewjon
## # … with 77 more rows, 4 more variables: species <chr>, films <list>,
## #   vehicles <list>, starships <list>, and abbreviated variable names
## #   ¹​hair_color, ²​skin_color, ³​eye_color, ⁴​birth_year, ⁵​homeworld

Para a criação dos dados, foi carregada abase dados starwars, do package ggplot2, que possui dados de alguns personagens da franquia Star Wars, e então atribuído ao objeto SW.

17.4 Criando os gráficos

G1<-SW %>% 
  ggplot(aes(sex,height,fill=sex))+
  geom_boxplot(color="black")+
  labs(title = "altura dos personagens em função do sexo",
       x="sexo",
       y="altura",
       fill="sexo")+
  tema

G1
## Warning: Removed 6 rows containing non-finite values (`stat_boxplot()`).

G2<-SW %>% 
  ggplot(aes(gender,height,fill=gender))+
  geom_boxplot(color="black")+
  labs(title = "altura dos personagens em função do gênero",
       x="gênero",
       y="altura",
       fill="gênero")+
  tema

G2
## Warning: Removed 6 rows containing non-finite values (`stat_boxplot()`).

G3<-SW %>% 
  ggplot(aes(hair_color,height,fill=hair_color))+
  geom_boxplot(color="black")+
  labs(title = "altura dos personagens em função da cor de cabelo",
       x="cor de cabelo",
       y="altura",
       fill="cor do cabelo")+
  tema

G3
## Warning: Removed 6 rows containing non-finite values (`stat_boxplot()`).

Foram criados três gráficos, a aprtir da base de dado SW, e atribuídos aos objetos G1,G2 e G3. Para poder plotar todos os gráficos juntos de uma vez, é preciso atribuir os gráficos à objetos.

17.5 Plotando os gráficos juntos de uma vez

plot_grid(G1,G2,G3)
## Warning: Removed 6 rows containing non-finite values (`stat_boxplot()`).
## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family
## 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family
## 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family
## 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family
## 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family
## 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family
## 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family
## 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family
## 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family
## 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family
## 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family
## 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family
## 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family
## 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family
## 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family
## 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family
## 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family
## 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family
## 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family
## 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family
## 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family
## 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family
## 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family
## 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family
## 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family
## 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family
## 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family
## 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family
## 'TimesNewRoman' not found in PostScript font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database
## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family
## 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family
## 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family
## 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family
## 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family
## 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family
## 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family
## 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family
## 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family
## 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family
## 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family
## 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family
## 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family
## 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family
## 'TimesNewRoman' not found in PostScript font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database
## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family
## 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family
## 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family
## 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family
## 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family
## 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family
## 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family
## 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family
## 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family
## 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family
## 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family
## 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family
## 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family
## 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family
## 'TimesNewRoman' not found in PostScript font database
## Warning: Removed 6 rows containing non-finite values (`stat_boxplot()`).
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database
## Warning: Removed 6 rows containing non-finite values (`stat_boxplot()`).
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

Através da função plot_grid() é possível plotar os 3 gráficos de uma vez, inserior os objetos dos gráficos, na ordem que deseja aparecerem.

17.6 Configurando

17.6.1 Nº de colunas

plot_grid(G1,G2,G3,ncol=1)
## Warning: Removed 6 rows containing non-finite values (`stat_boxplot()`).
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database
## Warning: Removed 6 rows containing non-finite values (`stat_boxplot()`).
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database
## Warning: Removed 6 rows containing non-finite values (`stat_boxplot()`).
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

Através do elemento ncol= é possível escolher o Nº de colunas. Se ncol=1, todos os gráficos ficarão em linhas diferentes, em que a quantidade de linhas será a quantidade de gráficos.

17.6.2 Nº de linhas

plot_grid(G1,G2,G3,nrow=1)
## Warning: Removed 6 rows containing non-finite values (`stat_boxplot()`).
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database
## Warning: Removed 6 rows containing non-finite values (`stat_boxplot()`).
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database
## Warning: Removed 6 rows containing non-finite values (`stat_boxplot()`).
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family 'TimesNewRoman' not found in PostScript font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
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## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
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## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
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## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
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## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
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## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
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## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
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## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
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## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
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## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
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## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
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## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
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## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
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## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
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## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
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## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
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## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
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## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
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## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
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## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
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## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
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## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
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## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
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## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
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## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
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## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
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## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
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## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
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## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
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## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
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## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
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## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
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## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
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## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
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## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
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## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
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## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
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## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
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## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
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## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
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Através do elemento nrows= é possível escolher o Nº de linhas. Se nrows=1, todos os gráficos ficarão em colunas diferentes, em que a quantidade de colunas será a quantidade de gráficos.

17.7 Utilizando facet_wrap()

SW %>% 
  mutate(`É humano?`=case_when(species=="Human"~"Humano",
                               species!="Human"~"Não-Humano",
                               species==NA~"Sem Identificação")) %>%
  ggplot(aes(mass,height,fill=`É humano?`))+
  geom_point(shape=21,color="black",size=4)+
  labs(x="Massa",
       y="Altura")+
  facet_wrap(~`É humano?`)+
  tema
## Warning: Removed 28 rows containing missing values (`geom_point()`).

A função facet_wrap() é do package ggplot2, e cria um plot dividido baseado em algum critério, alguma variável, da base de dados que está sendo utilizada na construção do ggplot. A grande vantagem do uso do facet_wrap() em relação ao cowplot() é que o facet_wrap() não depende que sejam criados objetos contendo os ggplots, mas sim que o critério de divisão esteja em alguma variável da base de dados. A única possível desvantagem do uso do facet_wrap() é que caso não exista a variável na base de dados, não será possível criar o gráfico particionado. Contudo, isso pode ser contornado com uma simples manipulação de dados: como existe uma qantidade muito grande de espécies na bse de dados SW, foi utilizada a função mutate(), para criar uma nova variável, em conjunto com a função case_when(), para criar uma seleção condicional, criando uma nova variável É Humano?, onde os personagens da espécie humana estariam como Humano e as outras espécies como Não-Humano ou NA.

17.7.1 Escolhendo o Nº de linhas e de colunas

SW %>% 
  mutate(`É humano?`=case_when(species=="Human"~"Humano",
                               species!="Human"~"Não-Humano",
                               species==NA~"Sem Identificação")) %>%
  ggplot(aes(mass,height,fill=`É humano?`))+
  geom_point(shape=21,color="black",size=4)+
  labs(x="Massa",
       y="Altura")+
  facet_wrap(~`É humano?`,ncol=2)+
  tema
## Warning: Removed 28 rows containing missing values (`geom_point()`).

SW %>% 
  mutate(`É humano?`=case_when(species=="Human"~"Humano",
                               species!="Human"~"Não-Humano",
                               species==NA~"Sem Identificação")) %>%
  ggplot(aes(mass,height,fill=`É humano?`))+
  geom_point(shape=21,color="black",size=4)+
  labs(x="Massa",
       y="Altura")+
  facet_wrap(~`É humano?`,nrow=3)+
  tema
## Warning: Removed 28 rows containing missing values (`geom_point()`).

Assim como no cowplot(), também é possível selecionar o nº de linhas e colunas desejadas no plot.

17.7.2 Alterando as escalas

SW %>% 
  mutate(`É humano?`=case_when(species=="Human"~"Humano",
                               species!="Human"~"Não-Humano",
                               species==NA~"Sem Identificação")) %>%
  ggplot(aes(mass,height,fill=`É humano?`))+
  geom_point(shape=21,color="black",size=4)+
  labs(x="Massa",
       y="Altura")+
  facet_wrap(~`É humano?`,scale="free")+
  tema
## Warning: Removed 28 rows containing missing values (`geom_point()`).

SW %>% 
  mutate(`É humano?`=case_when(species=="Human"~"Humano",
                               species!="Human"~"Não-Humano",
                               species==NA~"Sem Identificação")) %>%
  ggplot(aes(mass,height,fill=`É humano?`))+
  geom_point(shape=21,color="black",size=4)+
  labs(x="Massa",
       y="Altura")+
  facet_wrap(~`É humano?`,scale="free_x")+
  tema
## Warning: Removed 28 rows containing missing values (`geom_point()`).

SW %>% 
  mutate(`É humano?`=case_when(species=="Human"~"Humano",
                               species!="Human"~"Não-Humano",
                               species==NA~"Sem Identificação")) %>%
  ggplot(aes(mass,height,fill=`É humano?`))+
  geom_point(shape=21,color="black",size=4)+
  labs(x="Massa",
       y="Altura")+
  facet_wrap(~`É humano?`,scale="free_y")+
  tema
## Warning: Removed 28 rows containing missing values (`geom_point()`).

O padrão do facet_wrap() é de deixar uma escala padronizada para os dois eixos. Contudo, é possível observar nos ultimos plots que há espaços do gráfico sem a ocorrência de pontos. Isso acontece porque a padronização não leva em conta as diferenças nas escalas das distribuiçõe para os diferentes elementos da variável que divide os plots. É possível controlar essa escala com:

  • scale="free": para que as escalas de ambos os eixos estejam ajustadas para cada distribuição em particular;

  • scale="free_x": para que a escala dos eixos X estejam ajustadas para cada distribuição em particular;

  • scale="free_y": para que a escala dos eixos Y estejam ajustadas para cada distribuição em particular;

17.7.3 Usando mais de uma variável por vez

SW %>% 
  mutate(`É humano?`=case_when(species=="Human"~"Humano",
                               species!="Human"~"Não-Humano",
                               species==NA~"Sem Identificação")) %>%
  ggplot(aes(mass,height,fill=`É humano?`))+
  geom_point(shape=21,color="black",size=4)+
  labs(x="Massa",
       y="Altura")+
  facet_wrap(~`É humano?`+gender)+
  tema
## Warning: Removed 28 rows containing missing values (`geom_point()`).

Também é possível combinar variáveis, fazendo assim análises combinatória com diferentes variáveis.

17.7.4 Alterando a cor da caixa do facet_wrap()

tema_facet<-theme(text=element_text(family="TimesNewRoman"),
            title=element_text(color="black",size=15),
            axis.text = element_text(color="black",size=10),
            axis.title = element_text(color="black",size=10),
            panel.grid=element_line(color="grey75",linetype = "dashed",size=.5),
            axis.line=element_blank(),
            plot.background=element_rect(fill="white",color="white"),
            panel.background=element_rect(fill="white"),
            panel.border = element_rect(colour = "black", fill = NA,size=0.59),
            legend.key= element_rect(color="white",fill="white"),
            strip.background = element_rect(colour="black",fill="#4B8899"))

SW %>% 
  mutate(`É humano?`=case_when(species=="Human"~"Humano",
                               species!="Human"~"Não-Humano",
                               species==NA~"Sem Identificação")) %>%
  ggplot(aes(mass,height,fill=`É humano?`))+
  geom_point(shape=21,color="black",size=4)+
  labs(x="Massa",
       y="Altura")+
  facet_wrap(~`É humano?`)+
  tema_facet
## Warning: Removed 28 rows containing missing values (`geom_point()`).

Outra coisa que é possível de ser feita com o facet_wrap() é mudando a cor de prrenchimento e contorno das caixas. Para isso, é utilizado o comando strip.background=element_rect() na função theme().

17.8 Utilizando facet_grid()

SW %>% 
  mutate(`É humano?`=case_when(species=="Human"~"Humano",
                               species!="Human"~"Não-Humano",
                               species==NA~"Sem Identificação")) %>%
  ggplot(aes(mass,height,fill=`É humano?`))+
  geom_point(shape=21,color="black",size=4)+
  labs(x="Massa",
       y="Altura")+
  facet_grid(gender~`É humano?`)+
  tema
## Warning: Removed 28 rows containing missing values (`geom_point()`).

Enquanto que o facet_wrap() dividia baseado apenas em colunas, usando uma única variável ou um conjunto de variáveis, o facet_grid() também cria uma vombinação, mas baseado em formato de grade. Todas as propriedades anteriormente feitas no facet_wrap() são aplicáveis ao facet_grid().

18 Adicionando imagens ao ggplot

18.1 Quando utilizar

Em algumas situações, para melhor exemplificar aspectos de uma análise, ou apenas deixá-la mais didática, é muito utilizado a adição de imagens ao gráfico. Adição de imagens pode ser muito útil, como quando se deseja representar uma espécie, ou até apresentar as bandeiras de estados ou países.

18.2 Pacakges exigidos

library(tidyverse)
library(ggimage)

Foi carregado o package ggplot2 para criar os gráficos. Em seguida, foi carregado o package tidyverse, para melhor trabalahr com os dados que serão utilizados. Por último, foi carregado o package ggimage, para poder adicionar imagens ao gráfico ggplot

18.3 Criando os dados

n.spe1<-c(18,15,14,12,9,7,5)
n.spe1
## [1] 18 15 14 12  9  7  5
n.spe2<-c(18,16,13,11,10,4,3)
n.spe2
## [1] 18 16 13 11 10  4  3
red.hab1<-c(0.0,0.05,0.1,0.15,0.2,0.25,0.3)
red.hab1
## [1] 0.00 0.05 0.10 0.15 0.20 0.25 0.30
red.hab2<-c(0.0,0.05,0.1,0.15,0.2,0.25,0.3)
red.hab2
## [1] 0.00 0.05 0.10 0.15 0.20 0.25 0.30

Primeiro, foram criados os objetos n.spe1 e n.spe2, que descrevem o nº de indivíduos de duas espécies de serpentes do gênero Crotalus sp.. Após, foram criados os objetos red.hab1 e red.hab2, que descrevem as porcentagens de redução de habitat em que as espécies foram coletadas.

crotalus1<-data.frame(n.spe1,red.hab1)
crotalus1
##   n.spe1 red.hab1
## 1     18     0.00
## 2     15     0.05
## 3     14     0.10
## 4     12     0.15
## 5      9     0.20
## 6      7     0.25
## 7      5     0.30
crotalus2<-data.frame(n.spe2,red.hab2)
crotalus2
##   n.spe2 red.hab2
## 1     18     0.00
## 2     16     0.05
## 3     13     0.10
## 4     11     0.15
## 5     10     0.20
## 6      4     0.25
## 7      3     0.30

Após terem sido criadas as variáveis referentes à cada espécie, foram criados os data frames para a base de dados de cada espécie, através da função data.frame(), e atribuídos aos objetos crotalus1 e crotalus2.

g1<-crotalus1 %>% 
  ggplot()+
  geom_line(aes(red.hab1,n.spe1),color="black",size=1)+
  geom_point(aes(red.hab1,n.spe1),color="black",fill="yellow",shape=21,size=4)+
  scale_x_continuous(breaks=seq(0.0,0.30,0.05))+
  scale_y_continuous(breaks=seq(0,18,2))+
  labs(title=" ",
       x="% da redução de habitat",
       y="nº de indivíduos coletados")+
  tema+
  geom_image(aes(x=0.20,y=17,image = "crotalus1.png"),size=0.4)

g1

g2<-crotalus2 %>% 
  ggplot()+
  geom_line(aes(red.hab2,n.spe2),color="black",size=1)+
  geom_point(aes(red.hab2,n.spe2),color="black",fill="yellow",shape=21,size=4)+
  scale_x_continuous(breaks=seq(0.0,0.30,0.05))+
  scale_y_continuous(breaks=seq(0,18,2))+
  labs(title=" ",
       x="% da redução de habitat",
       y="nº de indivíduos coletados")+
  tema+
  geom_image(aes(x=0.20,y=17,image = "crotalus2.png"),size=0.4)

g2

Após definido o diretório, são feitos os gráficos. Nesse caso, a especificação dos eixos, no comando aes(), não é feita no elemento ggplot(), mas sim no elemento geom_line() e no geom_point(), para que o comando consiga adicionar a imagem. Ou seja: a especificação dos eixos deve ocorrer nos mesmos locais que se define o tipo de gráfico a ser feito, na ondem de sobreposição em que se deseja fazer (nesse caso, pontos por cima das linhas. Para asdicionar a imagem, é usada a função geom_image(), do package ggimage, onde dentro do comando aes() da função é especificado:

  • x: posição da imagem pelo eixo X;

  • y: posição da imagem pelo eixo Y;

  • image: imagem a ser carregada, com “nome o arquivo.formato do arquivo”.

Fora do comando aes(), é especificado o tamanho da imagem, pelo argumento size=, onde é aconselhável que o tamanho da imagem esteja entre 0 e 1.

18.4 plotando os dois gráficos de uma vez

Nestas situações, é muito útil ter os dois gráficos no campo de visão para serem comparados, como feito no tópico anterior do guia. Para isso, usa-se a função plot_grid()

library(cowplot)
plot_grid(g1,g2)

Carregando o package cowplot, e usando a sua função plot_grid(), é possível plot de uma única vez os dois plots.

19 Cluster nos gráficos

19.1 Quando utilizar

Em gráficos de dispersão, por exemplo, é comum usar oo comando aes(color=variável), ou alternativamente aes(fill=variável), para diferenciar os pontos em relação à variáveis qualitativas no gráfico, como espécies, locais e comunidades diferentes, e vizualizar de formas melhores como aqueles diferenntes dados estão dispersos nos dados. Uma forma de facilitar essa vizualização é delimitar círculos ou elípses que representem os diferentes tipos de dados, criando clusters.

19.2 Packages exigidos

library(ggforce)
library(tidyverse)
library(palmerpenguins)

Foi carregado o package ggforce, que é utilizado para criar estes clusters. Em seguida, foi carregado o package tidyverse, que carrega tanto o package ggplot2 quanto outros utilizados para trabalhar com os dados. Por último, foi carregado o package palmerpenguins, para utilizar dados morfométricos sobre pinguins.

19.3 Carregando os dados

pinguins<-penguins %>% 
  drop_na()
pinguins
## # A tibble: 333 × 8
##    species island    bill_length_mm bill_depth_mm flipper_…¹ body_…² sex    year
##    <fct>   <fct>              <dbl>         <dbl>      <int>   <int> <fct> <int>
##  1 Adelie  Torgersen           39.1          18.7        181    3750 male   2007
##  2 Adelie  Torgersen           39.5          17.4        186    3800 fema…  2007
##  3 Adelie  Torgersen           40.3          18          195    3250 fema…  2007
##  4 Adelie  Torgersen           36.7          19.3        193    3450 fema…  2007
##  5 Adelie  Torgersen           39.3          20.6        190    3650 male   2007
##  6 Adelie  Torgersen           38.9          17.8        181    3625 fema…  2007
##  7 Adelie  Torgersen           39.2          19.6        195    4675 male   2007
##  8 Adelie  Torgersen           41.1          17.6        182    3200 fema…  2007
##  9 Adelie  Torgersen           38.6          21.2        191    3800 male   2007
## 10 Adelie  Torgersen           34.6          21.1        198    4400 male   2007
## # … with 323 more rows, and abbreviated variable names ¹​flipper_length_mm,
## #   ²​body_mass_g

Usando a própia base de dados peguins, do package palmerpeguins, atribuimos ela ao objeto pinguins. Explorando esta base de dados, podemos ver as seguintes variáveis:

  • species: as três espécies de pinguins estudadas (Adélie, Chinstrap e Gentoo);

  • island: as três ilhas estudadas (Biscoe, Dream ou Torgersen);

  • bill_length_mm: o número do comprimento do bico em mm;

  • bill_depth_mm: o número da profundidade do bico em mm;

  • flipper_length_mm: o número inteiro do comprimento da asa/nadadeira em mm;

  • body_mass_g: massa corporal em g;

  • sex: sexo dos pinguins;

  • year: os anos do estudo (2007, 2008 e 2009).

19.4 Criango o plot

pinguins %>% 
  ggplot(aes(body_mass_g,bill_length_mm))+
  geom_point(size=4)+
  labs(title="Relação entre o tamanho do bico e a massa corporal",
       subtitle="Espécies mais pesadas possuem maiores bicos?",
       x="massa corporal (g)",
       y="comprimento do bico (mm)")+
  scale_x_continuous(breaks = seq(2500,7000,500))+
  tema

Conseguimos ter uma noção de inferência básica de que espécimes mais pesados possuem maiores comprimento de bico. Mas como isso reflete-se nas espécies?

19.5 Discrimando os pontos por cores

pinguins %>% 
  ggplot(aes(body_mass_g,bill_length_mm,fill=species))+
  geom_point(size=4,shape=21,color="black",alpha=0.65)+
  labs(title="Relação entre o tamanho do bico e a massa corporal",
       subtitle="O padrão observado anteriormente tem influência da espécie?",
       x="massa corporal (g)",
       y="comprimento do bico (mm)",
       fill="Espécies")+
  scale_x_continuous(breaks = seq(2500,7000,500))+
  scale_fill_manual(values=c("#FFAA52","#52FF73","#8952FF"))+
  tema

Dsicriminando os pontos em relação às espécies, é possível observar que existe sim uma inflência das espécies em relação aos dados observados. Agora, vamos delimitar os grupos utilizando clusters.

19.6 Criando os clusters

19.6.1 Círculos

pinguins %>% 
  ggplot(aes(body_mass_g,bill_length_mm,fill=species))+
  geom_point(size=4,shape=21,color="black",alpha=0.65)+
  labs(title="Relação entre o tamanho do bico e a massa corporal",
       subtitle="O padrão observado anteriormente tem influência da espécie?",
       x="massa corporal (g)",
       y="comprimento do bico (mm)",
       fill="Espécies",
       color="Espécies")+
  scale_x_continuous(breaks = seq(2500,7000,500))+
  geom_mark_circle(aes(color=species))+
  scale_fill_manual(values=c("#FFAA52","#52FF73","#8952FF"))+
  tema
## Warning: Using the `size` aesthetic in this geom was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` in the `default_aes` field and elsewhere instead.

Com a função geom_mark_circle(), é possível criar círculos que delimitam os dados discriminados no comando aes(). Contudo, os cícrlos criam área que cobrem quase toda a área dos dados, e não dão muita noção de dispersão dos dados. Vamos tentar de outra forma

19.6.2 Elípses

pinguins %>% 
  ggplot(aes(body_mass_g,bill_length_mm,fill=species))+
  geom_point(size=4,shape=21,color="black",alpha=0.65)+
  labs(title="Relação entre o tamanho do bico e a massa corporal",
       subtitle="O padrão observado anteriormente tem influência da espécie?",
       x="massa corporal (g)",
       y="comprimento do bico (mm)",
       fill="Espécies",
       color="Espécies")+
  scale_x_continuous(breaks = seq(2500,7000,500))+
  geom_mark_ellipse(aes(color=species))+
  scale_fill_manual(values=c("#FFAA52","#52FF73","#8952FF"))+
  tema

Com a função geom_mark_ellipse(), ao contrário de criar um círculo perfeito, este cria uma elípse, baseado na distribuição dos dados, não opucando tanto espaço, e dando melhor noção de distribuição. Aqui podemos observar que os dados tendem a se distribuir mais pela massa do que pelo comprimento do bico.

19.6.3 Quadrados

pinguins %>% 
  ggplot(aes(body_mass_g,bill_length_mm,fill=species))+
  geom_point(size=4,shape=21,color="black",alpha=0.65)+
  labs(title="Relação entre o tamanho do bico e a massa corporal",
       subtitle="O padrão observado anteriormente tem influência da espécie?",
       x="massa corporal (g)",
       y="comprimento do bico (mm)",
       fill="Espécies",
       color="Espécies")+
  scale_x_continuous(breaks = seq(2500,7000,500))+
  geom_mark_rect(aes(color=species))+
  scale_fill_manual(values=c("#FFAA52","#52FF73","#8952FF"))+
  tema

É um funcionamento semelhante ao cluster em círculos, mas com polígonos.

19.6.4 Forma não definida

pinguins %>% 
  ggplot(aes(body_mass_g,bill_length_mm,fill=species))+
  geom_point(size=4,shape=21,color="black",alpha=0.65)+
  labs(title="Relação entre o tamanho do bico e a massa corporal",
       subtitle="O padrão observado anteriormente tem influência da espécie?",
       x="massa corporal (g)",
       y="comprimento do bico (mm)",
       fill="Espécies",
       color="Espécies")+
  scale_x_continuous(breaks = seq(2500,7000,500))+
  geom_mark_hull(aes(color=species))+
  scale_fill_manual(values=c("#FFAA52","#52FF73","#8952FF"))+
  tema

Este é o “menos elegante” de todos. Aqui não é criada uma forma geométrica específica, mas baseada na distribuição dos dados.

19.7 Utilizando polígonos

clusterpolígonos<-pinguins %>% 
  group_by(species) %>% 
  slice(chull(body_mass_g,bill_length_mm))

pinguins %>% 
  ggplot(aes(body_mass_g,bill_length_mm,fill=species,color=species))+
  geom_point(size=4,shape=21,color="black",alpha=0.65)+
  geom_polygon(data=clusterpolígonos,alpha=0.35)+
  labs(title="Relação entre o tamanho do bico e a massa corporal",
       subtitle="O padrão observado anteriormente tem influência da espécie?",
       x="massa corporal (g)",
       y="comprimento do bico (mm)",
       fill="Espécies",
       color="Espécies")+
  scale_x_continuous(breaks = seq(2500,7000,500))+
  scale_fill_manual(values=c("#FFAA52","#52FF73","#8952FF"))+
  tema

Para criar os clúster baseados em polígonos, foi usada a função geom_polygon(), onde antes é necessário calcular a área do polígono: foi usada a função group_by() com a variável species, para diferenciar em função das espécies, em seguida usando a função slice*(), com chul() junto, utilizando o eixo X e o eixo Y utilizado no gráfico, para indicar com base em que produzir os polígonos. Com o novo objeto criado, foram então feitos os polígonos. Nesse caso, o que é feito é criar um mínimo polígono convexo. A vantagem deste em relação aos demais é que, ao usar um mínimo polígono convexo, os clusters ocupam o menor espaço possível, o que é útil para tentar diferenciar os grupos dentro de uma dispersão, já que usar o menor espaço possível também evita confundir áreas de intersseção.

20 Gráfico de Caminhada

20.1 Quando usar

Em algumas situações onde estão sendo trabalhado com dados espaciais de pontos em coordenadas específicas, busca-se entender a trajetória daqueles pontos num espaço geográfico. É uma abordagem muito utilizada ao trabalhar com objetos espaciais, como ruas, rios, trilhas ou o caminho percorrido por algum animal. A forma mais clara de vizualizar estes tipos de dados é através de um caminho, representado por uma linha. Contudo, por mais que a função geom_line() seja usada para criar linhas nos gráficos, esta não é a mais adequada, e sim, a função geom_path().

20.2 Packages exigidos

library(readxl)
library(tidyverse)

Além do package tidyverse, que carregará não apenas o package ggplot2 como também outros packages para trabalhar com os dados, foi carregado o package readxl, para poder carregar nossa base de dados.

20.3 Carregando a base de dados

bdr<-read_xlsx("G:/Meu Drive/R/Base de dados rio.xlsx")
bdr
## # A tibble: 30 × 14
##        X     Y   dfs   ele   slo   dis    pH   har   pho   nit   amm   oxy   bod
##    <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
##  1  85.7  20     0.3   934  48    0.84   7.9    45  0.01  0.2   0     12.2   2.7
##  2  85.0  20.1   2.2   932   3    1      8      40  0.02  0.2   0.1   10.3   1.9
##  3  92.3  23.8  10.2   914   3.7  1.8    8.3    52  0.05  0.22  0.05  10.5   3.5
##  4  91.3  26.4  18.5   854   3.2  2.53   8      72  0.1   0.21  0     11     1.3
##  5  92.0  29.2  21.5   849   2.3  2.64   8.1    84  0.38  0.52  0.2    8     6.2
##  6  96.0  36.3  32.4   846   3.2  2.86   7.9    60  0.2   0.15  0     10.2   5.3
##  7  98.2  38.8  36.8   841   6.6  4      8.1    88  0.07  0.15  0     11.1   2.2
##  8  99.5  46.4  49.1   792   2.5  1.3    8.1    94  0.2   0.41  0.12   7     8.1
##  9 110.   55.9  70.5   752   1.2  4.8    8      90  0.3   0.82  0.12   7.2   5.2
## 10 131.   66.6  99     617   9.9 10      7.7    82  0.06  0.75  0.01  10     4.3
## # … with 20 more rows, and 1 more variable: pontos <dbl>

Será utilizada uma base de dados que contém dados de coordenadas espaciais (X e Y) e dandos ambientais de trechos de um rio.

20.4 Porque não usar geom_line()

bdr %>% 
  ggplot(aes(X,Y))+
  geom_line(size=1)+
  labs(title = "Pontos do rio",
       x="Longitude",
       y="Latitude")+
  tema

Como pode ser observado, não é formado um caminho em si, mas uma linha que cresce e sobe. Isso acontece pois o geom_line() forma uma linha linear: ela vai da esquerda para a direita. Como o objetivo é formar uma linha que se comporte como um caminho, que possa fazer curvas e desvios, o mais adequada é usar a função geom_path().

20.5 Criando o gráfico

bdr %>% 
  ggplot(aes(X,Y,label=pontos))+
  geom_path(size=1)+
  geom_label(size=2.5)+
  labs(title = "Pontos do rio",
       x="Longitude",
       y="Latitude")+
  tema

Como observado acima, agora temos um caminho traçado. O próximo passo agora é customizar. Para isso, valos levantar as seguintes perguntas: como se comporta a elevação e a demanda biológica por oxigênio?

20.6 Plotando a elevação

bdr %>% 
  ggplot(aes(X,Y,color=ele,label=pontos))+
  geom_path(size=1.5)+
  geom_label(size=2.5,color="black")+
  labs(title = "Pontos do rio",
       x="Longitude",
       y="Latitude",
       color="elevação (m)")+
    scale_color_gradientn(colours =c("purple4","royalblue","dodgerblue","deepskyblue","mediumspringgreen","springgreen","green","lawngreen","greenyellow","yellow", "gold","darkorange","chocolate1","orangered","red","darkred"))+
  tema

Como é possível observar, o ponto 1 é o ponto com maior elevação do rio, e segue-se um gradiente até o último ponto.

20.7 Plotando elevação e a demanda biológica por exigênio

bdr %>% 
  ggplot(aes(X,Y,color=ele,label=pontos,fill=bod))+
  geom_path(size=1.5)+
  geom_label(size=2.5,color="black")+
  labs(title = "Pontos do rio",
       x="Longitude",
       y="Latitude",
       fill="BOD",
       color="Elevação (m)")+
  scale_fill_gradientn(colours=c("greenyellow","lawngreen","green","mediumspringgreen","dodgerblue","royalblue","purple4"),
                       breaks=seq(1,17,2))+
  scale_color_gradientn(colours=c("purple4","royalblue","dodgerblue","deepskyblue","mediumspringgreen","springgreen","green","lawngreen","greenyellow","yellow", "gold","darkorange","chocolate1","orangered","red","darkred"))+
  tema

Ao contrário do que foi observado nos dados de elevação, não foi possível observar um gradiente sobre o a demanda biológica por exigênio (BOD) ao longo do rio, onde os pontos 23 e 25 apresentaram altas taxas de BOD em relação às demais.

21 Gráfico de pontos “nervosos”

21.1 Quando usar

Uma desvantagem do uso de boxplots é que o boxplot não apresenta a distribuição dos pontos: os quartis apresenta apenas intervalos específicos. Em algumas situações, até não é aconselhável o uso de boxplots. Contudo, uma alternativa que tem se popularizado com o tempo é o uso de boxplots com pontos que representam dados.

21.2 Packages exigidos

library(tidyverse)

Foi carregado o package tidyverse, que permite não só utilizar outros packages para o tratamento de dados quanto o uso do package ggplot2.

21.3 Carregando os dados

Mpg<-mpg
Mpg
## # A tibble: 234 × 11
##    manufacturer model      displ  year   cyl trans drv     cty   hwy fl    class
##    <chr>        <chr>      <dbl> <int> <int> <chr> <chr> <int> <int> <chr> <chr>
##  1 audi         a4           1.8  1999     4 auto… f        18    29 p     comp…
##  2 audi         a4           1.8  1999     4 manu… f        21    29 p     comp…
##  3 audi         a4           2    2008     4 manu… f        20    31 p     comp…
##  4 audi         a4           2    2008     4 auto… f        21    30 p     comp…
##  5 audi         a4           2.8  1999     6 auto… f        16    26 p     comp…
##  6 audi         a4           2.8  1999     6 manu… f        18    26 p     comp…
##  7 audi         a4           3.1  2008     6 auto… f        18    27 p     comp…
##  8 audi         a4 quattro   1.8  1999     4 manu… 4        18    26 p     comp…
##  9 audi         a4 quattro   1.8  1999     4 auto… 4        16    25 p     comp…
## 10 audi         a4 quattro   2    2008     4 manu… 4        20    28 p     comp…
## # … with 224 more rows

Foi carregada a base de dados mpg, que armazena dados econômicos sobre 38 modelos de carros populares 1999-2008, e atribuído ao objeto Mpg. Essa e outras bases de dados, como a base de dados star wars está no sistema do package ggplot2

21.4 Criando gráfico boxplot+pontos

Mpg %>% 
  ggplot(aes(class,hwy))+
  geom_boxplot(color="black")+
  labs(title = "milhas/galão em relação à classe do carro",
       x="classe",
       y="mihas/galão",
       fill="classe")+
  tema

Para entender melhor como os dados se distribuem, usará agora pontos.

Mpg %>% 
  ggplot(aes(class,hwy,fill=class))+
  geom_point(size=3,color="black",shape=21)+
  geom_boxplot(color="black",fill=NA,size=0.643)+
  labs(title = "milhas/galão em relação à classe do carro",
       x="classe",
       y="mihas/galão",
       fill="classe")+
  scale_fill_manual(values=c("chocolate1","gold","royalblue","firebrick","seagreen1","darkorchid1","limegreen"))+
  tema

Para conseguirmos entender mais informações no gráfico.

Mpg %>% 
  ggplot(aes(class,hwy,fill=displ))+
  geom_point(shape=21,color="black",size=3)+
  geom_boxplot(fill=NA,color="black",size=0.643)+
  labs(title = "milhas/galão em relação à classe do carro",
       x="classe",
       y="mihas/galão",
       fill="cilidradas/motor(L)")+
  scale_fill_gradientn(colours=c("purple4","royalblue","dodgerblue","deepskyblue","mediumspringgreen","springgreen","green","lawngreen","greenyellow","yellow", "gold","darkorange","chocolate1","orangered","red","darkred"),breaks=seq(1.6,7.0,0.9))+
  tema

Dess forma, é mais visível observarr a distibuição dos dados que compõe o boxplot. Nesse exemplo, os pontos se comportam formando uma linha vertical. Alternativamente, é possível utilizar ontos distribuídos não em uma linha reta.

21.5 Criando o gráfico “nervoso”

Mpg %>% 
  ggplot(aes(class,hwy,fill=displ))+
  geom_jitter(shape=21,color="black",size=3)+
  geom_boxplot(fill=NA,color="black",size=0.643)+
  labs(title = "milhas/galão em relação à classe do carro",
       x="classe",
       y="mihas/galão",
       fill="cilidradas/motor(L)")+
  scale_fill_gradientn(colours=c("purple4","royalblue","dodgerblue","deepskyblue","mediumspringgreen","springgreen","green","lawngreen","greenyellow","yellow", "gold","darkorange","chocolate1","orangered","red","darkred"),breaks=seq(1.6,7.0,0.9))+
  tema

Usando o comando geom_jitterr(), ao invés de os pontos estarem distribuídos não como um linha reta, mas sim distribuídos como grupos também na horizontal. Importante ressaltar que a distribuição horizontal segue de forma aleatória, e cada novo plot, por mais que use os mesmos dados, trás uma nova distribuição.

Mpg %>% 
  ggplot(aes(class,hwy,fill=displ))+
  geom_jitter(shape=21,color="black",size=3)+
  geom_boxplot(fill=NA,color="black",size=0.643)+
  labs(title = "milhas/galão em relação à classe do carro",
       x="classe",
       y="mihas/galão",
       fill="cilidradas/motor(L)")+
  scale_fill_gradientn(colours=c("purple4","royalblue","dodgerblue","deepskyblue","mediumspringgreen","springgreen","green","lawngreen","greenyellow","yellow", "gold","darkorange","chocolate1","orangered","red","darkred"),breaks=seq(1.6,7.0,0.9))+
  tema

Como foi possível observar, uma nova distribuição. Uma possível desvantagem desse uso é que, pelos pontos também possuírem uma distribuição horizontal, é possível haja problemas de interpretações quanto às distribuições horizontais.

22 Gráfico Violino

22.1 Quando usar

É muito comum ao usar boxplots perder um pouco da noção sobre o quanto de dados cada intervalo possui. Os boxplots são úteis para sintetizar a distribuição dos dados de uma variável, mas não permite informar em que ponto daquela variável houve maior cinjunto de dados. Esse tipo de informação é útil quando deseja-se entender em que ponto uma variável apresentou mais observações.

22.2 Packages exigidos

library(tidyverse)

Foi carregado o package tidyverse, que permite não só utilizar outros packages para o tratamento de dados quanto o uso do package ggplot2.

22.3 Criando um gráfico como exemplo

Iris<-iris

Iris
##     Sepal.Length Sepal.Width Petal.Length Petal.Width    Species
## 1            5.1         3.5          1.4         0.2     setosa
## 2            4.9         3.0          1.4         0.2     setosa
## 3            4.7         3.2          1.3         0.2     setosa
## 4            4.6         3.1          1.5         0.2     setosa
## 5            5.0         3.6          1.4         0.2     setosa
## 6            5.4         3.9          1.7         0.4     setosa
## 7            4.6         3.4          1.4         0.3     setosa
## 8            5.0         3.4          1.5         0.2     setosa
## 9            4.4         2.9          1.4         0.2     setosa
## 10           4.9         3.1          1.5         0.1     setosa
## 11           5.4         3.7          1.5         0.2     setosa
## 12           4.8         3.4          1.6         0.2     setosa
## 13           4.8         3.0          1.4         0.1     setosa
## 14           4.3         3.0          1.1         0.1     setosa
## 15           5.8         4.0          1.2         0.2     setosa
## 16           5.7         4.4          1.5         0.4     setosa
## 17           5.4         3.9          1.3         0.4     setosa
## 18           5.1         3.5          1.4         0.3     setosa
## 19           5.7         3.8          1.7         0.3     setosa
## 20           5.1         3.8          1.5         0.3     setosa
## 21           5.4         3.4          1.7         0.2     setosa
## 22           5.1         3.7          1.5         0.4     setosa
## 23           4.6         3.6          1.0         0.2     setosa
## 24           5.1         3.3          1.7         0.5     setosa
## 25           4.8         3.4          1.9         0.2     setosa
## 26           5.0         3.0          1.6         0.2     setosa
## 27           5.0         3.4          1.6         0.4     setosa
## 28           5.2         3.5          1.5         0.2     setosa
## 29           5.2         3.4          1.4         0.2     setosa
## 30           4.7         3.2          1.6         0.2     setosa
## 31           4.8         3.1          1.6         0.2     setosa
## 32           5.4         3.4          1.5         0.4     setosa
## 33           5.2         4.1          1.5         0.1     setosa
## 34           5.5         4.2          1.4         0.2     setosa
## 35           4.9         3.1          1.5         0.2     setosa
## 36           5.0         3.2          1.2         0.2     setosa
## 37           5.5         3.5          1.3         0.2     setosa
## 38           4.9         3.6          1.4         0.1     setosa
## 39           4.4         3.0          1.3         0.2     setosa
## 40           5.1         3.4          1.5         0.2     setosa
## 41           5.0         3.5          1.3         0.3     setosa
## 42           4.5         2.3          1.3         0.3     setosa
## 43           4.4         3.2          1.3         0.2     setosa
## 44           5.0         3.5          1.6         0.6     setosa
## 45           5.1         3.8          1.9         0.4     setosa
## 46           4.8         3.0          1.4         0.3     setosa
## 47           5.1         3.8          1.6         0.2     setosa
## 48           4.6         3.2          1.4         0.2     setosa
## 49           5.3         3.7          1.5         0.2     setosa
## 50           5.0         3.3          1.4         0.2     setosa
## 51           7.0         3.2          4.7         1.4 versicolor
## 52           6.4         3.2          4.5         1.5 versicolor
## 53           6.9         3.1          4.9         1.5 versicolor
## 54           5.5         2.3          4.0         1.3 versicolor
## 55           6.5         2.8          4.6         1.5 versicolor
## 56           5.7         2.8          4.5         1.3 versicolor
## 57           6.3         3.3          4.7         1.6 versicolor
## 58           4.9         2.4          3.3         1.0 versicolor
## 59           6.6         2.9          4.6         1.3 versicolor
## 60           5.2         2.7          3.9         1.4 versicolor
## 61           5.0         2.0          3.5         1.0 versicolor
## 62           5.9         3.0          4.2         1.5 versicolor
## 63           6.0         2.2          4.0         1.0 versicolor
## 64           6.1         2.9          4.7         1.4 versicolor
## 65           5.6         2.9          3.6         1.3 versicolor
## 66           6.7         3.1          4.4         1.4 versicolor
## 67           5.6         3.0          4.5         1.5 versicolor
## 68           5.8         2.7          4.1         1.0 versicolor
## 69           6.2         2.2          4.5         1.5 versicolor
## 70           5.6         2.5          3.9         1.1 versicolor
## 71           5.9         3.2          4.8         1.8 versicolor
## 72           6.1         2.8          4.0         1.3 versicolor
## 73           6.3         2.5          4.9         1.5 versicolor
## 74           6.1         2.8          4.7         1.2 versicolor
## 75           6.4         2.9          4.3         1.3 versicolor
## 76           6.6         3.0          4.4         1.4 versicolor
## 77           6.8         2.8          4.8         1.4 versicolor
## 78           6.7         3.0          5.0         1.7 versicolor
## 79           6.0         2.9          4.5         1.5 versicolor
## 80           5.7         2.6          3.5         1.0 versicolor
## 81           5.5         2.4          3.8         1.1 versicolor
## 82           5.5         2.4          3.7         1.0 versicolor
## 83           5.8         2.7          3.9         1.2 versicolor
## 84           6.0         2.7          5.1         1.6 versicolor
## 85           5.4         3.0          4.5         1.5 versicolor
## 86           6.0         3.4          4.5         1.6 versicolor
## 87           6.7         3.1          4.7         1.5 versicolor
## 88           6.3         2.3          4.4         1.3 versicolor
## 89           5.6         3.0          4.1         1.3 versicolor
## 90           5.5         2.5          4.0         1.3 versicolor
## 91           5.5         2.6          4.4         1.2 versicolor
## 92           6.1         3.0          4.6         1.4 versicolor
## 93           5.8         2.6          4.0         1.2 versicolor
## 94           5.0         2.3          3.3         1.0 versicolor
## 95           5.6         2.7          4.2         1.3 versicolor
## 96           5.7         3.0          4.2         1.2 versicolor
## 97           5.7         2.9          4.2         1.3 versicolor
## 98           6.2         2.9          4.3         1.3 versicolor
## 99           5.1         2.5          3.0         1.1 versicolor
## 100          5.7         2.8          4.1         1.3 versicolor
## 101          6.3         3.3          6.0         2.5  virginica
## 102          5.8         2.7          5.1         1.9  virginica
## 103          7.1         3.0          5.9         2.1  virginica
## 104          6.3         2.9          5.6         1.8  virginica
## 105          6.5         3.0          5.8         2.2  virginica
## 106          7.6         3.0          6.6         2.1  virginica
## 107          4.9         2.5          4.5         1.7  virginica
## 108          7.3         2.9          6.3         1.8  virginica
## 109          6.7         2.5          5.8         1.8  virginica
## 110          7.2         3.6          6.1         2.5  virginica
## 111          6.5         3.2          5.1         2.0  virginica
## 112          6.4         2.7          5.3         1.9  virginica
## 113          6.8         3.0          5.5         2.1  virginica
## 114          5.7         2.5          5.0         2.0  virginica
## 115          5.8         2.8          5.1         2.4  virginica
## 116          6.4         3.2          5.3         2.3  virginica
## 117          6.5         3.0          5.5         1.8  virginica
## 118          7.7         3.8          6.7         2.2  virginica
## 119          7.7         2.6          6.9         2.3  virginica
## 120          6.0         2.2          5.0         1.5  virginica
## 121          6.9         3.2          5.7         2.3  virginica
## 122          5.6         2.8          4.9         2.0  virginica
## 123          7.7         2.8          6.7         2.0  virginica
## 124          6.3         2.7          4.9         1.8  virginica
## 125          6.7         3.3          5.7         2.1  virginica
## 126          7.2         3.2          6.0         1.8  virginica
## 127          6.2         2.8          4.8         1.8  virginica
## 128          6.1         3.0          4.9         1.8  virginica
## 129          6.4         2.8          5.6         2.1  virginica
## 130          7.2         3.0          5.8         1.6  virginica
## 131          7.4         2.8          6.1         1.9  virginica
## 132          7.9         3.8          6.4         2.0  virginica
## 133          6.4         2.8          5.6         2.2  virginica
## 134          6.3         2.8          5.1         1.5  virginica
## 135          6.1         2.6          5.6         1.4  virginica
## 136          7.7         3.0          6.1         2.3  virginica
## 137          6.3         3.4          5.6         2.4  virginica
## 138          6.4         3.1          5.5         1.8  virginica
## 139          6.0         3.0          4.8         1.8  virginica
## 140          6.9         3.1          5.4         2.1  virginica
## 141          6.7         3.1          5.6         2.4  virginica
## 142          6.9         3.1          5.1         2.3  virginica
## 143          5.8         2.7          5.1         1.9  virginica
## 144          6.8         3.2          5.9         2.3  virginica
## 145          6.7         3.3          5.7         2.5  virginica
## 146          6.7         3.0          5.2         2.3  virginica
## 147          6.3         2.5          5.0         1.9  virginica
## 148          6.5         3.0          5.2         2.0  virginica
## 149          6.2         3.4          5.4         2.3  virginica
## 150          5.9         3.0          5.1         1.8  virginica

Foi carregada a bse de dados iris, que descreve o comprimento e a largura das pétalas e das sépalas de 3 espécies de plantas do gênero Iris sp (I. setosa, I. versicolor e I. virginica) (Fisher, R. A. (1936) The use of multiple measurements in taxonomic problems. Annals of Eugenics, 7, Part II, 179–188, The data were collected by Anderson, Edgar (1935). The irises of the Gaspe Peninsula, Bulletin of the American Iris Society, 59, 2–5), e atribuído ao objeto iris. Essa base de dados é nativa do próprio sistema do R, então não é necessário baixá-la por fora nem instalar nenhum package para utiliza-la.

22.4 Gráfico de violino

Iris %>% 
  ggplot(aes(Species,Sepal.Length,fill=Species))+
  geom_violin(color="black",aes(fill=Species))+
  labs(x="espécies",
       y="comprimento da sépala",
       fill="espécies")+
  scale_fill_manual(values=c("#FFAA52","#52FF73","#8952FF"))+
  tema

Como foi possível observar, as 3 espécies possuem um padrão os dados possuem uma gaussiana: os valores do comprimento mais frequente para as 3 espécies foram valores médios. Também foi possível observar que a espécie I. setosa mais valores de comprimento mínimo da sépala em relação ao comprimento máximo observado, equanto que foi observado o oposto na espécie I. virginica.

22.5 Utilizando em conjunto com boxplot

Iris %>% 
  ggplot(aes(Species,Sepal.Length,fill=Species))+
  geom_violin(color="black",aes(fill=Species))+
  geom_boxplot(color="black",alpha=0)+
  labs(x="espécies",
       y="comprimento da sépala",
       fill="espécies")+
  scale_fill_manual(values=c("#FFAA52","#52FF73","#8952FF"))+
  tema

Foi criado um gráfico de boxplot em conjunto com o gráfico de violino, para somar as propriedades dos dois tipos de gráficos.

22.6 Utilizando em conjunto gráfico “nervoso”

Iris %>% 
  ggplot(aes(Species,Sepal.Length,fill=Species))+
  geom_violin(color="black",aes(fill=Species))+
  geom_boxplot(color="black",alpha=0)+
  geom_jitter(color="black",aes(fill=Species),size=4,shape=21,alpha=0.55)+
  labs(x="espécies",
       y="comprimento da sépala",
       fill="espécies")+
  scale_fill_manual(values=c("#FFAA52","#52FF73","#8952FF"))+
  tema

Outra forma de apresentar os dados é utilizando a função geom_jiter(). Como o geom_violin() e o geom_jiter(), na prátrica, apresentam a mesma coisa (distribuição e concentração dos dados ao longo de uma distribuição), é uma escolha interessante unir as duas funções. A vantagem do geom_violin() é que ele resolve um problema do geom_jiter(): enquanto que a distribuição horizontal aleatória dos pontos do geom_jiter() pode comprometer a interpretação, o geom_violin()consegue representar a mesma coisa, mas sem comprometer a interpretação.

23 Mapas

23.1 Quando utilizar

Nos últimos anos, o R ganhou notoriedade no quesito análises de dados espaciais, e isso faz com que o desenvolvimento da visualização destes dados também tenham ganhado notoriedade, principalmente o ggplot.

23.2 Packages exigidos

library(tidyverse)

library(geobr)

library(sf)

library(sp)

library(raster)

library(ggspatial)

Foi carregado o pacote o package tidyverse para o tratamento dos dados e para usar a função ggplot(), o package geobr foi carregado para extrair dados vetoriais do Brasil, os packages sf, sp e raster foram carregados para carregar e trabalhar com dados vetorais e matriciais, e o package ggspatial foi carregado para adicionar elementos aos mapas.

23.3 Carregando dados

23.3.1 Dados vetoriais

Dados vetoriais são polígonos, shapefiles, criados para demarcar uma área, baseado em coordenadas. Normalmente, estão no fromato .shp. A função read_sf(), do package sf, bastando apenas indicar o caminho do dispositivo. Por exemplo:

BR<-read_sf("G:/Meu Drive/QGIS/BR_Pais_2021.shp")

BR %>% plot

Arquivos .shp podem contar mais de uma propriedade dentro desses, como as variáveis de um dataset. Contudo, para facilitar, será utilizada o package geobr, onde a função read_country() carrega o shapefile Do Brasil, a função read_state() os estados e a função read_municipality() os municípios, onde foi filtrado apenas para Recife.

Brasil<-read_country()
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Brasil
## Simple feature collection with 1 feature and 0 fields
## Geometry type: MULTIPOLYGON
## Dimension:     XY
## Bounding box:  xmin: -73.99045 ymin: -33.75208 xmax: -28.83594 ymax: 5.271841
## Geodetic CRS:  SIRGAS 2000
##                             geom
## 1 MULTIPOLYGON (((-48.46837 -...
Estados<-read_state()
## 
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Estados
## Simple feature collection with 27 features and 5 fields
## Geometry type: MULTIPOLYGON
## Dimension:     XY
## Bounding box:  xmin: -66.81025 ymin: -13.6937 xmax: -59.77435 ymax: -7.969294
## Geodetic CRS:  SIRGAS 2000
## First 10 features:
##    code_state abbrev_state name_state code_region name_region
## 1          11           RO   Rondônia           1       Norte
## 2          12           AC       Acre           1       Norte
## 3          13           AM   Amazonas           1       Norte
## 4          14           RR    Roraima           1       Norte
## 5          15           PA       Pará           1       Norte
## 6          16           AP      Amapá           1       Norte
## 7          17           TO  Tocantins           1       Norte
## 8          21           MA   Maranhão           2    Nordeste
## 9          22           PI      Piauí           2    Nordeste
## 10         23           CE      Ceará           2    Nordeste
##                              geom
## 1  MULTIPOLYGON (((-63.32721 -...
## 2  MULTIPOLYGON (((-73.18253 -...
## 3  MULTIPOLYGON (((-67.32609 2...
## 4  MULTIPOLYGON (((-60.20051 5...
## 5  MULTIPOLYGON (((-54.95431 2...
## 6  MULTIPOLYGON (((-51.1797 4....
## 7  MULTIPOLYGON (((-48.35878 -...
## 8  MULTIPOLYGON (((-45.84073 -...
## 9  MULTIPOLYGON (((-41.74605 -...
## 10 MULTIPOLYGON (((-41.16703 -...
estados<-read_sf("G:/Meu Drive/QGIS/BR_UF_2021.shp")

estados
## Simple feature collection with 27 features and 4 fields
## Geometry type: MULTIPOLYGON
## Dimension:     XY
## Bounding box:  xmin: -73.99045 ymin: -33.75118 xmax: -28.84764 ymax: 5.271841
## Geodetic CRS:  SIRGAS 2000
## # A tibble: 27 × 5
##    CD_UF NM_UF     SIGLA NM_REGIAO                                      geometry
##    <chr> <chr>     <chr> <chr>                                <MULTIPOLYGON [°]>
##  1 11    Rondônia  RO    Norte     (((-62.86662 -7.975868, -62.86017 -7.982323,…
##  2 12    Acre      AC    Norte     (((-73.1655 -7.341657, -73.0548 -7.381713, -…
##  3 13    Amazonas  AM    Norte     (((-67.32609 2.029714, -67.31682 2.00125, -6…
##  4 14    Roraima   RR    Norte     (((-60.20051 5.264343, -60.19828 5.260453, -…
##  5 15    Pará      PA    Norte     (((-46.43676 -1.019055, -46.43723 -1.019144,…
##  6 16    Amapá     AP    Norte     (((-50.45011 2.109243, -50.44715 2.109169, -…
##  7 17    Tocantins TO    Norte     (((-48.35878 -5.170085, -48.35617 -5.171852,…
##  8 21    Maranhão  MA    Nordeste  (((-44.66115 -2.980178, -44.66157 -2.980344,…
##  9 22    Piauí     PI    Nordeste  (((-41.78076 -2.760779, -41.77935 -2.764125,…
## 10 23    Ceará     CE    Nordeste  (((-40.49582 -2.785405, -40.49242 -2.787038,…
## # … with 17 more rows
Recife<-read_municipality() %>% 
  filter(name_muni=="Recife")
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Recife
## Simple feature collection with 1 feature and 4 fields
## Geometry type: MULTIPOLYGON
## Dimension:     XY
## Bounding box:  xmin: -35.0167 ymin: -8.155123 xmax: -34.86058 ymax: -7.929206
## Geodetic CRS:  SIRGAS 2000
##   code_muni name_muni code_state abbrev_state                           geom
## 1   2611606    Recife         26           PE MULTIPOLYGON (((-34.96842 -...
Catimbau<-read_sf("G:/Meu Drive/QGIS/Catimbau.shp")

23.3.2 Dados matriciais

Já os dados matriciais, os raters, são dados que mostram diferentes valores em diferentes pontos, através de pixelagem. Eles são utilizados para gradientes em áreas espaciais, como em mapas de altitude, normalmente no formato .tif.

topo_catimbau <- raster("G:/Meu Drive/QGIS/TopoCatimbau.tif")

Assim como com os shapefiles, é possível carregar rasters do dispositivo, através da função raster(), do package raster. Contudo, também é possível baixar rasters usando o R. Um exemplo de bases de dados, é a plataforma online WorldClim. É possível acessá-la através do função worldclim_country(), do package geodata.

São 19 variáveis bioclimáticas do WorldClim, sendo estas:

  • BIO1= Temperatura Média Anual;

  • BIO2 = Intervalo Diurno Médio (Média do mês (temperatura máxima - temperatura mín.));

  • BIO3 = Isotermalidade (BIO2/BIO7) (×100);

  • BIO4 = Sazonalidade da Temperatura (desvio padrão ×100);

  • BIO5 = Temperatura máxima do mês mais quente;

  • BIO6 = Temperatura mínima do mês mais frio;

  • BIO7 = Faixa Anual de Temperatura (BIO5-BIO6);

  • BIO8 = Temperatura média do trimestre mais úmido;

  • BIO9 = Temperatura média do trimestre mais seco;

  • BIO10 = Temperatura Média do Trimestre Mais Quente;

  • BIO11 = Temperatura média do trimestre mais frio;

  • BIO12 = Precipitação Anual;

  • BIO13 = Precipitação do mês mais úmido;

  • BIO14 = Precipitação do Mês Mais Seco;

  • BIO15 = Sazonalidade de Precipitação (Coeficiente de Variação);

  • BIO16 = Precipitação do trimestre mais úmido;

  • BIO17 = Precipitação do trimestre mais seco;

  • BIO18 = Precipitação do Quarto Mais Quente;

  • BIO19 = Precipitação do trimestre mais frio;

Ao escolher a variável bio, no comando var=bio, escolhe-se as variáveis bioclimáticas, mas outras variáveis, como:

  • tmin;

  • tmax;

  • tavg;

  • prec;

  • bio;

  • elev

Existem outros pacotes e outros tipos de rasters que podem ser baixados, como dados de elevação, do pacote elevatr. Contudo, para facilitar esse guia, cujo objetivo é a costrução do ggplot, aqui será focado no que fazer tendo os dados em mãos, e não na aquisição destes dados. Em caso de dúvidas sobre aquisição de dados rasters, como citados acima, recomendamos que o leitor procure materiais sobre os pacotes e as funções citadas.

23.4 Construindo ggplot com polígonos

ggplot()+
  geom_sf(data=Brasil)+
  tema

De forma bem simples, utilizando a função geom_sf(), é possível carregar os shapefiles no ggplot. Assim como em outros ggplots, cor de contorno e preenchimento podem ser definidos.

ggplot()+
  geom_sf(data=Brasil,color="black",fill="yellow",alpha=0.5,linewidth=1)+
  tema

Além do básico já apresentado nesse guia, é posível definir a expessura da linha pelo comando linewidth=.

23.4.1 Mapa com diferenciação dos polígonos

ggplot()+
  geom_sf(data=Estados,aes(fill=name_region),color="black",linewidth=0.75)+
  scale_fill_manual(values = c("orangered",
                               "yellow",
                               "green",
                               "royalblue1",
                               "purple4"
                               ))+
  labs(fill="região")+
  tema

Alguns arquivos .shp possuem variáveis, semelhante aos arquivos dataframe e tibble. Assim como foi feito em outros ggplots, é possível fazer diferenças baseadas nestas variáveis. Nesse caso, foi divido pela variável da região correspondente ao estado.

23.4.2 Adicionando rótulos nos polígonos

ggplot()+
  geom_sf(data=Estados,aes(fill=name_region),color="black",linewidth=0.75)+
  geom_sf_text(data=Estados,
                aes(label=abbrev_state),
                color="black",
               size=3)+
  scale_fill_manual(values = c("orangered",
                               "yellow",
                               "green",
                               "royalblue1",
                               "purple4"
                               ))+
  labs(fill="região")+
  tema
## Warning in st_point_on_surface.sfc(sf::st_zm(x)): st_point_on_surface may not
## give correct results for longitude/latitude data

Quando se está trabalhando com dados vetoriasis, ao invés de se usar geom_label() ou geom_text(), deve-se usar geom_sf_label() ou geom_sf_text(), mas seguindo a mesma lógica de funcionamento que as outras funções de rótulo e texto.

23.4.3 Mapa com mais de uma camada

ggplot()+
  geom_sf(data=Brasil,color="black",aes(fill="Brasil"))+
  geom_sf(data=subset(Estados,name_region=="Nordeste"),aes(fill="Nordeste"),color="black")+
  geom_sf(data=subset(Estados,name_state=="Pernambuco"),aes(fill="Pernambuco"),color="black")+
  scale_fill_manual(values = c("darkgreen",
                               "gray",
                               "yellow"))+
  labs(fill=NULL)+
  tema

Na construção de mapas, cada arquivo vetorial funciona como uma camada, então é possível fazer camadas sobreporem camadas. Nesse caso, era desejado usar mais duas camadas: uma contendo apenas os estados do Nordeste e outra apenas o estado de Pernambuco. Para extrair estas informações, usou-se a função subset() para as camandas, selecionando apenas o que era desejado. Alternativamente, pode-se utilizar comandos de filtragem prévios com a função filter(). Contudo, não são vetores vindo de uma mesma fonte, então para divir as cores dos vetores, na função aes(), em fill=, ao invés de escolher uma cor, apenas deu-se o nome do preenchimento da camada, e na função scale_fill_manual(), foram escolhidas as cores.

23.4.4 Alterando a escala do mapa

ggplot()+
  geom_sf(data=Brasil,color="black",aes(fill="Brasil"))+
  geom_sf(data=subset(Estados,name_region=="Nordeste"),aes(fill="Nordeste"),color="black")+
  geom_sf(data=subset(Estados,name_state=="Pernambuco"),aes(fill="Pernambuco"),color="black")+
  geom_sf(data=Recife,aes(fill="Recife"),color="black")+
  scale_fill_manual(values = c("darkgreen",
                               "gray",
                               "yellow",
                               "orangered"))+
  labs(fill=NULL)+
  tema

Nessa situação, foi adicionada uma nova camada, correspondente à cidade de Recife. Contudo, a escala não permite vizualizar Recife de forma adquada. Para alterar a escala dos mapas feitos em ggplot, é usada a função coord_sf().

ggplot()+
  geom_sf(data=Brasil,color="black",aes(fill="Brasil"))+
  geom_sf(data=subset(Estados,name_region=="Nordeste"),aes(fill="Nordeste"),color="black")+
  geom_sf(data=subset(Estados,name_state=="Pernambuco"),aes(fill="Pernambuco"),color="black")+
  geom_sf(data=Recife,aes(fill="Recife"),color="black")+
  coord_sf(xlim=c(-41.15,-34.5),ylim=c(-9.5,-7.25))+
  scale_fill_manual(values = c("darkgreen",
                               "gray",
                               "yellow",
                               "orangered"))+
  labs(fill=NULL)+
  tema

Na função coord_sf(), é informado o intervalo da longitude, pelo comando xlim=c(), e o intervalo da latitude, pelo comando ylim=c(). Importante destacar que o comando funciona em coordenadas decimais, que não são as que aparecem nos eixos X e Y. Por isso, é importante conhecer os limites das coordenadas no formato decimal. Nesse caso, como não aparece mais a camada do Brasil, pode-se remover ela sem problemas.

ggplot()+
  geom_sf(data=subset(Estados,name_region=="Nordeste"),aes(fill="Nordeste"),color="black")+
  geom_sf(data=subset(Estados,name_state=="Pernambuco"),aes(fill="Pernambuco"),color="black")+
  geom_sf(data=Recife,aes(fill="Recife"),color="black")+
  coord_sf(xlim=c(-41.15,-34.5),ylim=c(-9.5,-7.25))+
  scale_fill_manual(values = c("gray",
                               "yellow",
                               "orangered"))+
  labs(fill=NULL)+
  tema

23.4.5 Adicionando elementos de escala e seta

ggplot()+
  geom_sf(data=Brasil,color="black",aes(fill="Brasil"))+
  geom_sf(data=subset(Estados,name_region=="Nordeste"),aes(fill="Nordeste"),color="black")+
  geom_sf(data=subset(Estados,name_state=="Pernambuco"),aes(fill="Pernambuco"),color="black")+
  scale_fill_manual(values = c("darkgreen",
                               "gray",
                               "yellow"))+
  coord_sf(xlim=c(-73,-35.5),ylim=c(-33,4))+
  annotation_scale(location="br",height = unit(0.3,"cm"),bar_cols=c("black","yellow"))+
  annotation_north_arrow(style = north_arrow_nautical(fill=c("black","yellow")), location="tr",height = unit(1.85,"cm"),width = unit(1.85,"cm"))+
  labs(fill=NULL)+
  tema

Usando a função annotation_scale(), é possível adicionar uma barra de escala, onde o comando location= comando onde onde a barra aparecerá no mapa, onde:

  • "br": abaixo e à direita;

  • "bl": abaixo e à esquerda;

  • "tr": acima e à direita;

  • "tl": acima e à esquerda.

Além deste comando, há o comando bar_cols=c(), onde é possível selecionar a cor das barras. O padrão é preto e branco (bar_cols=c("black","white")), que é o que aparecerá se este comando não for informado. O comando height=unit() comanda a altura da barra.

Além desta função, foi usada a função annotation_north_arrow(), que cria uma rosa dos ventos no mapa. O comando location= funciona exatamente como annotation_scale(). O comando style= comanda o estilo da seta, sendo estes:

  • north_arrow_orienteering;

  • north_arrow_fancy_orienteering;

  • north_arrow_minimal;

  • north_arrow_nautical.

No estilo de seta escolhida, o comando fill=c() comanda as cores da rosa dos ventos. Por fim, o comando heigth= comanda a altura e width= o comprimento.

Tanto annotation_scale() quanto annotation_north_arrow() são do pacote ggspatial.

23.5 Construindo ggplot com raster

Há formas automáticas de criar mapas raster no R, como com a função plot(). Contudo, o ggplot, a história é um pouco mais compexa. Acontece que, atualmente (23 de Novembro de 2022), não existem funções que leiam rasters no ggplot. Então, para serem trabalhados no ggplot, os rasters antes precisam ser convertidos em data framses.

23.5.1 Preparando os dados

topo_catimbau<-topo_catimbau %>% 
  mask(Catimbau) %>% 
  crop(Catimbau)

topo_catimbau_df<-topo_catimbau %>% 
  as.data.frame(xy=TRUE) %>% 
  na.omit()

colnames(topo_catimbau_df)[3]<-"altitude"

topo_catimbau_df
##                x         y altitude
## 999    -37.28125 -8.387639  542.826
## 2350   -37.28236 -8.387917  542.567
## 2351   -37.28208 -8.387917  542.216
## 2352   -37.28180 -8.387917  541.961
## 2353   -37.28152 -8.387917  542.200
## 2354   -37.28125 -8.387917  542.493
## 2355   -37.28097 -8.387917  542.824
## 2356   -37.28069 -8.387917  543.398
## 2357   -37.28041 -8.387917  543.971
## 3702   -37.28319 -8.388194  543.814
## 3703   -37.28291 -8.388194  543.328
## 3704   -37.28263 -8.388194  542.914
## 3705   -37.28236 -8.388194  542.407
## 3706   -37.28208 -8.388194  542.096
## 3707   -37.28180 -8.388194  542.022
## 3708   -37.28152 -8.388194  542.155
## 3709   -37.28125 -8.388194  542.458
## 3710   -37.28097 -8.388194  542.805
## 3711   -37.28069 -8.388194  543.244
## 3712   -37.28041 -8.388194  543.829
## 3713   -37.28013 -8.388194  544.410
## 3714   -37.27986 -8.388194  544.949
## 3715   -37.27958 -8.388194  545.687
## 5054   -37.28402 -8.388472  544.949
## 5055   -37.28375 -8.388472  544.071
## 5056   -37.28347 -8.388472  543.472
## 5057   -37.28319 -8.388472  543.174
## 5058   -37.28291 -8.388472  543.084
## 5059   -37.28263 -8.388472  542.893
## 5060   -37.28236 -8.388472  542.527
## 5061   -37.28208 -8.388472  542.325
## 5062   -37.28180 -8.388472  542.315
## 5063   -37.28152 -8.388472  542.380
## 5064   -37.28125 -8.388472  542.608
## 5065   -37.28097 -8.388472  542.911
## 5066   -37.28069 -8.388472  543.378
## 5067   -37.28041 -8.388472  543.918
## 5068   -37.28013 -8.388472  544.420
## 5069   -37.27986 -8.388472  544.813
## 5070   -37.27958 -8.388472  545.230
## 5071   -37.27930 -8.388472  545.798
## 5072   -37.27902 -8.388472  546.632
## 6406   -37.28486 -8.388750  546.309
## 6407   -37.28458 -8.388750  545.341
## 6408   -37.28430 -8.388750  544.418
## 6409   -37.28402 -8.388750  543.487
## 6410   -37.28375 -8.388750  542.829
## 6411   -37.28347 -8.388750  542.405
## 6412   -37.28319 -8.388750  542.586
## 6413   -37.28291 -8.388750  542.841
## 6414   -37.28263 -8.388750  543.018
## 6415   -37.28236 -8.388750  542.940
## 6416   -37.28208 -8.388750  542.789
## 6417   -37.28180 -8.388750  542.630
## 6418   -37.28152 -8.388750  542.782
## 6419   -37.28125 -8.388750  543.015
## 6420   -37.28097 -8.388750  543.366
## 6421   -37.28069 -8.388750  543.856
## 6422   -37.28041 -8.388750  544.360
## 6423   -37.28013 -8.388750  544.808
## 6424   -37.27986 -8.388750  545.099
## 6425   -37.27958 -8.388750  545.383
## 6426   -37.27930 -8.388750  545.669
## 6427   -37.27902 -8.388750  546.214
## 6428   -37.27875 -8.388750  546.832
## 6429   -37.27847 -8.388750  547.559
## 7757   -37.28597 -8.389028  546.036
## 7758   -37.28569 -8.389028  545.895
## 7759   -37.28541 -8.389028  545.672
## 7760   -37.28513 -8.389028  545.402
## 7761   -37.28486 -8.389028  544.788
## 7762   -37.28458 -8.389028  544.069
## 7763   -37.28430 -8.389028  543.184
## 7764   -37.28402 -8.389028  542.450
## 7765   -37.28375 -8.389028  542.034
## 7766   -37.28347 -8.389028  541.927
## 7767   -37.28319 -8.389028  542.500
## 7768   -37.28291 -8.389028  543.079
## 7769   -37.28263 -8.389028  543.616
## 7770   -37.28236 -8.389028  543.760
## 7771   -37.28208 -8.389028  543.556
## 7772   -37.28180 -8.389028  543.341
## 7773   -37.28152 -8.389028  543.403
## 7774   -37.28125 -8.389028  543.649
## 7775   -37.28097 -8.389028  543.979
## 7776   -37.28069 -8.389028  544.489
## 7777   -37.28041 -8.389028  545.004
## 7778   -37.28013 -8.389028  545.454
## 7779   -37.27986 -8.389028  545.702
## 7780   -37.27958 -8.389028  545.850
## 7781   -37.27930 -8.389028  546.026
## 7782   -37.27902 -8.389028  546.234
## 7783   -37.27875 -8.389028  546.496
## 7784   -37.27847 -8.389028  546.918
## 9109   -37.28680 -8.389306  545.273
## 9110   -37.28652 -8.389306  544.971
## 9111   -37.28625 -8.389306  544.645
## 9112   -37.28597 -8.389306  544.356
## 9113   -37.28569 -8.389306  544.346
## 9114   -37.28541 -8.389306  544.410
## 9115   -37.28513 -8.389306  544.422
## 9116   -37.28486 -8.389306  543.944
## 9117   -37.28458 -8.389306  543.461
## 9118   -37.28430 -8.389306  542.817
## 9119   -37.28402 -8.389306  542.435
## 9120   -37.28375 -8.389306  542.389
## 9121   -37.28347 -8.389306  542.509
## 9122   -37.28319 -8.389306  543.438
## 9123   -37.28291 -8.389306  544.374
## 9124   -37.28263 -8.389306  545.130
## 9125   -37.28236 -8.389306  545.181
## 9126   -37.28208 -8.389306  544.814
## 9127   -37.28180 -8.389306  544.472
## 9128   -37.28152 -8.389306  544.259
## 9129   -37.28125 -8.389306  544.137
## 9130   -37.28097 -8.389306  544.370
## 9131   -37.28069 -8.389306  545.080
## 9132   -37.28041 -8.389306  545.866
## 9133   -37.28013 -8.389306  546.435
## 9134   -37.27986 -8.389306  546.582
## 9135   -37.27958 -8.389306  546.623
## 9136   -37.27930 -8.389306  546.554
## 9137   -37.27902 -8.389306  546.636
## 9138   -37.27875 -8.389306  546.628
## 9139   -37.27847 -8.389306  546.811
## 9140   -37.27819 -8.389306  547.045
## 10461  -37.28763 -8.389583  542.359
## 10462  -37.28736 -8.389583  542.795
## 10463  -37.28708 -8.389583  543.559
## 10464  -37.28680 -8.389583  544.098
## 10465  -37.28652 -8.389583  543.930
## 10466  -37.28625 -8.389583  543.583
## 10467  -37.28597 -8.389583  543.269
## 10468  -37.28569 -8.389583  543.471
## 10469  -37.28541 -8.389583  543.737
## 10470  -37.28513 -8.389583  543.909
## 10471  -37.28486 -8.389583  543.778
## 10472  -37.28458 -8.389583  543.576
## 10473  -37.28430 -8.389583  543.400
## 10474  -37.28402 -8.389583  543.389
## 10475  -37.28375 -8.389583  543.631
## 10476  -37.28347 -8.389583  544.190
## 10477  -37.28319 -8.389583  545.281
## 10478  -37.28291 -8.389583  546.349
## 10479  -37.28263 -8.389583  547.042
## 10480  -37.28236 -8.389583  546.917
## 10481  -37.28208 -8.389583  546.404
## 10482  -37.28180 -8.389583  545.750
## 10483  -37.28152 -8.389583  545.184
## 10484  -37.28125 -8.389583  544.850
## 10485  -37.28097 -8.389583  544.894
## 10486  -37.28069 -8.389583  545.607
## 10487  -37.28041 -8.389583  546.498
## 10488  -37.28013 -8.389583  547.260
## 10489  -37.27986 -8.389583  547.546
## 10490  -37.27958 -8.389583  547.586
## 10491  -37.27930 -8.389583  547.451
## 10492  -37.27902 -8.389583  547.272
## 10493  -37.27875 -8.389583  547.045
## 10494  -37.27847 -8.389583  546.839
## 10495  -37.27819 -8.389583  546.710
## 11813  -37.28847 -8.389861  543.844
## 11814  -37.28819 -8.389861  542.588
## 11815  -37.28791 -8.389861  542.047
## 11816  -37.28763 -8.389861  541.224
## 11817  -37.28736 -8.389861  541.846
## 11818  -37.28708 -8.389861  542.657
## 11819  -37.28680 -8.389861  543.344
## 11820  -37.28652 -8.389861  543.329
## 11821  -37.28625 -8.389861  543.048
## 11822  -37.28597 -8.389861  542.763
## 11823  -37.28569 -8.389861  543.208
## 11824  -37.28541 -8.389861  543.577
## 11825  -37.28513 -8.389861  543.864
## 11826  -37.28486 -8.389861  544.061
## 11827  -37.28458 -8.389861  544.176
## 11828  -37.28430 -8.389861  544.366
## 11829  -37.28402 -8.389861  544.693
## 11830  -37.28375 -8.389861  545.157
## 11831  -37.28347 -8.389861  546.102
## 11832  -37.28319 -8.389861  547.268
## 11833  -37.28291 -8.389861  548.324
## 11834  -37.28263 -8.389861  548.958
## 11835  -37.28236 -8.389861  548.597
## 11836  -37.28208 -8.389861  548.023
## 11837  -37.28180 -8.389861  546.973
## 11838  -37.28152 -8.389861  546.155
## 11839  -37.28125 -8.389861  545.630
## 11840  -37.28097 -8.389861  545.485
## 11841  -37.28069 -8.389861  546.170
## 11842  -37.28041 -8.389861  547.010
## 11843  -37.28013 -8.389861  548.006
## 11844  -37.27986 -8.389861  548.373
## 11845  -37.27958 -8.389861  548.539
## 11846  -37.27930 -8.389861  548.309
## 11847  -37.27902 -8.389861  547.940
## 11848  -37.27875 -8.389861  547.445
## 11849  -37.27847 -8.389861  546.981
## 11850  -37.27819 -8.389861  546.543
## 11851  -37.27791 -8.389861  546.296
## 13165  -37.28930 -8.390139  544.292
## 13166  -37.28902 -8.390139  543.702
## 13167  -37.28875 -8.390139  542.701
## 13168  -37.28847 -8.390139  542.019
## 13169  -37.28819 -8.390139  541.671
## 13170  -37.28791 -8.390139  541.457
## 13171  -37.28763 -8.390139  541.686
## 13172  -37.28736 -8.390139  541.942
## 13173  -37.28708 -8.390139  542.323
## 13174  -37.28680 -8.390139  542.869
## 13175  -37.28652 -8.390139  543.198
## 13176  -37.28625 -8.390139  543.345
## 13177  -37.28597 -8.390139  543.242
## 13178  -37.28569 -8.390139  543.432
## 13179  -37.28541 -8.390139  543.679
## 13180  -37.28513 -8.390139  543.997
## 13181  -37.28486 -8.390139  544.506
## 13182  -37.28458 -8.390139  544.894
## 13183  -37.28430 -8.390139  545.421
## 13184  -37.28402 -8.390139  545.806
## 13185  -37.28375 -8.390139  546.428
## 13186  -37.28347 -8.390139  547.405
## 13187  -37.28319 -8.390139  548.559
## 13188  -37.28291 -8.390139  549.587
## 13189  -37.28263 -8.390139  550.069
## 13190  -37.28236 -8.390139  549.812
## 13191  -37.28208 -8.390139  549.223
## 13192  -37.28180 -8.390139  548.149
## 13193  -37.28152 -8.390139  547.174
## 13194  -37.28125 -8.390139  546.470
## 13195  -37.28097 -8.390139  546.250
## 13196  -37.28069 -8.390139  546.697
## 13197  -37.28041 -8.390139  547.285
## 13198  -37.28013 -8.390139  548.223
## 13199  -37.27986 -8.390139  548.743
## 13200  -37.27958 -8.390139  548.990
## 13201  -37.27930 -8.390139  548.863
## 13202  -37.27902 -8.390139  548.433
## 13203  -37.27875 -8.390139  547.827
## 13204  -37.27847 -8.390139  547.157
## 13205  -37.27819 -8.390139  546.645
## 13206  -37.27791 -8.390139  546.228
## 13309  -37.24930 -8.390139  556.604
## 14516  -37.29041 -8.390417  542.351
## 14517  -37.29013 -8.390417  542.978
## 14518  -37.28986 -8.390417  543.113
## 14519  -37.28958 -8.390417  543.418
## 14520  -37.28930 -8.390417  543.503
## 14521  -37.28902 -8.390417  542.890
## 14522  -37.28875 -8.390417  542.160
## 14523  -37.28847 -8.390417  541.656
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## 14525  -37.28791 -8.390417  541.843
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## 21302  -37.28736 -8.391806  544.517
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## 22648  -37.28986 -8.392083  541.955
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## 25514  -37.24652 -8.392639  555.884
## 25515  -37.24625 -8.392639  555.070
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## 49908  -37.24541 -8.397639  569.720
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## 51109  -37.28819 -8.397917  549.960
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## 51113  -37.28708 -8.397917  550.723
## 51114  -37.28680 -8.397917  550.043
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## 59277  -37.27763 -8.399583  565.911
## 59278  -37.27736 -8.399583  566.049
## 59279  -37.27708 -8.399583  566.218
## 59280  -37.27680 -8.399583  566.723
## 59281  -37.27652 -8.399583  567.854
## 59282  -37.27625 -8.399583  569.159
## 59283  -37.27597 -8.399583  570.415
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## 59286  -37.27513 -8.399583  572.227
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## 59288  -37.27458 -8.399583  571.920
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## 59290  -37.27402 -8.399583  571.469
## 59291  -37.27375 -8.399583  571.000
## 59292  -37.27347 -8.399583  570.006
## 59293  -37.27319 -8.399583  568.114
## 59294  -37.27291 -8.399583  565.805
## 59295  -37.27263 -8.399583  563.364
## 59296  -37.27236 -8.399583  560.992
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## 59298  -37.27180 -8.399583  558.042
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## 59315  -37.26708 -8.399583  559.941
## 59316  -37.26680 -8.399583  560.113
## 59317  -37.26652 -8.399583  559.474
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## 59319  -37.26597 -8.399583  557.639
## 59320  -37.26569 -8.399583  557.231
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## 60758  -37.24263 -8.399861  567.926
## 60759  -37.24236 -8.399861  566.933
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## 61909  -37.29930 -8.400139  542.495
## 61910  -37.29902 -8.400139  541.888
## 61911  -37.29875 -8.400139  541.623
## 61912  -37.29847 -8.400139  541.830
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## 61928  -37.29402 -8.400139  552.909
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## 70010  -37.30736 -8.401806  536.561
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## 70024  -37.30347 -8.401806  541.642
## 70025  -37.30319 -8.401806  540.945
## 70026  -37.30291 -8.401806  540.890
## 70027  -37.30263 -8.401806  541.553
## 70028  -37.30236 -8.401806  542.296
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## 70031  -37.30152 -8.401806  542.084
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## 70035  -37.30041 -8.401806  539.394
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## 70037  -37.29986 -8.401806  540.899
## 70038  -37.29958 -8.401806  541.637
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## 70041  -37.29875 -8.401806  541.878
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## 71421  -37.29180 -8.402083  553.079
## 71422  -37.29152 -8.402083  552.938
## 71423  -37.29125 -8.402083  552.835
## 71424  -37.29097 -8.402083  552.856
## 71425  -37.29069 -8.402083  553.167
## 71426  -37.29041 -8.402083  553.501
## 71427  -37.29013 -8.402083  553.694
## 71428  -37.28986 -8.402083  553.540
## 71429  -37.28958 -8.402083  553.511
## 71430  -37.28930 -8.402083  553.821
## 71431  -37.28902 -8.402083  555.259
## 71432  -37.28875 -8.402083  556.955
## 71433  -37.28847 -8.402083  558.554
## 71434  -37.28819 -8.402083  559.267
## 71435  -37.28791 -8.402083  559.772
## 71436  -37.28763 -8.402083  560.350
## 71437  -37.28736 -8.402083  561.456
## 71438  -37.28708 -8.402083  562.655
## 71439  -37.28680 -8.402083  563.755
## 71440  -37.28652 -8.402083  564.576
## 71441  -37.28625 -8.402083  565.088
## 71442  -37.28597 -8.402083  565.246
## 71443  -37.28569 -8.402083  564.959
## 71444  -37.28541 -8.402083  564.578
## 71445  -37.28513 -8.402083  564.367
## 71446  -37.28486 -8.402083  564.566
## 71447  -37.28458 -8.402083  564.931
## 71448  -37.28430 -8.402083  565.233
## 71449  -37.28402 -8.402083  565.230
## 71450  -37.28375 -8.402083  565.288
## 71451  -37.28347 -8.402083  565.543
## 71452  -37.28319 -8.402083  566.445
## 71453  -37.28291 -8.402083  567.328
## 71454  -37.28263 -8.402083  567.882
## 71455  -37.28236 -8.402083  567.758
## 71456  -37.28208 -8.402083  567.355
## 71457  -37.28180 -8.402083  566.949
## 71458  -37.28152 -8.402083  566.770
## 71459  -37.28125 -8.402083  566.448
## 71460  -37.28097 -8.402083  565.800
## 71461  -37.28069 -8.402083  564.355
## 71462  -37.28041 -8.402083  562.847
## 71463  -37.28013 -8.402083  561.671
## 71464  -37.27986 -8.402083  561.348
## 71465  -37.27958 -8.402083  561.521
## 71466  -37.27930 -8.402083  562.088
## 71467  -37.27902 -8.402083  562.880
## 71468  -37.27875 -8.402083  563.791
## 71469  -37.27847 -8.402083  564.691
## 71470  -37.27819 -8.402083  565.269
## 71471  -37.27791 -8.402083  565.802
## 71472  -37.27763 -8.402083  566.398
## 71473  -37.27736 -8.402083  567.247
## 71474  -37.27708 -8.402083  568.095
## 71475  -37.27680 -8.402083  568.842
## 71476  -37.27652 -8.402083  569.422
## 71477  -37.27625 -8.402083  569.913
## 71478  -37.27597 -8.402083  570.335
## 71479  -37.27569 -8.402083  570.670
## 71480  -37.27541 -8.402083  570.998
## 71481  -37.27513 -8.402083  571.363
## 71482  -37.27486 -8.402083  571.859
## 71483  -37.27458 -8.402083  572.095
## 71484  -37.27430 -8.402083  571.788
## 71485  -37.27402 -8.402083  570.677
## 71486  -37.27375 -8.402083  569.241
## 71487  -37.27347 -8.402083  567.740
## 71488  -37.27319 -8.402083  566.556
## 71489  -37.27291 -8.402083  565.722
## 71490  -37.27263 -8.402083  565.400
## 71491  -37.27236 -8.402083  565.777
## 71492  -37.27208 -8.402083  566.192
## 71493  -37.27180 -8.402083  566.073
## 71494  -37.27152 -8.402083  564.935
## 71495  -37.27125 -8.402083  563.399
## 71496  -37.27097 -8.402083  561.794
## 71497  -37.27069 -8.402083  560.714
## 71498  -37.27041 -8.402083  559.903
## 71499  -37.27013 -8.402083  559.403
## 71500  -37.26986 -8.402083  559.218
## 71501  -37.26958 -8.402083  559.141
## 71502  -37.26930 -8.402083  559.012
## 71503  -37.26902 -8.402083  558.526
## 71504  -37.26875 -8.402083  557.925
## 71505  -37.26847 -8.402083  557.360
## 71506  -37.26819 -8.402083  556.918
## 71507  -37.26791 -8.402083  556.883
## 71508  -37.26763 -8.402083  557.485
## 71509  -37.26736 -8.402083  558.975
## 71510  -37.26708 -8.402083  560.795
## 71511  -37.26680 -8.402083  562.515
## 71512  -37.26652 -8.402083  563.742
## 71513  -37.26625 -8.402083  564.512
## 71514  -37.26597 -8.402083  564.765
## 71515  -37.26569 -8.402083  564.500
## 71516  -37.26541 -8.402083  563.694
## 71517  -37.26513 -8.402083  562.358
## 71518  -37.26486 -8.402083  560.513
## 71519  -37.26458 -8.402083  558.606
## 71520  -37.26430 -8.402083  557.039
## 71521  -37.26402 -8.402083  556.134
## 71522  -37.26375 -8.402083  555.647
## 71523  -37.26347 -8.402083  555.461
## 71524  -37.26319 -8.402083  555.261
## 71525  -37.26291 -8.402083  555.200
## 71526  -37.26263 -8.402083  555.287
## 71527  -37.26236 -8.402083  555.676
## 71528  -37.26208 -8.402083  555.876
## 71529  -37.26180 -8.402083  555.614
## 71530  -37.26152 -8.402083  554.563
## 71531  -37.26125 -8.402083  553.328
## 71532  -37.26097 -8.402083  552.528
## 71533  -37.26069 -8.402083  553.008
## 71534  -37.26041 -8.402083  553.788
## 71535  -37.26013 -8.402083  554.369
## 71536  -37.25986 -8.402083  554.142
## 71537  -37.25958 -8.402083  553.794
## 71538  -37.25930 -8.402083  553.794
## 71539  -37.25902 -8.402083  554.512
## 71540  -37.25875 -8.402083  555.303
## 71541  -37.25847 -8.402083  555.795
## 71542  -37.25819 -8.402083  555.366
## 71543  -37.25791 -8.402083  554.689
## 71544  -37.25763 -8.402083  554.086
## 71545  -37.25736 -8.402083  553.959
## 71546  -37.25708 -8.402083  554.104
## 71547  -37.25680 -8.402083  554.448
## 71548  -37.25652 -8.402083  554.947
## 71549  -37.25625 -8.402083  555.470
## 71550  -37.25597 -8.402083  555.942
## 71551  -37.25569 -8.402083  556.102
## 71552  -37.25541 -8.402083  556.304
## 71553  -37.25513 -8.402083  556.692
## 71554  -37.25486 -8.402083  557.474
## 71555  -37.25458 -8.402083  558.428
## 71556  -37.25430 -8.402083  559.451
## 71557  -37.25402 -8.402083  560.456
## 71558  -37.25375 -8.402083  561.373
## 71559  -37.25347 -8.402083  562.161
## 71560  -37.25319 -8.402083  562.725
## 71561  -37.25291 -8.402083  563.245
## 71562  -37.25263 -8.402083  563.849
## 71563  -37.25236 -8.402083  564.695
## 71564  -37.25208 -8.402083  565.540
## 71565  -37.25180 -8.402083  566.230
## 71566  -37.25152 -8.402083  566.621
## 71567  -37.25125 -8.402083  566.715
## 71568  -37.25097 -8.402083  566.488
## 71569  -37.25069 -8.402083  565.777
## 71570  -37.25041 -8.402083  565.043
## 71571  -37.25013 -8.402083  564.584
## 71572  -37.24986 -8.402083  564.740
## 71573  -37.24958 -8.402083  565.223
## 71574  -37.24930 -8.402083  565.888
## 71575  -37.24902 -8.402083  566.607
## 71576  -37.24875 -8.402083  567.366
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## 71578  -37.24819 -8.402083  568.814
## 71579  -37.24791 -8.402083  569.547
## 71580  -37.24763 -8.402083  570.400
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## 71584  -37.24652 -8.402083  574.758
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## 71588  -37.24541 -8.402083  577.669
## 71589  -37.24513 -8.402083  578.063
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## 71603  -37.24125 -8.402083  578.377
## 71604  -37.24097 -8.402083  578.941
## 71605  -37.24069 -8.402083  578.822
## 71606  -37.24041 -8.402083  578.343
## 71607  -37.24013 -8.402083  577.639
## 71608  -37.23986 -8.402083  576.951
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## 71611  -37.23902 -8.402083  576.488
## 71612  -37.23875 -8.402083  576.898
## 71613  -37.23847 -8.402083  577.116
## 71614  -37.23819 -8.402083  576.556
## 71615  -37.23791 -8.402083  576.035
## 71616  -37.23763 -8.402083  575.955
## 71617  -37.23736 -8.402083  576.790
## 71618  -37.23708 -8.402083  577.729
## 71619  -37.23680 -8.402083  578.213
## 71620  -37.23652 -8.402083  577.756
## 71621  -37.23625 -8.402083  576.918
## 71622  -37.23597 -8.402083  575.968
## 71623  -37.23569 -8.402083  575.450
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## 71625  -37.23513 -8.402083  573.942
## 71626  -37.23486 -8.402083  572.504
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## 71628  -37.23430 -8.402083  569.119
## 71629  -37.23402 -8.402083  567.448
## 71630  -37.23375 -8.402083  566.061
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## 72575  -37.34763 -8.402361  524.296
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## 72660  -37.32402 -8.402361  533.516
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## 72668  -37.32180 -8.402361  533.515
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## 72671  -37.32097 -8.402361  532.361
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## 72683  -37.31763 -8.402361  534.729
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## 72686  -37.31680 -8.402361  536.316
## 72687  -37.31652 -8.402361  537.315
## 72688  -37.31625 -8.402361  538.403
## 72689  -37.31597 -8.402361  539.385
## 72690  -37.31569 -8.402361  539.617
## 72691  -37.31541 -8.402361  539.621
## 72692  -37.31513 -8.402361  539.287
## 72693  -37.31486 -8.402361  539.015
## 72694  -37.31458 -8.402361  538.726
## 72695  -37.31430 -8.402361  538.381
## 72696  -37.31402 -8.402361  538.153
## 72697  -37.31375 -8.402361  537.892
## 72698  -37.31347 -8.402361  537.540
## 72699  -37.31319 -8.402361  537.215
## 72700  -37.31291 -8.402361  536.899
## 72701  -37.31263 -8.402361  537.033
## 72702  -37.31236 -8.402361  537.687
## 72703  -37.31208 -8.402361  538.436
## 72704  -37.31180 -8.402361  538.733
## 72705  -37.31152 -8.402361  538.507
## 72706  -37.31125 -8.402361  538.277
## 72707  -37.31097 -8.402361  538.204
## 72708  -37.31069 -8.402361  538.711
## 72709  -37.31041 -8.402361  539.309
## 72710  -37.31013 -8.402361  539.689
## 72711  -37.30986 -8.402361  539.012
## 72712  -37.30958 -8.402361  538.078
## 72713  -37.30930 -8.402361  536.889
## 72714  -37.30902 -8.402361  535.776
## 72715  -37.30875 -8.402361  535.007
## 72716  -37.30847 -8.402361  534.520
## 72717  -37.30819 -8.402361  535.091
## 72718  -37.30791 -8.402361  535.701
## 72719  -37.30763 -8.402361  536.093
## 72720  -37.30736 -8.402361  535.952
## 72721  -37.30708 -8.402361  535.692
## 72722  -37.30680 -8.402361  536.302
## 72723  -37.30652 -8.402361  537.275
## 72724  -37.30625 -8.402361  538.680
## 72725  -37.30597 -8.402361  540.459
## 72726  -37.30569 -8.402361  542.313
## 72727  -37.30541 -8.402361  544.134
## 72728  -37.30513 -8.402361  544.834
## 72729  -37.30486 -8.402361  544.968
## 72730  -37.30458 -8.402361  544.507
## 72731  -37.30430 -8.402361  544.082
## 72732  -37.30402 -8.402361  543.978
## 72733  -37.30375 -8.402361  543.463
## 72734  -37.30347 -8.402361  543.315
## 72735  -37.30319 -8.402361  542.928
## 72736  -37.30291 -8.402361  542.206
## 72737  -37.30263 -8.402361  541.878
## 72738  -37.30236 -8.402361  542.438
## 72739  -37.30208 -8.402361  543.341
## 72740  -37.30180 -8.402361  544.083
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## 72742  -37.30125 -8.402361  543.252
## 72743  -37.30097 -8.402361  542.603
## 72744  -37.30069 -8.402361  542.154
## 72745  -37.30041 -8.402361  541.680
## 72746  -37.30013 -8.402361  541.186
## 72747  -37.29986 -8.402361  541.561
## 72748  -37.29958 -8.402361  542.026
## 72749  -37.29930 -8.402361  542.744
## 72750  -37.29902 -8.402361  543.108
## 72751  -37.29875 -8.402361  543.239
## 72752  -37.29847 -8.402361  543.516
## 72753  -37.29819 -8.402361  543.312
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## 72755  -37.29763 -8.402361  543.161
## 72756  -37.29736 -8.402361  543.592
## 72757  -37.29708 -8.402361  544.208
## 72758  -37.29680 -8.402361  544.626
## 72759  -37.29652 -8.402361  544.379
## 72760  -37.29625 -8.402361  544.210
## 72761  -37.29597 -8.402361  544.450
## 72762  -37.29569 -8.402361  545.265
## 72763  -37.29541 -8.402361  545.991
## 72764  -37.29513 -8.402361  546.762
## 72765  -37.29486 -8.402361  547.023
## 72766  -37.29458 -8.402361  547.301
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## 72768  -37.29402 -8.402361  547.599
## 72769  -37.29375 -8.402361  547.882
## 72770  -37.29347 -8.402361  548.531
## 72771  -37.29319 -8.402361  549.456
## 72772  -37.29291 -8.402361  550.403
## 72773  -37.29263 -8.402361  550.998
## 72774  -37.29236 -8.402361  551.183
## 72775  -37.29208 -8.402361  551.089
## 72776  -37.29180 -8.402361  551.300
## 72777  -37.29152 -8.402361  551.220
## 72778  -37.29125 -8.402361  551.379
## 72779  -37.29097 -8.402361  551.357
## 72780  -37.29069 -8.402361  551.660
## 72781  -37.29041 -8.402361  551.992
## 72782  -37.29013 -8.402361  552.147
## 72783  -37.28986 -8.402361  552.063
## 72784  -37.28958 -8.402361  552.164
## 72785  -37.28930 -8.402361  552.274
## 72786  -37.28902 -8.402361  553.601
## 72787  -37.28875 -8.402361  555.229
## 72788  -37.28847 -8.402361  556.614
## 72789  -37.28819 -8.402361  557.317
## 72790  -37.28791 -8.402361  558.662
## 72791  -37.28763 -8.402361  559.536
## 72792  -37.28736 -8.402361  561.083
## 72793  -37.28708 -8.402361  562.430
## 72794  -37.28680 -8.402361  563.677
## 72795  -37.28652 -8.402361  564.584
## 72796  -37.28625 -8.402361  565.129
## 72797  -37.28597 -8.402361  565.460
## 72798  -37.28569 -8.402361  565.077
## 72799  -37.28541 -8.402361  564.714
## 72800  -37.28513 -8.402361  564.349
## 72801  -37.28486 -8.402361  564.248
## 72802  -37.28458 -8.402361  564.436
## 72803  -37.28430 -8.402361  564.729
## 72804  -37.28402 -8.402361  564.956
## 72805  -37.28375 -8.402361  565.213
## 72806  -37.28347 -8.402361  565.660
## 72807  -37.28319 -8.402361  566.818
## 72808  -37.28291 -8.402361  567.557
## 72809  -37.28263 -8.402361  568.240
## 72810  -37.28236 -8.402361  568.159
## 72811  -37.28208 -8.402361  567.997
## 72812  -37.28180 -8.402361  567.673
## 72813  -37.28152 -8.402361  567.586
## 72814  -37.28125 -8.402361  567.332
## 72815  -37.28097 -8.402361  566.513
## 72816  -37.28069 -8.402361  565.070
## 72817  -37.28041 -8.402361  563.540
## 72818  -37.28013 -8.402361  562.355
## 72819  -37.27986 -8.402361  562.117
## 72820  -37.27958 -8.402361  562.217
## 72821  -37.27930 -8.402361  562.716
## 72822  -37.27902 -8.402361  563.111
## 72823  -37.27875 -8.402361  563.777
## 72824  -37.27847 -8.402361  564.383
## 72825  -37.27819 -8.402361  564.686
## 72826  -37.27791 -8.402361  565.513
## 72827  -37.27763 -8.402361  565.905
## 72828  -37.27736 -8.402361  566.617
## 72829  -37.27708 -8.402361  567.006
## 72830  -37.27680 -8.402361  568.097
## 72831  -37.27652 -8.402361  568.777
## 72832  -37.27625 -8.402361  569.398
## 72833  -37.27597 -8.402361  570.025
## 72834  -37.27569 -8.402361  570.625
## 72835  -37.27541 -8.402361  571.068
## 72836  -37.27513 -8.402361  571.478
## 72837  -37.27486 -8.402361  571.943
## 72838  -37.27458 -8.402361  572.119
## 72839  -37.27430 -8.402361  571.909
## 72840  -37.27402 -8.402361  570.779
## 72841  -37.27375 -8.402361  569.431
## 72842  -37.27347 -8.402361  567.920
## 72843  -37.27319 -8.402361  566.711
## 72844  -37.27291 -8.402361  566.011
## 72845  -37.27263 -8.402361  565.724
## 72846  -37.27236 -8.402361  565.780
## 72847  -37.27208 -8.402361  565.801
## 72848  -37.27180 -8.402361  565.186
## 72849  -37.27152 -8.402361  563.673
## 72850  -37.27125 -8.402361  562.158
## 72851  -37.27097 -8.402361  560.648
## 72852  -37.27069 -8.402361  560.011
## 72853  -37.27041 -8.402361  559.574
## 72854  -37.27013 -8.402361  559.838
## 72855  -37.26986 -8.402361  560.089
## 72856  -37.26958 -8.402361  560.306
## 72857  -37.26930 -8.402361  560.374
## 72858  -37.26902 -8.402361  559.773
## 72859  -37.26875 -8.402361  559.162
## 72860  -37.26847 -8.402361  558.302
## 72861  -37.26819 -8.402361  557.659
## 72862  -37.26791 -8.402361  557.311
## 72863  -37.26763 -8.402361  557.899
## 72864  -37.26736 -8.402361  559.437
## 72865  -37.26708 -8.402361  561.273
## 72866  -37.26680 -8.402361  563.141
## 72867  -37.26652 -8.402361  564.493
## 72868  -37.26625 -8.402361  565.370
## 72869  -37.26597 -8.402361  565.740
## 72870  -37.26569 -8.402361  565.452
## 72871  -37.26541 -8.402361  564.640
## 72872  -37.26513 -8.402361  563.294
## 72873  -37.26486 -8.402361  561.225
## 72874  -37.26458 -8.402361  559.107
## 72875  -37.26430 -8.402361  557.447
## 72876  -37.26402 -8.402361  556.330
## 72877  -37.26375 -8.402361  555.957
## 72878  -37.26347 -8.402361  555.621
## 72879  -37.26319 -8.402361  555.515
## 72880  -37.26291 -8.402361  555.569
## 72881  -37.26263 -8.402361  555.828
## 72882  -37.26236 -8.402361  556.310
## 72883  -37.26208 -8.402361  556.449
## 72884  -37.26180 -8.402361  556.557
## 72885  -37.26152 -8.402361  555.544
## 72886  -37.26125 -8.402361  554.290
## 72887  -37.26097 -8.402361  553.122
## 72888  -37.26069 -8.402361  553.255
## 72889  -37.26041 -8.402361  553.800
## 72890  -37.26013 -8.402361  554.248
## 72891  -37.25986 -8.402361  553.722
## 72892  -37.25958 -8.402361  553.232
## 72893  -37.25930 -8.402361  553.248
## 72894  -37.25902 -8.402361  554.054
## 72895  -37.25875 -8.402361  554.850
## 72896  -37.25847 -8.402361  555.100
## 72897  -37.25819 -8.402361  554.865
## 72898  -37.25791 -8.402361  554.436
## 72899  -37.25763 -8.402361  554.142
## 72900  -37.25736 -8.402361  554.425
## 72901  -37.25708 -8.402361  554.706
## 72902  -37.25680 -8.402361  555.520
## 72903  -37.25652 -8.402361  556.353
## 72904  -37.25625 -8.402361  556.909
## 72905  -37.25597 -8.402361  557.233
## 72906  -37.25569 -8.402361  557.283
## 72907  -37.25541 -8.402361  557.353
## 72908  -37.25513 -8.402361  557.496
## 72909  -37.25486 -8.402361  558.232
## 72910  -37.25458 -8.402361  559.138
## 72911  -37.25430 -8.402361  560.204
## 72912  -37.25402 -8.402361  561.379
## 72913  -37.25375 -8.402361  562.372
## 72914  -37.25347 -8.402361  563.243
## 72915  -37.25319 -8.402361  563.834
## 72916  -37.25291 -8.402361  564.651
## 72917  -37.25263 -8.402361  565.319
## 72918  -37.25236 -8.402361  566.058
## 72919  -37.25208 -8.402361  566.802
## 72920  -37.25180 -8.402361  567.524
## 72921  -37.25152 -8.402361  567.798
## 72922  -37.25125 -8.402361  567.819
## 72923  -37.25097 -8.402361  567.309
## 72924  -37.25069 -8.402361  566.406
## 72925  -37.25041 -8.402361  565.406
## 72926  -37.25013 -8.402361  564.641
## 72927  -37.24986 -8.402361  564.749
## 72928  -37.24958 -8.402361  565.190
## 72929  -37.24930 -8.402361  566.145
## 72930  -37.24902 -8.402361  566.920
## 72931  -37.24875 -8.402361  567.738
## 72932  -37.24847 -8.402361  568.457
## 72933  -37.24819 -8.402361  569.074
## 72934  -37.24791 -8.402361  569.622
## 72935  -37.24763 -8.402361  570.064
## 72936  -37.24736 -8.402361  571.082
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## 72938  -37.24680 -8.402361  573.511
## 72939  -37.24652 -8.402361  574.746
## 72940  -37.24625 -8.402361  575.747
## 72941  -37.24597 -8.402361  576.845
## 72942  -37.24569 -8.402361  577.698
## 72943  -37.24541 -8.402361  578.332
## 72944  -37.24513 -8.402361  578.715
## 72945  -37.24486 -8.402361  578.925
## 72946  -37.24458 -8.402361  578.935
## 72947  -37.24430 -8.402361  578.806
## 72948  -37.24402 -8.402361  578.046
## 72949  -37.24375 -8.402361  577.036
## 72950  -37.24347 -8.402361  575.815
## 72951  -37.24319 -8.402361  574.596
## 72952  -37.24291 -8.402361  573.686
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## 72954  -37.24236 -8.402361  574.134
## 72955  -37.24208 -8.402361  575.354
## 72956  -37.24180 -8.402361  576.989
## 72957  -37.24152 -8.402361  577.949
## 72958  -37.24125 -8.402361  578.745
## 72959  -37.24097 -8.402361  578.879
## 72960  -37.24069 -8.402361  578.671
## 72961  -37.24041 -8.402361  578.324
## 72962  -37.24013 -8.402361  577.722
## 72963  -37.23986 -8.402361  577.380
## 72964  -37.23958 -8.402361  576.996
## 72965  -37.23930 -8.402361  577.080
## 72966  -37.23902 -8.402361  577.627
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## 72968  -37.23847 -8.402361  578.446
## 72969  -37.23819 -8.402361  577.849
## 72970  -37.23791 -8.402361  577.263
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## 72972  -37.23736 -8.402361  577.785
## 72973  -37.23708 -8.402361  578.526
## 72974  -37.23680 -8.402361  578.633
## 72975  -37.23652 -8.402361  577.836
## 72976  -37.23625 -8.402361  576.990
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## 72982  -37.23458 -8.402361  570.219
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## 73934  -37.34652 -8.402639  525.958
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## 74027  -37.32069 -8.402639  532.989
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## 74057  -37.31236 -8.402639  537.877
## 74058  -37.31208 -8.402639  538.496
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## 74060  -37.31152 -8.402639  538.536
## 74061  -37.31125 -8.402639  538.461
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## 74063  -37.31069 -8.402639  538.967
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## 74072  -37.30819 -8.402639  535.591
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## 74078  -37.30652 -8.402639  537.611
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## 74080  -37.30597 -8.402639  541.102
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## 74087  -37.30402 -8.402639  544.421
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## 74090  -37.30319 -8.402639  543.273
## 74091  -37.30291 -8.402639  542.500
## 74092  -37.30263 -8.402639  541.689
## 74093  -37.30236 -8.402639  542.472
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## 74096  -37.30152 -8.402639  544.888
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## 74099  -37.30069 -8.402639  543.613
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## 74125  -37.29347 -8.402639  547.613
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## 74129  -37.29236 -8.402639  549.764
## 74130  -37.29208 -8.402639  549.507
## 74131  -37.29180 -8.402639  549.516
## 74132  -37.29152 -8.402639  549.986
## 74133  -37.29125 -8.402639  550.367
## 74134  -37.29097 -8.402639  550.564
## 74135  -37.29069 -8.402639  550.734
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## 74140  -37.28930 -8.402639  551.495
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## 74146  -37.28763 -8.402639  559.256
## 74147  -37.28736 -8.402639  560.613
## 74148  -37.28708 -8.402639  561.764
## 74149  -37.28680 -8.402639  562.944
## 74150  -37.28652 -8.402639  563.864
## 74151  -37.28625 -8.402639  564.411
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## 74155  -37.28513 -8.402639  563.582
## 74156  -37.28486 -8.402639  563.360
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## 74158  -37.28430 -8.402639  563.540
## 74159  -37.28402 -8.402639  564.335
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## 75512  -37.28458 -8.402917  561.973
## 75513  -37.28430 -8.402917  562.745
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## 75527  -37.28041 -8.402917  565.392
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## 76850  -37.28930 -8.403194  550.476
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## 78175  -37.29763 -8.403472  546.935
## 78176  -37.29736 -8.403472  547.269
## 78177  -37.29708 -8.403472  547.499
## 78178  -37.29680 -8.403472  548.021
## 78179  -37.29652 -8.403472  549.114
## 78180  -37.29625 -8.403472  549.872
## 78181  -37.29597 -8.403472  550.035
## 78182  -37.29569 -8.403472  549.913
## 78183  -37.29541 -8.403472  549.682
## 78184  -37.29513 -8.403472  549.693
## 78185  -37.29486 -8.403472  550.160
## 78186  -37.29458 -8.403472  550.405
## 78187  -37.29430 -8.403472  550.516
## 78188  -37.29402 -8.403472  549.840
## 78189  -37.29375 -8.403472  549.157
## 78190  -37.29347 -8.403472  548.335
## 78191  -37.29319 -8.403472  548.320
## 78192  -37.29291 -8.403472  548.599
## 78193  -37.29263 -8.403472  548.819
## 78194  -37.29236 -8.403472  548.715
## 78195  -37.29208 -8.403472  548.527
## 78196  -37.29180 -8.403472  548.495
## 78197  -37.29152 -8.403472  548.955
## 78198  -37.29125 -8.403472  549.382
## 78199  -37.29097 -8.403472  550.249
## 78200  -37.29069 -8.403472  550.668
## 78201  -37.29041 -8.403472  550.806
## 78202  -37.29013 -8.403472  550.829
## 78203  -37.28986 -8.403472  550.550
## 78204  -37.28958 -8.403472  550.366
## 78205  -37.28930 -8.403472  549.983
## 78206  -37.28902 -8.403472  549.586
## 78207  -37.28875 -8.403472  550.025
## 78208  -37.28847 -8.403472  551.095
## 78209  -37.28819 -8.403472  552.768
## 78210  -37.28791 -8.403472  554.550
## 78211  -37.28763 -8.403472  556.303
## 78212  -37.28736 -8.403472  557.485
## 78213  -37.28708 -8.403472  558.199
## 78214  -37.28680 -8.403472  558.485
## 78215  -37.28652 -8.403472  558.200
## 78216  -37.28625 -8.403472  557.821
## 78217  -37.28597 -8.403472  557.665
## 78218  -37.28569 -8.403472  557.744
## 78219  -37.28541 -8.403472  558.106
## 78220  -37.28513 -8.403472  558.302
## 78221  -37.28486 -8.403472  558.965
## 78222  -37.28458 -8.403472  560.036
## 78223  -37.28430 -8.403472  561.818
## 78224  -37.28402 -8.403472  563.702
## 78225  -37.28375 -8.403472  565.331
## 78226  -37.28347 -8.403472  566.802
## 78227  -37.28319 -8.403472  567.254
## 78228  -37.28291 -8.403472  567.188
## 78229  -37.28263 -8.403472  566.858
## 78230  -37.28236 -8.403472  566.531
## 78231  -37.28208 -8.403472  566.371
## 78232  -37.28180 -8.403472  566.459
## 78233  -37.28152 -8.403472  567.149
## 78234  -37.28125 -8.403472  567.803
## 78235  -37.28097 -8.403472  568.125
## 78236  -37.28069 -8.403472  567.646
## 78237  -37.28041 -8.403472  566.927
## 78238  -37.28013 -8.403472  566.310
## 78239  -37.27986 -8.403472  565.395
## 78240  -37.27958 -8.403472  564.817
## 78241  -37.27930 -8.403472  563.557
## 78242  -37.27902 -8.403472  563.224
## 78243  -37.27875 -8.403472  563.432
## 78244  -37.27847 -8.403472  564.000
## 78245  -37.27819 -8.403472  565.011
## 78246  -37.27791 -8.403472  565.738
## 78247  -37.27763 -8.403472  566.541
## 78248  -37.27736 -8.403472  566.120
## 78249  -37.27708 -8.403472  565.427
## 78250  -37.27680 -8.403472  564.495
## 78251  -37.27652 -8.403472  564.977
## 78252  -37.27625 -8.403472  566.055
## 78253  -37.27597 -8.403472  567.313
## 78254  -37.27569 -8.403472  567.788
## 78255  -37.27541 -8.403472  567.943
## 78256  -37.27513 -8.403472  568.069
## 78257  -37.27486 -8.403472  568.041
## 78258  -37.27458 -8.403472  567.909
## 78259  -37.27430 -8.403472  567.586
## 78260  -37.27402 -8.403472  567.643
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## 78262  -37.27347 -8.403472  567.801
## 78263  -37.27319 -8.403472  567.336
## 78264  -37.27291 -8.403472  566.681
## 78265  -37.27263 -8.403472  565.792
## 78266  -37.27236 -8.403472  564.715
## 78267  -37.27208 -8.403472  563.751
## 78268  -37.27180 -8.403472  562.894
## 78269  -37.27152 -8.403472  562.185
## 78270  -37.27125 -8.403472  561.732
## 78271  -37.27097 -8.403472  561.450
## 78272  -37.27069 -8.403472  561.393
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## 78275  -37.26986 -8.403472  562.100
## 78276  -37.26958 -8.403472  562.263
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## 78278  -37.26902 -8.403472  562.330
## 78279  -37.26875 -8.403472  561.993
## 78280  -37.26847 -8.403472  561.405
## 78281  -37.26819 -8.403472  560.366
## 78282  -37.26791 -8.403472  559.495
## 78283  -37.26763 -8.403472  559.320
## 78284  -37.26736 -8.403472  559.778
## 78285  -37.26708 -8.403472  560.814
## 78286  -37.26680 -8.403472  561.946
## 78287  -37.26652 -8.403472  563.532
## 78288  -37.26625 -8.403472  564.901
## 78289  -37.26597 -8.403472  565.537
## 78290  -37.26569 -8.403472  565.042
## 78291  -37.26541 -8.403472  563.844
## 78292  -37.26513 -8.403472  562.267
## 78293  -37.26486 -8.403472  560.896
## 78294  -37.26458 -8.403472  559.293
## 78295  -37.26430 -8.403472  558.059
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## 78297  -37.26375 -8.403472  556.698
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## 78299  -37.26319 -8.403472  557.816
## 78300  -37.26291 -8.403472  558.444
## 78301  -37.26263 -8.403472  558.760
## 78302  -37.26236 -8.403472  558.470
## 78303  -37.26208 -8.403472  558.175
## 78304  -37.26180 -8.403472  557.646
## 78305  -37.26152 -8.403472  557.230
## 78306  -37.26125 -8.403472  557.198
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## 78308  -37.26069 -8.403472  557.627
## 78309  -37.26041 -8.403472  557.375
## 78310  -37.26013 -8.403472  556.702
## 78311  -37.25986 -8.403472  555.849
## 78312  -37.25958 -8.403472  555.020
## 78313  -37.25930 -8.403472  554.388
## 78314  -37.25902 -8.403472  554.152
## 78315  -37.25875 -8.403472  554.145
## 78316  -37.25847 -8.403472  554.739
## 78317  -37.25819 -8.403472  554.758
## 78318  -37.25791 -8.403472  554.915
## 78319  -37.25763 -8.403472  554.985
## 78320  -37.25736 -8.403472  555.370
## 78321  -37.25708 -8.403472  556.137
## 78322  -37.25680 -8.403472  556.573
## 78323  -37.25652 -8.403472  557.174
## 78324  -37.25625 -8.403472  557.724
## 78325  -37.25597 -8.403472  558.435
## 78326  -37.25569 -8.403472  559.130
## 78327  -37.25541 -8.403472  559.754
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## 78329  -37.25486 -8.403472  561.420
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## 78331  -37.25430 -8.403472  563.175
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## 78334  -37.25347 -8.403472  566.895
## 78335  -37.25319 -8.403472  567.704
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## 78339  -37.25208 -8.403472  569.198
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## 78341  -37.25152 -8.403472  569.578
## 78342  -37.25125 -8.403472  569.871
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## 78359  -37.24652 -8.403472  574.578
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## 78361  -37.24597 -8.403472  575.931
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## 78366  -37.24458 -8.403472  579.306
## 78367  -37.24430 -8.403472  579.280
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## 78372  -37.24291 -8.403472  579.775
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## 78375  -37.24208 -8.403472  579.647
## 78376  -37.24180 -8.403472  579.620
## 78377  -37.24152 -8.403472  579.629
## 78378  -37.24125 -8.403472  579.929
## 78379  -37.24097 -8.403472  580.524
## 78380  -37.24069 -8.403472  581.802
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## 78384  -37.23958 -8.403472  583.864
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## 78386  -37.23902 -8.403472  583.054
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## 78388  -37.23847 -8.403472  582.354
## 78389  -37.23819 -8.403472  582.032
## 78390  -37.23791 -8.403472  581.719
## 78391  -37.23763 -8.403472  581.328
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## 79402  -37.33319 -8.403750  529.221
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## 79405  -37.33236 -8.403750  529.469
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## 79411  -37.33069 -8.403750  531.037
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## 79417  -37.32902 -8.403750  530.932
## 79418  -37.32875 -8.403750  531.478
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## 79429  -37.32569 -8.403750  534.883
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## 79431  -37.32513 -8.403750  534.850
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## 79439  -37.32291 -8.403750  539.590
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## 79449  -37.32013 -8.403750  537.489
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## 79452  -37.31930 -8.403750  536.608
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## 79456  -37.31819 -8.403750  537.752
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## 79462  -37.31652 -8.403750  543.275
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## 79465  -37.31569 -8.403750  544.516
## 79466  -37.31541 -8.403750  544.227
## 79467  -37.31513 -8.403750  543.985
## 79468  -37.31486 -8.403750  544.048
## 79469  -37.31458 -8.403750  544.135
## 79470  -37.31430 -8.403750  543.948
## 79471  -37.31402 -8.403750  543.504
## 79472  -37.31375 -8.403750  542.815
## 79473  -37.31347 -8.403750  541.945
## 79474  -37.31319 -8.403750  541.404
## 79475  -37.31291 -8.403750  540.884
## 79476  -37.31263 -8.403750  540.540
## 79477  -37.31236 -8.403750  540.441
## 79478  -37.31208 -8.403750  540.379
## 79479  -37.31180 -8.403750  540.314
## 79480  -37.31152 -8.403750  539.732
## 79481  -37.31125 -8.403750  539.226
## 79482  -37.31097 -8.403750  538.748
## 79483  -37.31069 -8.403750  538.945
## 79484  -37.31041 -8.403750  539.166
## 79485  -37.31013 -8.403750  539.347
## 79486  -37.30986 -8.403750  539.326
## 79487  -37.30958 -8.403750  539.326
## 79488  -37.30930 -8.403750  539.569
## 79489  -37.30902 -8.403750  540.050
## 79490  -37.30875 -8.403750  540.649
## 79491  -37.30847 -8.403750  541.141
## 79492  -37.30819 -8.403750  541.415
## 79493  -37.30791 -8.403750  541.387
## 79494  -37.30763 -8.403750  541.048
## 79495  -37.30736 -8.403750  540.392
## 79496  -37.30708 -8.403750  539.759
## 79497  -37.30680 -8.403750  539.470
## 79498  -37.30652 -8.403750  539.673
## 79499  -37.30625 -8.403750  540.367
## 79500  -37.30597 -8.403750  541.673
## 79501  -37.30569 -8.403750  542.844
## 79502  -37.30541 -8.403750  544.309
## 79503  -37.30513 -8.403750  545.666
## 79504  -37.30486 -8.403750  546.730
## 79505  -37.30458 -8.403750  547.410
## 79506  -37.30430 -8.403750  547.592
## 79507  -37.30402 -8.403750  547.342
## 79508  -37.30375 -8.403750  546.649
## 79509  -37.30347 -8.403750  545.568
## 79510  -37.30319 -8.403750  544.547
## 79511  -37.30291 -8.403750  543.792
## 79512  -37.30263 -8.403750  544.020
## 79513  -37.30236 -8.403750  545.472
## 79514  -37.30208 -8.403750  547.416
## 79515  -37.30180 -8.403750  549.022
## 79516  -37.30152 -8.403750  549.043
## 79517  -37.30125 -8.403750  548.667
## 79518  -37.30097 -8.403750  548.169
## 79519  -37.30069 -8.403750  547.932
## 79520  -37.30041 -8.403750  547.841
## 79521  -37.30013 -8.403750  547.760
## 79522  -37.29986 -8.403750  547.563
## 79523  -37.29958 -8.403750  547.300
## 79524  -37.29930 -8.403750  546.696
## 79525  -37.29902 -8.403750  546.420
## 79526  -37.29875 -8.403750  546.061
## 79527  -37.29847 -8.403750  545.980
## 79528  -37.29819 -8.403750  546.653
## 79529  -37.29791 -8.403750  547.485
## 79530  -37.29763 -8.403750  548.203
## 79531  -37.29736 -8.403750  548.372
## 79532  -37.29708 -8.403750  548.452
## 79533  -37.29680 -8.403750  548.615
## 79534  -37.29652 -8.403750  549.413
## 79535  -37.29625 -8.403750  550.222
## 79536  -37.29597 -8.403750  550.824
## 79537  -37.29569 -8.403750  550.601
## 79538  -37.29541 -8.403750  550.221
## 79539  -37.29513 -8.403750  550.014
## 79540  -37.29486 -8.403750  550.208
## 79541  -37.29458 -8.403750  550.460
## 79542  -37.29430 -8.403750  550.248
## 79543  -37.29402 -8.403750  549.702
## 79544  -37.29375 -8.403750  548.942
## 79545  -37.29347 -8.403750  548.184
## 79546  -37.29319 -8.403750  548.523
## 79547  -37.29291 -8.403750  548.923
## 79548  -37.29263 -8.403750  549.337
## 79549  -37.29236 -8.403750  549.505
## 79550  -37.29208 -8.403750  549.624
## 79551  -37.29180 -8.403750  549.874
## 79552  -37.29152 -8.403750  550.084
## 79553  -37.29125 -8.403750  550.402
## 79554  -37.29097 -8.403750  550.881
## 79555  -37.29069 -8.403750  550.867
## 79556  -37.29041 -8.403750  550.884
## 79557  -37.29013 -8.403750  550.728
## 79558  -37.28986 -8.403750  550.355
## 79559  -37.28958 -8.403750  549.958
## 79560  -37.28930 -8.403750  549.718
## 79561  -37.28902 -8.403750  549.572
## 79562  -37.28875 -8.403750  549.869
## 79563  -37.28847 -8.403750  550.675
## 79564  -37.28819 -8.403750  552.039
## 79565  -37.28791 -8.403750  553.611
## 79566  -37.28763 -8.403750  554.992
## 79567  -37.28736 -8.403750  555.858
## 79568  -37.28708 -8.403750  556.279
## 79569  -37.28680 -8.403750  556.342
## 79570  -37.28652 -8.403750  555.956
## 79571  -37.28625 -8.403750  555.567
## 79572  -37.28597 -8.403750  555.100
## 79573  -37.28569 -8.403750  555.639
## 79574  -37.28541 -8.403750  556.311
## 79575  -37.28513 -8.403750  557.294
## 79576  -37.28486 -8.403750  558.600
## 79577  -37.28458 -8.403750  560.162
## 79578  -37.28430 -8.403750  562.128
## 79579  -37.28402 -8.403750  563.920
## 79580  -37.28375 -8.403750  565.591
## 79581  -37.28347 -8.403750  566.826
## 79582  -37.28319 -8.403750  566.884
## 79583  -37.28291 -8.403750  566.548
## 79584  -37.28263 -8.403750  566.009
## 79585  -37.28236 -8.403750  565.572
## 79586  -37.28208 -8.403750  565.370
## 79587  -37.28180 -8.403750  565.497
## 79588  -37.28152 -8.403750  566.322
## 79589  -37.28125 -8.403750  567.152
## 79590  -37.28097 -8.403750  567.840
## 79591  -37.28069 -8.403750  567.702
## 79592  -37.28041 -8.403750  567.271
## 79593  -37.28013 -8.403750  566.578
## 79594  -37.27986 -8.403750  565.738
## 79595  -37.27958 -8.403750  564.949
## 79596  -37.27930 -8.403750  564.284
## 79597  -37.27902 -8.403750  564.255
## 79598  -37.27875 -8.403750  564.462
## 79599  -37.27847 -8.403750  565.153
## 79600  -37.27819 -8.403750  565.659
## 79601  -37.27791 -8.403750  566.201
## 79602  -37.27763 -8.403750  566.288
## 79603  -37.27736 -8.403750  565.481
## 79604  -37.27708 -8.403750  564.582
## 79605  -37.27680 -8.403750  563.911
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## 79609  -37.27569 -8.403750  567.194
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## 79611  -37.27513 -8.403750  567.153
## 79612  -37.27486 -8.403750  566.899
## 79613  -37.27458 -8.403750  566.654
## 79614  -37.27430 -8.403750  566.622
## 79615  -37.27402 -8.403750  566.869
## 79616  -37.27375 -8.403750  567.160
## 79617  -37.27347 -8.403750  567.253
## 79618  -37.27319 -8.403750  566.981
## 79619  -37.27291 -8.403750  566.420
## 79620  -37.27263 -8.403750  565.673
## 79621  -37.27236 -8.403750  564.828
## 79622  -37.27208 -8.403750  564.010
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## 79624  -37.27152 -8.403750  563.011
## 79625  -37.27125 -8.403750  562.870
## 79626  -37.27097 -8.403750  562.807
## 79627  -37.27069 -8.403750  563.061
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## 79632  -37.26930 -8.403750  563.557
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## 79639  -37.26736 -8.403750  559.852
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## 79642  -37.26652 -8.403750  563.847
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## 79652  -37.26375 -8.403750  557.076
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## 79658  -37.26208 -8.403750  558.610
## 79659  -37.26180 -8.403750  558.451
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## 79661  -37.26125 -8.403750  558.305
## 79662  -37.26097 -8.403750  558.427
## 79663  -37.26069 -8.403750  558.053
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## 79665  -37.26013 -8.403750  557.002
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## 79668  -37.25930 -8.403750  554.494
## 79669  -37.25902 -8.403750  553.982
## 79670  -37.25875 -8.403750  553.812
## 79671  -37.25847 -8.403750  553.841
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## 79676  -37.25708 -8.403750  556.832
## 79677  -37.25680 -8.403750  557.598
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## 79698  -37.25097 -8.403750  570.067
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## 79728  -37.24263 -8.403750  580.616
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## 79730  -37.24208 -8.403750  580.754
## 79731  -37.24180 -8.403750  580.785
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## 79733  -37.24125 -8.403750  581.279
## 79734  -37.24097 -8.403750  581.950
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## 79741  -37.23902 -8.403750  583.813
## 79742  -37.23875 -8.403750  583.441
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## 79744  -37.23819 -8.403750  582.850
## 79745  -37.23791 -8.403750  582.538
## 79746  -37.23763 -8.403750  582.106
## 79747  -37.23736 -8.403750  581.496
## 79748  -37.23708 -8.403750  580.768
## 79749  -37.23680 -8.403750  580.113
## 79750  -37.23652 -8.403750  579.133
## 79751  -37.23625 -8.403750  578.192
## 79752  -37.23597 -8.403750  577.041
## 79753  -37.23569 -8.403750  575.924
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## 79758  -37.23430 -8.403750  570.257
## 79759  -37.23402 -8.403750  569.588
## 79760  -37.23375 -8.403750  569.082
## 79761  -37.23347 -8.403750  569.054
## 79762  -37.23319 -8.403750  568.768
## 79763  -37.23291 -8.403750  568.927
## 79764  -37.23263 -8.403750  569.342
## 79765  -37.23236 -8.403750  569.993
## 79766  -37.23208 -8.403750  570.565
## 79767  -37.23180 -8.403750  570.542
## 79768  -37.23152 -8.403750  570.392
## 79769  -37.23125 -8.403750  569.712
## 79770  -37.23097 -8.403750  568.689
## 79771  -37.23069 -8.403750  567.973
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## 79776  -37.22930 -8.403750  566.182
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## 80674  -37.35625 -8.404028  524.890
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## 80681  -37.35430 -8.404028  524.033
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## 80683  -37.35375 -8.404028  523.756
## 80684  -37.35347 -8.404028  523.283
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## 80686  -37.35291 -8.404028  522.078
## 80687  -37.35263 -8.404028  521.799
## 80688  -37.35236 -8.404028  521.974
## 80689  -37.35208 -8.404028  522.250
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## 80692  -37.35125 -8.404028  523.901
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## 80712  -37.34569 -8.404028  526.501
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## 80717  -37.34430 -8.404028  526.959
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## 80719  -37.34375 -8.404028  526.348
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## 80724  -37.34236 -8.404028  525.429
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## 80727  -37.34152 -8.404028  528.231
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## 80740  -37.33791 -8.404028  528.491
## 80741  -37.33763 -8.404028  528.504
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## 80743  -37.33708 -8.404028  528.491
## 80744  -37.33680 -8.404028  528.524
## 80745  -37.33652 -8.404028  528.333
## 80746  -37.33625 -8.404028  528.049
## 80747  -37.33597 -8.404028  527.834
## 80748  -37.33569 -8.404028  527.856
## 80749  -37.33541 -8.404028  528.161
## 80750  -37.33513 -8.404028  528.552
## 80751  -37.33486 -8.404028  529.464
## 80752  -37.33458 -8.404028  530.318
## 80753  -37.33430 -8.404028  531.076
## 80754  -37.33402 -8.404028  531.135
## 80755  -37.33375 -8.404028  530.840
## 80756  -37.33347 -8.404028  530.463
## 80757  -37.33319 -8.404028  530.552
## 80758  -37.33291 -8.404028  530.569
## 80759  -37.33263 -8.404028  530.872
## 80760  -37.33236 -8.404028  531.379
## 80761  -37.33208 -8.404028  531.791
## 80762  -37.33180 -8.404028  532.299
## 80763  -37.33152 -8.404028  532.256
## 80764  -37.33125 -8.404028  532.315
## 80765  -37.33097 -8.404028  532.439
## 80766  -37.33069 -8.404028  532.742
## 80767  -37.33041 -8.404028  532.913
## 80768  -37.33013 -8.404028  533.132
## 80769  -37.32986 -8.404028  532.787
## 80770  -37.32958 -8.404028  532.508
## 80771  -37.32930 -8.404028  532.453
## 80772  -37.32902 -8.404028  532.636
## 80773  -37.32875 -8.404028  532.856
## 80774  -37.32847 -8.404028  533.237
## 80775  -37.32819 -8.404028  533.261
## 80776  -37.32791 -8.404028  533.398
## 80777  -37.32763 -8.404028  533.311
## 80778  -37.32736 -8.404028  533.336
## 80779  -37.32708 -8.404028  533.595
## 80780  -37.32680 -8.404028  534.199
## 80781  -37.32652 -8.404028  534.850
## 80782  -37.32625 -8.404028  535.287
## 80783  -37.32597 -8.404028  535.450
## 80784  -37.32569 -8.404028  535.303
## 80785  -37.32541 -8.404028  535.170
## 80786  -37.32513 -8.404028  535.030
## 80787  -37.32486 -8.404028  535.571
## 80788  -37.32458 -8.404028  536.430
## 80789  -37.32430 -8.404028  537.446
## 80790  -37.32402 -8.404028  538.836
## 80791  -37.32375 -8.404028  540.060
## 80792  -37.32347 -8.404028  540.856
## 80793  -37.32319 -8.404028  541.001
## 80794  -37.32291 -8.404028  540.771
## 80795  -37.32263 -8.404028  540.500
## 80796  -37.32236 -8.404028  540.114
## 80797  -37.32208 -8.404028  539.722
## 80798  -37.32180 -8.404028  539.347
## 80799  -37.32152 -8.404028  539.119
## 80800  -37.32125 -8.404028  539.050
## 80801  -37.32097 -8.404028  539.003
## 80802  -37.32069 -8.404028  538.536
## 80803  -37.32041 -8.404028  538.086
## 80804  -37.32013 -8.404028  537.584
## 80805  -37.31986 -8.404028  537.263
## 80806  -37.31958 -8.404028  537.048
## 80807  -37.31930 -8.404028  536.727
## 80808  -37.31902 -8.404028  536.982
## 80809  -37.31875 -8.404028  537.296
## 80810  -37.31847 -8.404028  537.997
## 80811  -37.31819 -8.404028  538.438
## 80812  -37.31791 -8.404028  538.856
## 80813  -37.31763 -8.404028  539.550
## 80814  -37.31736 -8.404028  540.542
## 80815  -37.31708 -8.404028  541.679
## 80816  -37.31680 -8.404028  543.010
## 80817  -37.31652 -8.404028  543.998
## 80818  -37.31625 -8.404028  544.873
## 80819  -37.31597 -8.404028  545.484
## 80820  -37.31569 -8.404028  545.463
## 80821  -37.31541 -8.404028  545.114
## 80822  -37.31513 -8.404028  544.659
## 80823  -37.31486 -8.404028  544.687
## 80824  -37.31458 -8.404028  544.733
## 80825  -37.31430 -8.404028  544.588
## 80826  -37.31402 -8.404028  544.091
## 80827  -37.31375 -8.404028  543.451
## 80828  -37.31347 -8.404028  542.760
## 80829  -37.31319 -8.404028  542.202
## 80830  -37.31291 -8.404028  541.735
## 80831  -37.31263 -8.404028  541.682
## 80832  -37.31236 -8.404028  541.666
## 80833  -37.31208 -8.404028  541.714
## 80834  -37.31180 -8.404028  541.071
## 80835  -37.31152 -8.404028  540.364
## 80836  -37.31125 -8.404028  539.711
## 80837  -37.31097 -8.404028  539.130
## 80838  -37.31069 -8.404028  539.077
## 80839  -37.31041 -8.404028  539.228
## 80840  -37.31013 -8.404028  539.726
## 80841  -37.30986 -8.404028  540.038
## 80842  -37.30958 -8.404028  540.404
## 80843  -37.30930 -8.404028  540.648
## 80844  -37.30902 -8.404028  541.295
## 80845  -37.30875 -8.404028  541.993
## 80846  -37.30847 -8.404028  542.507
## 80847  -37.30819 -8.404028  542.714
## 80848  -37.30791 -8.404028  542.696
## 80849  -37.30763 -8.404028  542.557
## 80850  -37.30736 -8.404028  542.085
## 80851  -37.30708 -8.404028  541.588
## 80852  -37.30680 -8.404028  541.152
## 80853  -37.30652 -8.404028  541.039
## 80854  -37.30625 -8.404028  541.378
## 80855  -37.30597 -8.404028  541.826
## 80856  -37.30569 -8.404028  542.779
## 80857  -37.30541 -8.404028  544.092
## 80858  -37.30513 -8.404028  545.388
## 80859  -37.30486 -8.404028  546.510
## 80860  -37.30458 -8.404028  547.359
## 80861  -37.30430 -8.404028  547.788
## 80862  -37.30402 -8.404028  547.744
## 80863  -37.30375 -8.404028  547.340
## 80864  -37.30347 -8.404028  546.629
## 80865  -37.30319 -8.404028  545.773
## 80866  -37.30291 -8.404028  545.104
## 80867  -37.30263 -8.404028  545.360
## 80868  -37.30236 -8.404028  546.846
## 80869  -37.30208 -8.404028  548.661
## 80870  -37.30180 -8.404028  549.985
## 80871  -37.30152 -8.404028  549.875
## 80872  -37.30125 -8.404028  549.283
## 80873  -37.30097 -8.404028  548.610
## 80874  -37.30069 -8.404028  548.309
## 80875  -37.30041 -8.404028  548.177
## 80876  -37.30013 -8.404028  548.020
## 80877  -37.29986 -8.404028  547.926
## 80878  -37.29958 -8.404028  547.800
## 80879  -37.29930 -8.404028  547.495
## 80880  -37.29902 -8.404028  547.083
## 80881  -37.29875 -8.404028  546.725
## 80882  -37.29847 -8.404028  546.917
## 80883  -37.29819 -8.404028  547.746
## 80884  -37.29791 -8.404028  548.649
## 80885  -37.29763 -8.404028  549.460
## 80886  -37.29736 -8.404028  549.330
## 80887  -37.29708 -8.404028  549.150
## 80888  -37.29680 -8.404028  549.008
## 80889  -37.29652 -8.404028  549.479
## 80890  -37.29625 -8.404028  550.368
## 80891  -37.29597 -8.404028  551.256
## 80892  -37.29569 -8.404028  551.142
## 80893  -37.29541 -8.404028  550.752
## 80894  -37.29513 -8.404028  550.156
## 80895  -37.29486 -8.404028  550.306
## 80896  -37.29458 -8.404028  550.515
## 80897  -37.29430 -8.404028  550.319
## 80898  -37.29402 -8.404028  549.578
## 80899  -37.29375 -8.404028  548.868
## 80900  -37.29347 -8.404028  548.487
## 80901  -37.29319 -8.404028  548.877
## 80902  -37.29291 -8.404028  549.410
## 80903  -37.29263 -8.404028  550.087
## 80904  -37.29236 -8.404028  550.527
## 80905  -37.29208 -8.404028  550.977
## 80906  -37.29180 -8.404028  551.298
## 80907  -37.29152 -8.404028  551.539
## 80908  -37.29125 -8.404028  551.755
## 80909  -37.29097 -8.404028  551.521
## 80910  -37.29069 -8.404028  551.338
## 80911  -37.29041 -8.404028  551.200
## 80912  -37.29013 -8.404028  550.843
## 80913  -37.28986 -8.404028  550.411
## 80914  -37.28958 -8.404028  549.898
## 80915  -37.28930 -8.404028  549.781
## 80916  -37.28902 -8.404028  549.953
## 80917  -37.28875 -8.404028  550.062
## 80918  -37.28847 -8.404028  550.540
## 80919  -37.28819 -8.404028  551.616
## 80920  -37.28791 -8.404028  552.874
## 80921  -37.28763 -8.404028  553.906
## 80922  -37.28736 -8.404028  554.320
## 80923  -37.28708 -8.404028  554.461
## 80924  -37.28680 -8.404028  554.384
## 80925  -37.28652 -8.404028  554.052
## 80926  -37.28625 -8.404028  553.724
## 80927  -37.28597 -8.404028  553.528
## 80928  -37.28569 -8.404028  554.085
## 80929  -37.28541 -8.404028  554.951
## 80930  -37.28513 -8.404028  556.673
## 80931  -37.28486 -8.404028  558.461
## 80932  -37.28458 -8.404028  560.455
## 80933  -37.28430 -8.404028  562.158
## 80934  -37.28402 -8.404028  564.068
## 80935  -37.28375 -8.404028  565.654
## 80936  -37.28347 -8.404028  566.519
## 80937  -37.28319 -8.404028  566.318
## 80938  -37.28291 -8.404028  565.766
## 80939  -37.28263 -8.404028  565.031
## 80940  -37.28236 -8.404028  564.610
## 80941  -37.28208 -8.404028  564.415
## 80942  -37.28180 -8.404028  564.623
## 80943  -37.28152 -8.404028  565.443
## 80944  -37.28125 -8.404028  566.393
## 80945  -37.28097 -8.404028  567.195
## 80946  -37.28069 -8.404028  567.512
## 80947  -37.28041 -8.404028  567.397
## 80948  -37.28013 -8.404028  566.756
## 80949  -37.27986 -8.404028  565.960
## 80950  -37.27958 -8.404028  565.008
## 80951  -37.27930 -8.404028  565.186
## 80952  -37.27902 -8.404028  565.361
## 80953  -37.27875 -8.404028  565.548
## 80954  -37.27847 -8.404028  565.985
## 80955  -37.27819 -8.404028  566.422
## 80956  -37.27791 -8.404028  566.784
## 80957  -37.27763 -8.404028  566.260
## 80958  -37.27736 -8.404028  565.054
## 80959  -37.27708 -8.404028  564.061
## 80960  -37.27680 -8.404028  564.058
## 80961  -37.27652 -8.404028  564.981
## 80962  -37.27625 -8.404028  565.896
## 80963  -37.27597 -8.404028  566.618
## 80964  -37.27569 -8.404028  566.817
## 80965  -37.27541 -8.404028  566.865
## 80966  -37.27513 -8.404028  566.519
## 80967  -37.27486 -8.404028  566.113
## 80968  -37.27458 -8.404028  565.818
## 80969  -37.27430 -8.404028  565.934
## 80970  -37.27402 -8.404028  566.452
## 80971  -37.27375 -8.404028  566.897
## 80972  -37.27347 -8.404028  567.068
## 80973  -37.27319 -8.404028  566.777
## 80974  -37.27291 -8.404028  566.320
## 80975  -37.27263 -8.404028  565.804
## 80976  -37.27236 -8.404028  565.265
## 80977  -37.27208 -8.404028  564.750
## 80978  -37.27180 -8.404028  564.229
## 80979  -37.27152 -8.404028  564.207
## 80980  -37.27125 -8.404028  564.242
## 80981  -37.27097 -8.404028  564.550
## 80982  -37.27069 -8.404028  564.795
## 80983  -37.27041 -8.404028  565.019
## 80984  -37.27013 -8.404028  565.231
## 80985  -37.26986 -8.404028  565.241
## 80986  -37.26958 -8.404028  565.103
## 80987  -37.26930 -8.404028  564.719
## 80988  -37.26902 -8.404028  564.226
## 80989  -37.26875 -8.404028  563.620
## 80990  -37.26847 -8.404028  562.844
## 80991  -37.26819 -8.404028  561.537
## 80992  -37.26791 -8.404028  560.463
## 80993  -37.26763 -8.404028  559.711
## 80994  -37.26736 -8.404028  559.996
## 80995  -37.26708 -8.404028  560.961
## 80996  -37.26680 -8.404028  562.506
## 80997  -37.26652 -8.404028  564.383
## 80998  -37.26625 -8.404028  565.820
## 80999  -37.26597 -8.404028  566.497
## 81000  -37.26569 -8.404028  565.832
## 81001  -37.26541 -8.404028  564.604
## 81002  -37.26513 -8.404028  563.020
## 81003  -37.26486 -8.404028  561.594
## 81004  -37.26458 -8.404028  560.422
## 81005  -37.26430 -8.404028  559.308
## 81006  -37.26402 -8.404028  558.213
## 81007  -37.26375 -8.404028  557.524
## 81008  -37.26347 -8.404028  556.792
## 81009  -37.26319 -8.404028  557.120
## 81010  -37.26291 -8.404028  557.715
## 81011  -37.26263 -8.404028  558.562
## 81012  -37.26236 -8.404028  558.986
## 81013  -37.26208 -8.404028  559.207
## 81014  -37.26180 -8.404028  559.168
## 81015  -37.26152 -8.404028  559.411
## 81016  -37.26125 -8.404028  559.288
## 81017  -37.26097 -8.404028  558.783
## 81018  -37.26069 -8.404028  558.220
## 81019  -37.26041 -8.404028  557.750
## 81020  -37.26013 -8.404028  557.183
## 81021  -37.25986 -8.404028  556.296
## 81022  -37.25958 -8.404028  555.257
## 81023  -37.25930 -8.404028  554.403
## 81024  -37.25902 -8.404028  553.823
## 81025  -37.25875 -8.404028  553.457
## 81026  -37.25847 -8.404028  553.146
## 81027  -37.25819 -8.404028  553.498
## 81028  -37.25791 -8.404028  554.102
## 81029  -37.25763 -8.404028  555.206
## 81030  -37.25736 -8.404028  556.502
## 81031  -37.25708 -8.404028  557.584
## 81032  -37.25680 -8.404028  558.815
## 81033  -37.25652 -8.404028  559.537
## 81034  -37.25625 -8.404028  560.153
## 81035  -37.25597 -8.404028  560.618
## 81036  -37.25569 -8.404028  561.251
## 81037  -37.25541 -8.404028  562.036
## 81038  -37.25513 -8.404028  562.670
## 81039  -37.25486 -8.404028  563.185
## 81040  -37.25458 -8.404028  563.764
## 81041  -37.25430 -8.404028  564.609
## 81042  -37.25402 -8.404028  565.900
## 81043  -37.25375 -8.404028  566.848
## 81044  -37.25347 -8.404028  567.596
## 81045  -37.25319 -8.404028  568.020
## 81046  -37.25291 -8.404028  568.406
## 81047  -37.25263 -8.404028  568.482
## 81048  -37.25236 -8.404028  568.468
## 81049  -37.25208 -8.404028  568.526
## 81050  -37.25180 -8.404028  568.955
## 81051  -37.25152 -8.404028  569.578
## 81052  -37.25125 -8.404028  569.965
## 81053  -37.25097 -8.404028  569.989
## 81054  -37.25069 -8.404028  569.399
## 81055  -37.25041 -8.404028  568.652
## 81056  -37.25013 -8.404028  567.847
## 81057  -37.24986 -8.404028  567.244
## 81058  -37.24958 -8.404028  566.987
## 81059  -37.24930 -8.404028  567.285
## 81060  -37.24902 -8.404028  568.195
## 81061  -37.24875 -8.404028  569.245
## 81062  -37.24847 -8.404028  570.161
## 81063  -37.24819 -8.404028  570.635
## 81064  -37.24791 -8.404028  570.978
## 81065  -37.24763 -8.404028  571.242
## 81066  -37.24736 -8.404028  571.891
## 81067  -37.24708 -8.404028  572.536
## 81068  -37.24680 -8.404028  573.330
## 81069  -37.24652 -8.404028  574.012
## 81070  -37.24625 -8.404028  574.862
## 81071  -37.24597 -8.404028  575.960
## 81072  -37.24569 -8.404028  577.816
## 81073  -37.24541 -8.404028  579.493
## 81074  -37.24513 -8.404028  580.695
## 81075  -37.24486 -8.404028  580.939
## 81076  -37.24458 -8.404028  580.695
## 81077  -37.24430 -8.404028  580.656
## 81078  -37.24402 -8.404028  581.003
## 81079  -37.24375 -8.404028  581.410
## 81080  -37.24347 -8.404028  581.685
## 81081  -37.24319 -8.404028  581.691
## 81082  -37.24291 -8.404028  581.677
## 81083  -37.24263 -8.404028  581.719
## 81084  -37.24236 -8.404028  581.881
## 81085  -37.24208 -8.404028  581.996
## 81086  -37.24180 -8.404028  582.288
## 81087  -37.24152 -8.404028  582.513
## 81088  -37.24125 -8.404028  582.790
## 81089  -37.24097 -8.404028  583.516
## 81090  -37.24069 -8.404028  584.775
## 81091  -37.24041 -8.404028  585.983
## 81092  -37.24013 -8.404028  586.677
## 81093  -37.23986 -8.404028  586.266
## 81094  -37.23958 -8.404028  585.635
## 81095  -37.23930 -8.404028  584.819
## 81096  -37.23902 -8.404028  584.293
## 81097  -37.23875 -8.404028  583.903
## 81098  -37.23847 -8.404028  583.705
## 81099  -37.23819 -8.404028  583.531
## 81100  -37.23791 -8.404028  583.190
## 81101  -37.23763 -8.404028  582.738
## 81102  -37.23736 -8.404028  581.887
## 81103  -37.23708 -8.404028  580.842
## 81104  -37.23680 -8.404028  579.580
## 81105  -37.23652 -8.404028  578.574
## 81106  -37.23625 -8.404028  577.576
## 81107  -37.23597 -8.404028  576.369
## 81108  -37.23569 -8.404028  575.152
## 81109  -37.23541 -8.404028  573.933
## 81110  -37.23513 -8.404028  573.037
## 81111  -37.23486 -8.404028  572.301
## 81112  -37.23458 -8.404028  571.566
## 81113  -37.23430 -8.404028  570.875
## 81114  -37.23402 -8.404028  570.208
## 81115  -37.23375 -8.404028  569.509
## 81116  -37.23347 -8.404028  568.821
## 81117  -37.23319 -8.404028  568.361
## 81118  -37.23291 -8.404028  568.407
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## 83645  -37.28375 -8.404583  564.318
## 83646  -37.28347 -8.404583  564.904
## 83647  -37.28319 -8.404583  564.748
## 83648  -37.28291 -8.404583  564.238
## 83649  -37.28263 -8.404583  563.673
## 83650  -37.28236 -8.404583  563.394
## 83651  -37.28208 -8.404583  563.367
## 83652  -37.28180 -8.404583  563.629
## 83653  -37.28152 -8.404583  564.148
## 83654  -37.28125 -8.404583  564.850
## 83655  -37.28097 -8.404583  565.651
## 83656  -37.28069 -8.404583  566.596
## 83657  -37.28041 -8.404583  567.282
## 83658  -37.28013 -8.404583  567.432
## 83659  -37.27986 -8.404583  566.668
## 83660  -37.27958 -8.404583  565.803
## 83661  -37.27930 -8.404583  565.443
## 83662  -37.27902 -8.404583  566.041
## 83663  -37.27875 -8.404583  566.913
## 83664  -37.27847 -8.404583  567.712
## 83665  -37.27819 -8.404583  567.839
## 83666  -37.27791 -8.404583  567.638
## 83667  -37.27763 -8.404583  567.134
## 83668  -37.27736 -8.404583  566.471
## 83669  -37.27708 -8.404583  565.855
## 83670  -37.27680 -8.404583  565.590
## 83671  -37.27652 -8.404583  565.850
## 83672  -37.27625 -8.404583  566.296
## 83673  -37.27597 -8.404583  566.740
## 83674  -37.27569 -8.404583  566.760
## 83675  -37.27541 -8.404583  566.657
## 83676  -37.27513 -8.404583  566.500
## 83677  -37.27486 -8.404583  566.438
## 83678  -37.27458 -8.404583  566.499
## 83679  -37.27430 -8.404583  566.786
## 83680  -37.27402 -8.404583  567.325
## 83681  -37.27375 -8.404583  567.844
## 83682  -37.27347 -8.404583  568.144
## 83683  -37.27319 -8.404583  567.881
## 83684  -37.27291 -8.404583  567.469
## 83685  -37.27263 -8.404583  567.153
## 83686  -37.27236 -8.404583  567.273
## 83687  -37.27208 -8.404583  567.473
## 83688  -37.27180 -8.404583  567.541
## 83689  -37.27152 -8.404583  567.301
## 83690  -37.27125 -8.404583  567.020
## 83691  -37.27097 -8.404583  566.826
## 83692  -37.27069 -8.404583  566.889
## 83693  -37.27041 -8.404583  566.985
## 83694  -37.27013 -8.404583  566.985
## 83695  -37.26986 -8.404583  566.769
## 83696  -37.26958 -8.404583  566.341
## 83697  -37.26930 -8.404583  565.676
## 83698  -37.26902 -8.404583  564.778
## 83699  -37.26875 -8.404583  563.710
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## 83701  -37.26819 -8.404583  561.424
## 83702  -37.26791 -8.404583  560.593
## 83703  -37.26763 -8.404583  560.375
## 83704  -37.26736 -8.404583  561.048
## 83705  -37.26708 -8.404583  562.254
## 83706  -37.26680 -8.404583  563.763
## 83707  -37.26652 -8.404583  565.277
## 83708  -37.26625 -8.404583  566.371
## 83709  -37.26597 -8.404583  566.736
## 83710  -37.26569 -8.404583  565.833
## 83711  -37.26541 -8.404583  564.398
## 83712  -37.26513 -8.404583  562.856
## 83713  -37.26486 -8.404583  561.740
## 83714  -37.26458 -8.404583  560.793
## 83715  -37.26430 -8.404583  559.933
## 83716  -37.26402 -8.404583  559.072
## 83717  -37.26375 -8.404583  558.390
## 83718  -37.26347 -8.404583  557.940
## 83719  -37.26319 -8.404583  557.767
## 83720  -37.26291 -8.404583  557.926
## 83721  -37.26263 -8.404583  558.486
## 83722  -37.26236 -8.404583  559.580
## 83723  -37.26208 -8.404583  560.608
## 83724  -37.26180 -8.404583  561.520
## 83725  -37.26152 -8.404583  560.866
## 83726  -37.26125 -8.404583  560.032
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## 83728  -37.26069 -8.404583  558.395
## 83729  -37.26041 -8.404583  557.791
## 83730  -37.26013 -8.404583  557.175
## 83731  -37.25986 -8.404583  556.448
## 83732  -37.25958 -8.404583  555.683
## 83733  -37.25930 -8.404583  554.918
## 83734  -37.25902 -8.404583  554.230
## 83735  -37.25875 -8.404583  553.784
## 83736  -37.25847 -8.404583  553.702
## 83737  -37.25819 -8.404583  554.193
## 83738  -37.25791 -8.404583  555.050
## 83739  -37.25763 -8.404583  556.171
## 83740  -37.25736 -8.404583  557.419
## 83741  -37.25708 -8.404583  558.628
## 83742  -37.25680 -8.404583  559.608
## 83743  -37.25652 -8.404583  560.193
## 83744  -37.25625 -8.404583  560.710
## 83745  -37.25597 -8.404583  561.323
## 83746  -37.25569 -8.404583  562.366
## 83747  -37.25541 -8.404583  563.495
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## 83749  -37.25486 -8.404583  565.423
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## 83751  -37.25430 -8.404583  566.548
## 83752  -37.25402 -8.404583  566.963
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## 83756  -37.25291 -8.404583  568.314
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## 83758  -37.25236 -8.404583  569.129
## 83759  -37.25208 -8.404583  569.523
## 83760  -37.25180 -8.404583  569.984
## 83761  -37.25152 -8.404583  570.496
## 83762  -37.25125 -8.404583  570.868
## 83763  -37.25097 -8.404583  570.936
## 83764  -37.25069 -8.404583  570.463
## 83765  -37.25041 -8.404583  569.750
## 83766  -37.25013 -8.404583  568.994
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## 83771  -37.24875 -8.404583  569.146
## 83772  -37.24847 -8.404583  569.845
## 83773  -37.24819 -8.404583  570.448
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## 83782  -37.24569 -8.404583  579.019
## 83783  -37.24541 -8.404583  581.284
## 83784  -37.24513 -8.404583  582.833
## 83785  -37.24486 -8.404583  582.998
## 83786  -37.24458 -8.404583  582.639
## 83787  -37.24430 -8.404583  582.289
## 83788  -37.24402 -8.404583  582.366
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## 83790  -37.24347 -8.404583  582.973
## 83791  -37.24319 -8.404583  583.314
## 83792  -37.24291 -8.404583  583.680
## 83793  -37.24263 -8.404583  584.075
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## 83796  -37.24180 -8.404583  585.311
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## 83798  -37.24125 -8.404583  585.607
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## 84861  -37.32236 -8.404861  541.753
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## 84863  -37.32180 -8.404861  541.517
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## 84868  -37.32041 -8.404861  540.988
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## 84870  -37.31986 -8.404861  541.701
## 84871  -37.31958 -8.404861  542.116
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## 84873  -37.31902 -8.404861  542.154
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## 84875  -37.31847 -8.404861  541.007
## 84876  -37.31819 -8.404861  540.821
## 84877  -37.31791 -8.404861  541.088
## 84878  -37.31763 -8.404861  541.378
## 84879  -37.31736 -8.404861  541.691
## 84880  -37.31708 -8.404861  542.171
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## 84886  -37.31541 -8.404861  548.420
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## 84890  -37.31430 -8.404861  547.510
## 84891  -37.31402 -8.404861  546.776
## 84892  -37.31375 -8.404861  546.074
## 84893  -37.31347 -8.404861  545.075
## 84894  -37.31319 -8.404861  544.321
## 84895  -37.31291 -8.404861  543.806
## 84896  -37.31263 -8.404861  543.553
## 84897  -37.31236 -8.404861  543.956
## 84898  -37.31208 -8.404861  544.240
## 84899  -37.31180 -8.404861  544.475
## 84900  -37.31152 -8.404861  543.607
## 84901  -37.31125 -8.404861  542.403
## 84902  -37.31097 -8.404861  541.284
## 84903  -37.31069 -8.404861  540.822
## 84904  -37.31041 -8.404861  540.681
## 84905  -37.31013 -8.404861  540.917
## 84906  -37.30986 -8.404861  541.550
## 84907  -37.30958 -8.404861  542.569
## 84908  -37.30930 -8.404861  543.418
## 84909  -37.30902 -8.404861  544.364
## 84910  -37.30875 -8.404861  545.009
## 84911  -37.30847 -8.404861  545.293
## 84912  -37.30819 -8.404861  545.344
## 84913  -37.30791 -8.404861  545.013
## 84914  -37.30763 -8.404861  544.723
## 84915  -37.30736 -8.404861  544.449
## 84916  -37.30708 -8.404861  544.233
## 84917  -37.30680 -8.404861  543.671
## 84918  -37.30652 -8.404861  543.075
## 84919  -37.30625 -8.404861  542.805
## 84920  -37.30597 -8.404861  542.881
## 84921  -37.30569 -8.404861  543.617
## 84922  -37.30541 -8.404861  544.609
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## 84926  -37.30430 -8.404861  549.683
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## 84929  -37.30347 -8.404861  550.953
## 84930  -37.30319 -8.404861  550.453
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## 84936  -37.30152 -8.404861  551.103
## 84937  -37.30125 -8.404861  550.964
## 84938  -37.30097 -8.404861  550.519
## 84939  -37.30069 -8.404861  550.174
## 84940  -37.30041 -8.404861  549.773
## 84941  -37.30013 -8.404861  549.683
## 84942  -37.29986 -8.404861  550.034
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## 84944  -37.29930 -8.404861  550.349
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## 84950  -37.29763 -8.404861  550.346
## 84951  -37.29736 -8.404861  550.172
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## 84953  -37.29680 -8.404861  549.712
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## 84966  -37.29319 -8.404861  551.089
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## 84968  -37.29263 -8.404861  551.561
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## 84970  -37.29208 -8.404861  553.891
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## 84980  -37.28930 -8.404861  552.590
## 84981  -37.28902 -8.404861  552.450
## 84982  -37.28875 -8.404861  552.567
## 84983  -37.28847 -8.404861  552.725
## 84984  -37.28819 -8.404861  552.719
## 84985  -37.28791 -8.404861  552.755
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## 84989  -37.28680 -8.404861  552.511
## 84990  -37.28652 -8.404861  552.982
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## 85008  -37.28152 -8.404861  563.519
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## 85010  -37.28097 -8.404861  565.055
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## 85161  -37.23902 -8.404861  584.974
## 85162  -37.23875 -8.404861  584.975
## 85163  -37.23847 -8.404861  584.923
## 85164  -37.23819 -8.404861  584.618
## 85165  -37.23791 -8.404861  584.016
## 85166  -37.23763 -8.404861  582.831
## 85167  -37.23736 -8.404861  581.294
## 85168  -37.23708 -8.404861  579.551
## 85169  -37.23680 -8.404861  578.196
## 85170  -37.23652 -8.404861  576.988
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## 85172  -37.23597 -8.404861  575.064
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## 85176  -37.23486 -8.404861  570.911
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## 85186  -37.23208 -8.404861  570.988
## 85187  -37.23180 -8.404861  572.448
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## 85203  -37.22736 -8.404861  570.783
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## 85206  -37.22652 -8.404861  572.490
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## 85208  -37.22597 -8.404861  572.988
## 85209  -37.22569 -8.404861  572.964
## 85210  -37.22541 -8.404861  572.410
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## 85212  -37.22486 -8.404861  569.724
## 85213  -37.22458 -8.404861  568.084
## 85214  -37.22430 -8.404861  566.951
## 85215  -37.22402 -8.404861  566.894
## 85216  -37.22375 -8.404861  567.668
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## 86088  -37.35791 -8.405139  523.200
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## 86090  -37.35736 -8.405139  523.059
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## 86107  -37.35263 -8.405139  528.456
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## 86109  -37.35208 -8.405139  527.828
## 86110  -37.35180 -8.405139  527.896
## 86111  -37.35152 -8.405139  528.561
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## 86113  -37.35097 -8.405139  530.099
## 86114  -37.35069 -8.405139  530.776
## 86115  -37.35041 -8.405139  531.136
## 86116  -37.35013 -8.405139  531.433
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## 86515  -37.23930 -8.405139  585.126
## 86516  -37.23902 -8.405139  585.075
## 86517  -37.23875 -8.405139  585.030
## 86518  -37.23847 -8.405139  584.899
## 86519  -37.23819 -8.405139  584.556
## 86520  -37.23791 -8.405139  583.884
## 86521  -37.23763 -8.405139  582.632
## 86522  -37.23736 -8.405139  580.900
## 86523  -37.23708 -8.405139  579.011
## 86524  -37.23680 -8.405139  577.520
## 86525  -37.23652 -8.405139  576.370
## 86526  -37.23625 -8.405139  575.419
## 86527  -37.23597 -8.405139  574.648
## 86528  -37.23569 -8.405139  573.868
## 86529  -37.23541 -8.405139  573.067
## 86530  -37.23513 -8.405139  572.028
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## 86532  -37.23458 -8.405139  570.070
## 86533  -37.23430 -8.405139  569.009
## 86534  -37.23402 -8.405139  568.217
## 86535  -37.23375 -8.405139  567.617
## 86536  -37.23347 -8.405139  567.199
## 86537  -37.23319 -8.405139  567.057
## 86538  -37.23291 -8.405139  567.194
## 86539  -37.23263 -8.405139  568.129
## 86540  -37.23236 -8.405139  569.450
## 86541  -37.23208 -8.405139  570.939
## 86542  -37.23180 -8.405139  572.313
## 86543  -37.23152 -8.405139  573.366
## 86544  -37.23125 -8.405139  573.914
## 86545  -37.23097 -8.405139  573.936
## 86546  -37.23069 -8.405139  573.662
## 86547  -37.23041 -8.405139  573.298
## 86548  -37.23013 -8.405139  572.789
## 86549  -37.22986 -8.405139  572.091
## 86550  -37.22958 -8.405139  571.412
## 86551  -37.22930 -8.405139  570.801
## 86552  -37.22902 -8.405139  570.492
## 86553  -37.22875 -8.405139  569.950
## 86554  -37.22847 -8.405139  569.461
## 86555  -37.22819 -8.405139  569.454
## 86556  -37.22791 -8.405139  569.718
## 86557  -37.22763 -8.405139  570.391
## 86558  -37.22736 -8.405139  571.400
## 86559  -37.22708 -8.405139  572.387
## 86560  -37.22680 -8.405139  573.337
## 86561  -37.22652 -8.405139  573.946
## 86562  -37.22625 -8.405139  574.385
## 86563  -37.22597 -8.405139  574.587
## 86564  -37.22569 -8.405139  574.506
## 86565  -37.22541 -8.405139  574.051
## 86566  -37.22513 -8.405139  572.931
## 86567  -37.22486 -8.405139  571.217
## 86568  -37.22458 -8.405139  569.618
## 86569  -37.22430 -8.405139  568.065
## 86570  -37.22402 -8.405139  567.470
## 86571  -37.22375 -8.405139  567.229
## 87427  -37.36236 -8.405417  523.114
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## 87429  -37.36180 -8.405417  523.405
## 87430  -37.36152 -8.405417  523.724
## 87431  -37.36125 -8.405417  524.056
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## 87433  -37.36069 -8.405417  524.214
## 87434  -37.36041 -8.405417  524.013
## 87435  -37.36013 -8.405417  523.617
## 87436  -37.35986 -8.405417  523.288
## 87437  -37.35958 -8.405417  523.008
## 87438  -37.35930 -8.405417  523.065
## 87439  -37.35902 -8.405417  523.659
## 87440  -37.35875 -8.405417  524.391
## 87441  -37.35847 -8.405417  524.743
## 87442  -37.35819 -8.405417  524.180
## 87443  -37.35791 -8.405417  523.309
## 87444  -37.35763 -8.405417  522.715
## 87445  -37.35736 -8.405417  522.790
## 87446  -37.35708 -8.405417  523.337
## 87447  -37.35680 -8.405417  524.204
## 87448  -37.35652 -8.405417  524.792
## 87449  -37.35625 -8.405417  525.508
## 87450  -37.35597 -8.405417  526.090
## 87451  -37.35569 -8.405417  526.783
## 87452  -37.35541 -8.405417  527.342
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## 87454  -37.35486 -8.405417  528.349
## 87455  -37.35458 -8.405417  528.768
## 87456  -37.35430 -8.405417  528.922
## 87457  -37.35402 -8.405417  529.325
## 87458  -37.35375 -8.405417  529.504
## 87459  -37.35347 -8.405417  529.832
## 87460  -37.35319 -8.405417  530.082
## 87461  -37.35291 -8.405417  530.429
## 87462  -37.35263 -8.405417  530.729
## 87463  -37.35236 -8.405417  530.431
## 87464  -37.35208 -8.405417  530.186
## 87465  -37.35180 -8.405417  529.941
## 87466  -37.35152 -8.405417  530.282
## 87467  -37.35125 -8.405417  530.738
## 87468  -37.35097 -8.405417  531.253
## 87469  -37.35069 -8.405417  531.727
## 87470  -37.35041 -8.405417  532.192
## 87471  -37.35013 -8.405417  532.657
## 87472  -37.34986 -8.405417  533.414
## 87473  -37.34958 -8.405417  534.087
## 87474  -37.34930 -8.405417  534.529
## 87475  -37.34902 -8.405417  535.035
## 87476  -37.34875 -8.405417  535.236
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## 87478  -37.34819 -8.405417  535.159
## 87479  -37.34791 -8.405417  534.943
## 87480  -37.34763 -8.405417  534.605
## 87481  -37.34736 -8.405417  534.349
## 87482  -37.34708 -8.405417  533.920
## 87483  -37.34680 -8.405417  533.322
## 87484  -37.34652 -8.405417  532.494
## 87485  -37.34625 -8.405417  531.649
## 87486  -37.34597 -8.405417  530.915
## 87487  -37.34569 -8.405417  530.477
## 87488  -37.34541 -8.405417  530.315
## 87489  -37.34513 -8.405417  530.406
## 87490  -37.34486 -8.405417  530.839
## 87491  -37.34458 -8.405417  531.213
## 87492  -37.34430 -8.405417  531.295
## 87493  -37.34402 -8.405417  530.791
## 87494  -37.34375 -8.405417  530.090
## 87495  -37.34347 -8.405417  529.342
## 87496  -37.34319 -8.405417  529.027
## 87497  -37.34291 -8.405417  528.809
## 87498  -37.34263 -8.405417  528.784
## 87499  -37.34236 -8.405417  528.438
## 87500  -37.34208 -8.405417  528.207
## 87501  -37.34180 -8.405417  528.017
## 87502  -37.34152 -8.405417  527.544
## 87503  -37.34125 -8.405417  527.256
## 87504  -37.34097 -8.405417  527.097
## 87505  -37.34069 -8.405417  527.502
## 87506  -37.34041 -8.405417  527.981
## 87507  -37.34013 -8.405417  528.396
## 87508  -37.33986 -8.405417  528.661
## 87509  -37.33958 -8.405417  528.771
## 87510  -37.33930 -8.405417  528.816
## 87511  -37.33902 -8.405417  528.753
## 87512  -37.33875 -8.405417  528.756
## 87513  -37.33847 -8.405417  528.875
## 87514  -37.33819 -8.405417  529.398
## 87515  -37.33791 -8.405417  530.050
## 87516  -37.33763 -8.405417  530.786
## 87517  -37.33736 -8.405417  531.378
## 87518  -37.33708 -8.405417  531.946
## 87519  -37.33680 -8.405417  532.303
## 87520  -37.33652 -8.405417  532.786
## 87521  -37.33625 -8.405417  533.061
## 87522  -37.33597 -8.405417  533.192
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## 87524  -37.33541 -8.405417  533.750
## 87525  -37.33513 -8.405417  533.909
## 87526  -37.33486 -8.405417  533.909
## 87527  -37.33458 -8.405417  534.033
## 87528  -37.33430 -8.405417  534.222
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## 87530  -37.33375 -8.405417  536.334
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## 87556  -37.32652 -8.405417  539.647
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## 87565  -37.32402 -8.405417  539.858
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## 87628  -37.30652 -8.405417  543.483
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## 87642  -37.30263 -8.405417  551.096
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## 87645  -37.30180 -8.405417  552.014
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## 87647  -37.30125 -8.405417  551.563
## 87648  -37.30097 -8.405417  551.195
## 87649  -37.30069 -8.405417  550.938
## 87650  -37.30041 -8.405417  550.833
## 87651  -37.30013 -8.405417  550.904
## 87652  -37.29986 -8.405417  551.163
## 87653  -37.29958 -8.405417  551.328
## 87654  -37.29930 -8.405417  551.110
## 87655  -37.29902 -8.405417  550.227
## 87656  -37.29875 -8.405417  549.279
## 87657  -37.29847 -8.405417  548.662
## 87658  -37.29819 -8.405417  548.770
## 87659  -37.29791 -8.405417  549.245
## 87660  -37.29763 -8.405417  549.735
## 87661  -37.29736 -8.405417  549.786
## 87662  -37.29708 -8.405417  549.912
## 87663  -37.29680 -8.405417  550.238
## 87664  -37.29652 -8.405417  551.440
## 87665  -37.29625 -8.405417  552.816
## 87666  -37.29597 -8.405417  554.133
## 87667  -37.29569 -8.405417  554.901
## 87668  -37.29541 -8.405417  555.455
## 87669  -37.29513 -8.405417  555.949
## 87670  -37.29486 -8.405417  556.581
## 87671  -37.29458 -8.405417  556.991
## 87672  -37.29430 -8.405417  556.998
## 87673  -37.29402 -8.405417  556.043
## 87674  -37.29375 -8.405417  554.914
## 87675  -37.29347 -8.405417  553.684
## 87676  -37.29319 -8.405417  552.888
## 87677  -37.29291 -8.405417  552.501
## 87678  -37.29263 -8.405417  552.819
## 87679  -37.29236 -8.405417  554.047
## 87680  -37.29208 -8.405417  555.543
## 87681  -37.29180 -8.405417  556.706
## 87682  -37.29152 -8.405417  557.296
## 87683  -37.29125 -8.405417  557.357
## 87684  -37.29097 -8.405417  557.042
## 87685  -37.29069 -8.405417  556.858
## 87686  -37.29041 -8.405417  556.409
## 87687  -37.29013 -8.405417  555.701
## 87688  -37.28986 -8.405417  554.598
## 87689  -37.28958 -8.405417  553.536
## 87690  -37.28930 -8.405417  552.772
## 87691  -37.28902 -8.405417  552.573
## 87692  -37.28875 -8.405417  552.773
## 87693  -37.28847 -8.405417  553.269
## 87694  -37.28819 -8.405417  553.577
## 87695  -37.28791 -8.405417  553.859
## 87696  -37.28763 -8.405417  553.843
## 87697  -37.28736 -8.405417  553.338
## 87698  -37.28708 -8.405417  552.819
## 87699  -37.28680 -8.405417  552.531
## 87700  -37.28652 -8.405417  553.377
## 87701  -37.28625 -8.405417  554.245
## 87702  -37.28597 -8.405417  555.223
## 87703  -37.28569 -8.405417  555.264
## 87704  -37.28541 -8.405417  555.385
## 87705  -37.28513 -8.405417  555.590
## 87706  -37.28486 -8.405417  556.080
## 87707  -37.28458 -8.405417  556.796
## 87708  -37.28430 -8.405417  557.626
## 87709  -37.28402 -8.405417  558.976
## 87710  -37.28375 -8.405417  560.030
## 87711  -37.28347 -8.405417  560.694
## 87712  -37.28319 -8.405417  560.561
## 87713  -37.28291 -8.405417  560.226
## 87714  -37.28263 -8.405417  560.056
## 87715  -37.28236 -8.405417  560.486
## 87716  -37.28208 -8.405417  561.125
## 87717  -37.28180 -8.405417  561.833
## 87718  -37.28152 -8.405417  562.107
## 87719  -37.28125 -8.405417  562.466
## 87720  -37.28097 -8.405417  562.807
## 87721  -37.28069 -8.405417  563.553
## 87722  -37.28041 -8.405417  564.283
## 87723  -37.28013 -8.405417  565.044
## 87724  -37.27986 -8.405417  565.816
## 87725  -37.27958 -8.405417  566.556
## 87726  -37.27930 -8.405417  567.435
## 87727  -37.27902 -8.405417  567.918
## 87728  -37.27875 -8.405417  568.493
## 87729  -37.27847 -8.405417  568.802
## 87730  -37.27819 -8.405417  569.329
## 87731  -37.27791 -8.405417  569.568
## 87732  -37.27763 -8.405417  569.720
## 87733  -37.27736 -8.405417  569.821
## 87734  -37.27708 -8.405417  569.813
## 87735  -37.27680 -8.405417  569.773
## 87736  -37.27652 -8.405417  569.166
## 87737  -37.27625 -8.405417  568.727
## 87738  -37.27597 -8.405417  568.242
## 87739  -37.27569 -8.405417  568.561
## 87740  -37.27541 -8.405417  568.786
## 87741  -37.27513 -8.405417  568.953
## 87742  -37.27486 -8.405417  568.833
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## 87751  -37.27236 -8.405417  570.665
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## 87753  -37.27180 -8.405417  570.546
## 87754  -37.27152 -8.405417  569.899
## 87755  -37.27125 -8.405417  569.075
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## 87774  -37.26597 -8.405417  565.622
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## 87776  -37.26541 -8.405417  563.792
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## 87788  -37.26208 -8.405417  561.571
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## 87851  -37.24458 -8.405417  582.201
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## 87853  -37.24402 -8.405417  583.437
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## 87855  -37.24347 -8.405417  584.932
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## 90222  -37.33875 -8.405972  532.305
## 90223  -37.33847 -8.405972  532.258
## 90224  -37.33819 -8.405972  532.919
## 90225  -37.33791 -8.405972  533.516
## 90226  -37.33763 -8.405972  534.496
## 90227  -37.33736 -8.405972  535.088
## 90228  -37.33708 -8.405972  535.503
## 90229  -37.33680 -8.405972  535.641
## 90230  -37.33652 -8.405972  536.042
## 90231  -37.33625 -8.405972  536.509
## 90232  -37.33597 -8.405972  536.817
## 90233  -37.33569 -8.405972  536.825
## 90234  -37.33541 -8.405972  536.738
## 90235  -37.33513 -8.405972  536.664
## 90236  -37.33486 -8.405972  536.537
## 90237  -37.33458 -8.405972  536.476
## 90238  -37.33430 -8.405972  536.544
## 90239  -37.33402 -8.405972  536.979
## 90240  -37.33375 -8.405972  537.735
## 90241  -37.33347 -8.405972  538.558
## 90242  -37.33319 -8.405972  539.695
## 90243  -37.33291 -8.405972  540.683
## 90244  -37.33263 -8.405972  541.329
## 90245  -37.33236 -8.405972  541.417
## 90246  -37.33208 -8.405972  541.070
## 90247  -37.33180 -8.405972  540.539
## 90248  -37.33152 -8.405972  540.137
## 90249  -37.33125 -8.405972  539.745
## 90250  -37.33097 -8.405972  539.415
## 90251  -37.33069 -8.405972  538.712
## 90252  -37.33041 -8.405972  538.129
## 90253  -37.33013 -8.405972  537.997
## 90254  -37.32986 -8.405972  538.896
## 90255  -37.32958 -8.405972  539.935
## 90256  -37.32930 -8.405972  540.629
## 90257  -37.32902 -8.405972  540.367
## 90258  -37.32875 -8.405972  539.915
## 90259  -37.32847 -8.405972  539.317
## 90260  -37.32819 -8.405972  539.220
## 90261  -37.32791 -8.405972  539.341
## 90262  -37.32763 -8.405972  539.942
## 90263  -37.32736 -8.405972  540.811
## 90264  -37.32708 -8.405972  541.761
## 90265  -37.32680 -8.405972  542.804
## 90266  -37.32652 -8.405972  543.307
## 90267  -37.32625 -8.405972  543.569
## 90268  -37.32597 -8.405972  543.532
## 90269  -37.32569 -8.405972  543.398
## 90270  -37.32541 -8.405972  543.205
## 90271  -37.32513 -8.405972  542.562
## 90272  -37.32486 -8.405972  541.615
## 90273  -37.32458 -8.405972  540.957
## 90274  -37.32430 -8.405972  540.605
## 90275  -37.32402 -8.405972  541.212
## 90276  -37.32375 -8.405972  541.956
## 90277  -37.32347 -8.405972  543.124
## 90278  -37.32319 -8.405972  544.107
## 90279  -37.32291 -8.405972  544.959
## 90280  -37.32263 -8.405972  545.559
## 90281  -37.32236 -8.405972  546.132
## 90282  -37.32208 -8.405972  546.539
## 90283  -37.32180 -8.405972  546.722
## 90284  -37.32152 -8.405972  546.146
## 90285  -37.32125 -8.405972  545.649
## 90286  -37.32097 -8.405972  545.440
## 90287  -37.32069 -8.405972  546.179
## 90288  -37.32041 -8.405972  547.282
## 90289  -37.32013 -8.405972  548.251
## 90290  -37.31986 -8.405972  548.661
## 90291  -37.31958 -8.405972  548.898
## 90292  -37.31930 -8.405972  548.829
## 90293  -37.31902 -8.405972  548.489
## 90294  -37.31875 -8.405972  547.899
## 90295  -37.31847 -8.405972  547.588
## 90296  -37.31819 -8.405972  547.846
## 90297  -37.31791 -8.405972  548.346
## 90298  -37.31763 -8.405972  548.886
## 90299  -37.31736 -8.405972  549.233
## 90300  -37.31708 -8.405972  549.837
## 90301  -37.31680 -8.405972  550.679
## 90302  -37.31652 -8.405972  552.277
## 90303  -37.31625 -8.405972  553.750
## 90304  -37.31597 -8.405972  554.946
## 90305  -37.31569 -8.405972  553.930
## 90306  -37.31541 -8.405972  552.243
## 90307  -37.31513 -8.405972  550.182
## 90308  -37.31486 -8.405972  549.370
## 90309  -37.31458 -8.405972  548.861
## 90310  -37.31430 -8.405972  549.125
## 90311  -37.31402 -8.405972  549.458
## 90312  -37.31375 -8.405972  549.821
## 90313  -37.31347 -8.405972  550.626
## 90314  -37.31319 -8.405972  549.999
## 90315  -37.31291 -8.405972  548.901
## 90316  -37.31263 -8.405972  547.848
## 90317  -37.31236 -8.405972  547.133
## 90318  -37.31208 -8.405972  546.671
## 90319  -37.31180 -8.405972  545.552
## 90320  -37.31152 -8.405972  544.646
## 90321  -37.31125 -8.405972  543.953
## 90322  -37.31097 -8.405972  543.185
## 90323  -37.31069 -8.405972  542.703
## 90324  -37.31041 -8.405972  542.614
## 90325  -37.31013 -8.405972  543.357
## 90326  -37.30986 -8.405972  544.926
## 90327  -37.30958 -8.405972  546.624
## 90328  -37.30930 -8.405972  548.467
## 90329  -37.30902 -8.405972  549.526
## 90330  -37.30875 -8.405972  550.069
## 90331  -37.30847 -8.405972  549.979
## 90332  -37.30819 -8.405972  549.497
## 90333  -37.30791 -8.405972  548.863
## 90334  -37.30763 -8.405972  547.616
## 90335  -37.30736 -8.405972  546.202
## 90336  -37.30708 -8.405972  545.116
## 90337  -37.30680 -8.405972  544.782
## 90338  -37.30652 -8.405972  544.725
## 90339  -37.30625 -8.405972  544.992
## 90340  -37.30597 -8.405972  544.934
## 90341  -37.30569 -8.405972  544.934
## 90342  -37.30541 -8.405972  545.235
## 90343  -37.30513 -8.405972  545.883
## 90344  -37.30486 -8.405972  547.496
## 90345  -37.30458 -8.405972  549.494
## 90346  -37.30430 -8.405972  551.568
## 90347  -37.30402 -8.405972  553.619
## 90348  -37.30375 -8.405972  554.895
## 90349  -37.30347 -8.405972  555.198
## 90350  -37.30319 -8.405972  554.976
## 90351  -37.30291 -8.405972  554.638
## 90352  -37.30263 -8.405972  554.298
## 90353  -37.30236 -8.405972  554.380
## 90354  -37.30208 -8.405972  554.495
## 90355  -37.30180 -8.405972  554.520
## 90356  -37.30152 -8.405972  554.076
## 90357  -37.30125 -8.405972  553.516
## 90358  -37.30097 -8.405972  553.018
## 90359  -37.30069 -8.405972  552.505
## 90360  -37.30041 -8.405972  552.083
## 90361  -37.30013 -8.405972  552.035
## 90362  -37.29986 -8.405972  552.473
## 90363  -37.29958 -8.405972  552.868
## 90364  -37.29930 -8.405972  552.685
## 90365  -37.29902 -8.405972  552.016
## 90366  -37.29875 -8.405972  551.284
## 90367  -37.29847 -8.405972  550.677
## 90368  -37.29819 -8.405972  550.447
## 90369  -37.29791 -8.405972  550.343
## 90370  -37.29763 -8.405972  550.232
## 90371  -37.29736 -8.405972  550.363
## 90372  -37.29708 -8.405972  550.638
## 90373  -37.29680 -8.405972  551.318
## 90374  -37.29652 -8.405972  552.550
## 90375  -37.29625 -8.405972  553.762
## 90376  -37.29597 -8.405972  554.832
## 90377  -37.29569 -8.405972  555.414
## 90378  -37.29541 -8.405972  555.744
## 90379  -37.29513 -8.405972  556.041
## 90380  -37.29486 -8.405972  556.816
## 90381  -37.29458 -8.405972  557.412
## 90382  -37.29430 -8.405972  557.716
## 90383  -37.29402 -8.405972  557.099
## 90384  -37.29375 -8.405972  556.061
## 90385  -37.29347 -8.405972  554.735
## 90386  -37.29319 -8.405972  553.530
## 90387  -37.29291 -8.405972  552.939
## 90388  -37.29263 -8.405972  553.169
## 90389  -37.29236 -8.405972  554.782
## 90390  -37.29208 -8.405972  556.757
## 90391  -37.29180 -8.405972  558.378
## 90392  -37.29152 -8.405972  558.957
## 90393  -37.29125 -8.405972  558.879
## 90394  -37.29097 -8.405972  558.550
## 90395  -37.29069 -8.405972  557.763
## 90396  -37.29041 -8.405972  556.612
## 90397  -37.29013 -8.405972  555.373
## 90398  -37.28986 -8.405972  554.145
## 90399  -37.28958 -8.405972  552.930
## 90400  -37.28930 -8.405972  552.233
## 90401  -37.28902 -8.405972  551.943
## 90402  -37.28875 -8.405972  552.195
## 90403  -37.28847 -8.405972  553.037
## 90404  -37.28819 -8.405972  553.926
## 90405  -37.28791 -8.405972  554.754
## 90406  -37.28763 -8.405972  555.198
## 90407  -37.28736 -8.405972  555.081
## 90408  -37.28708 -8.405972  554.846
## 90409  -37.28680 -8.405972  554.545
## 90410  -37.28652 -8.405972  554.627
## 90411  -37.28625 -8.405972  554.967
## 90412  -37.28597 -8.405972  555.584
## 90413  -37.28569 -8.405972  555.688
## 90414  -37.28541 -8.405972  555.605
## 90415  -37.28513 -8.405972  555.594
## 90416  -37.28486 -8.405972  555.675
## 90417  -37.28458 -8.405972  555.877
## 90418  -37.28430 -8.405972  556.088
## 90419  -37.28402 -8.405972  556.373
## 90420  -37.28375 -8.405972  556.757
## 90421  -37.28347 -8.405972  557.215
## 90422  -37.28319 -8.405972  557.389
## 90423  -37.28291 -8.405972  557.597
## 90424  -37.28263 -8.405972  557.833
## 90425  -37.28236 -8.405972  558.361
## 90426  -37.28208 -8.405972  559.158
## 90427  -37.28180 -8.405972  560.041
## 90428  -37.28152 -8.405972  560.745
## 90429  -37.28125 -8.405972  561.294
## 90430  -37.28097 -8.405972  561.389
## 90431  -37.28069 -8.405972  561.955
## 90432  -37.28041 -8.405972  562.691
## 90433  -37.28013 -8.405972  563.644
## 90434  -37.27986 -8.405972  565.077
## 90435  -37.27958 -8.405972  566.419
## 90436  -37.27930 -8.405972  568.060
## 90437  -37.27902 -8.405972  569.267
## 90438  -37.27875 -8.405972  570.085
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## 90441  -37.27791 -8.405972  570.045
## 90442  -37.27763 -8.405972  570.058
## 90443  -37.27736 -8.405972  570.534
## 90444  -37.27708 -8.405972  570.807
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## 90446  -37.27652 -8.405972  570.864
## 90447  -37.27625 -8.405972  570.454
## 90448  -37.27597 -8.405972  570.073
## 90449  -37.27569 -8.405972  570.071
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## 90451  -37.27513 -8.405972  570.243
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## 90453  -37.27458 -8.405972  570.372
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## 90455  -37.27402 -8.405972  571.192
## 90456  -37.27375 -8.405972  571.623
## 90457  -37.27347 -8.405972  571.989
## 90458  -37.27319 -8.405972  572.277
## 90459  -37.27291 -8.405972  572.468
## 90460  -37.27263 -8.405972  572.473
## 90461  -37.27236 -8.405972  571.943
## 90462  -37.27208 -8.405972  571.651
## 90463  -37.27180 -8.405972  570.835
## 90464  -37.27152 -8.405972  570.504
## 90465  -37.27125 -8.405972  570.284
## 90466  -37.27097 -8.405972  569.909
## 90467  -37.27069 -8.405972  569.074
## 90468  -37.27041 -8.405972  567.936
## 90469  -37.27013 -8.405972  566.702
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## 90471  -37.26958 -8.405972  563.422
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## 90479  -37.26736 -8.405972  565.857
## 90480  -37.26708 -8.405972  566.605
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## 90482  -37.26652 -8.405972  567.305
## 90483  -37.26625 -8.405972  566.997
## 90484  -37.26597 -8.405972  566.289
## 90485  -37.26569 -8.405972  565.372
## 90486  -37.26541 -8.405972  564.211
## 90487  -37.26513 -8.405972  563.073
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## 90489  -37.26458 -8.405972  560.652
## 90490  -37.26430 -8.405972  559.740
## 90491  -37.26402 -8.405972  559.298
## 90492  -37.26375 -8.405972  559.098
## 90493  -37.26347 -8.405972  558.949
## 90494  -37.26319 -8.405972  558.675
## 90495  -37.26291 -8.405972  558.603
## 90496  -37.26263 -8.405972  559.128
## 90497  -37.26236 -8.405972  560.040
## 90498  -37.26208 -8.405972  561.168
## 90499  -37.26180 -8.405972  561.688
## 90500  -37.26152 -8.405972  561.494
## 90501  -37.26125 -8.405972  561.025
## 90502  -37.26097 -8.405972  560.408
## 90503  -37.26069 -8.405972  560.320
## 90504  -37.26041 -8.405972  560.320
## 90505  -37.26013 -8.405972  560.645
## 90506  -37.25986 -8.405972  560.728
## 90507  -37.25958 -8.405972  560.295
## 90508  -37.25930 -8.405972  559.567
## 90509  -37.25902 -8.405972  558.441
## 90510  -37.25875 -8.405972  557.407
## 90511  -37.25847 -8.405972  556.360
## 90512  -37.25819 -8.405972  556.200
## 90513  -37.25791 -8.405972  556.326
## 90514  -37.25763 -8.405972  556.764
## 90515  -37.25736 -8.405972  557.117
## 90516  -37.25708 -8.405972  557.559
## 90517  -37.25680 -8.405972  558.063
## 90518  -37.25652 -8.405972  558.890
## 90519  -37.25625 -8.405972  559.902
## 90520  -37.25597 -8.405972  561.283
## 90521  -37.25569 -8.405972  561.659
## 90522  -37.25541 -8.405972  561.774
## 90523  -37.25513 -8.405972  561.708
## 90524  -37.25486 -8.405972  561.793
## 90525  -37.25458 -8.405972  561.951
## 90526  -37.25430 -8.405972  562.196
## 90527  -37.25402 -8.405972  562.512
## 90528  -37.25375 -8.405972  563.184
## 90529  -37.25347 -8.405972  564.340
## 90530  -37.25319 -8.405972  564.974
## 90531  -37.25291 -8.405972  565.461
## 90532  -37.25263 -8.405972  565.650
## 90533  -37.25236 -8.405972  566.198
## 90534  -37.25208 -8.405972  566.766
## 90535  -37.25180 -8.405972  567.866
## 90536  -37.25152 -8.405972  569.125
## 90537  -37.25125 -8.405972  570.379
## 90538  -37.25097 -8.405972  572.065
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## 90540  -37.25041 -8.405972  573.854
## 90541  -37.25013 -8.405972  574.153
## 90542  -37.24986 -8.405972  574.129
## 90543  -37.24958 -8.405972  573.951
## 90544  -37.24930 -8.405972  573.390
## 90545  -37.24902 -8.405972  572.491
## 90546  -37.24875 -8.405972  571.790
## 90547  -37.24847 -8.405972  571.256
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## 90550  -37.24763 -8.405972  572.772
## 90551  -37.24736 -8.405972  572.826
## 90552  -37.24708 -8.405972  572.828
## 90553  -37.24680 -8.405972  573.631
## 90554  -37.24652 -8.405972  574.778
## 90555  -37.24625 -8.405972  575.940
## 90556  -37.24597 -8.405972  576.651
## 90557  -37.24569 -8.405972  577.106
## 90558  -37.24541 -8.405972  577.634
## 90559  -37.24513 -8.405972  578.088
## 90560  -37.24486 -8.405972  579.315
## 90561  -37.24458 -8.405972  580.660
## 90562  -37.24430 -8.405972  582.411
## 90563  -37.24402 -8.405972  583.993
## 90564  -37.24375 -8.405972  585.379
## 90565  -37.24347 -8.405972  586.599
## 90566  -37.24319 -8.405972  587.341
## 90567  -37.24291 -8.405972  587.811
## 90568  -37.24263 -8.405972  588.123
## 90569  -37.24236 -8.405972  588.315
## 90570  -37.24208 -8.405972  588.413
## 90571  -37.24180 -8.405972  588.350
## 90572  -37.24152 -8.405972  588.293
## 90573  -37.24125 -8.405972  588.341
## 90574  -37.24097 -8.405972  588.376
## 90575  -37.24069 -8.405972  588.610
## 90576  -37.24041 -8.405972  588.657
## 90577  -37.24013 -8.405972  588.474
## 90578  -37.23986 -8.405972  587.723
## 90579  -37.23958 -8.405972  586.774
## 90580  -37.23930 -8.405972  585.797
## 90581  -37.23902 -8.405972  585.036
## 90582  -37.23875 -8.405972  584.276
## 90583  -37.23847 -8.405972  583.680
## 90584  -37.23819 -8.405972  583.152
## 90585  -37.23791 -8.405972  582.499
## 90586  -37.23763 -8.405972  581.425
## 90587  -37.23736 -8.405972  579.867
## 90588  -37.23708 -8.405972  578.204
## 90589  -37.23680 -8.405972  576.482
## 90590  -37.23652 -8.405972  575.347
## 90591  -37.23625 -8.405972  574.519
## 90592  -37.23597 -8.405972  574.163
## 90593  -37.23569 -8.405972  574.197
## 90594  -37.23541 -8.405972  574.174
## 90595  -37.23513 -8.405972  574.056
## 90596  -37.23486 -8.405972  573.352
## 90597  -37.23458 -8.405972  572.420
## 90598  -37.23430 -8.405972  571.372
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## 90601  -37.23347 -8.405972  569.258
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## 90609  -37.23125 -8.405972  574.686
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## 90631  -37.22513 -8.405972  573.771
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## 91834  -37.26736 -8.406250  566.874
## 91835  -37.26708 -8.406250  567.384
## 91836  -37.26680 -8.406250  567.675
## 91837  -37.26652 -8.406250  567.809
## 91838  -37.26625 -8.406250  567.607
## 91839  -37.26597 -8.406250  567.131
## 91840  -37.26569 -8.406250  566.192
## 91841  -37.26541 -8.406250  565.037
## 91842  -37.26513 -8.406250  563.680
## 91843  -37.26486 -8.406250  562.179
## 91844  -37.26458 -8.406250  560.783
## 91845  -37.26430 -8.406250  559.821
## 91846  -37.26402 -8.406250  559.220
## 91847  -37.26375 -8.406250  558.973
## 91848  -37.26347 -8.406250  558.829
## 91849  -37.26319 -8.406250  558.488
## 91850  -37.26291 -8.406250  558.327
## 91851  -37.26263 -8.406250  558.567
## 91852  -37.26236 -8.406250  559.447
## 91853  -37.26208 -8.406250  560.479
## 91854  -37.26180 -8.406250  561.374
## 91855  -37.26152 -8.406250  561.654
## 91856  -37.26125 -8.406250  561.660
## 91857  -37.26097 -8.406250  561.604
## 91858  -37.26069 -8.406250  561.583
## 91859  -37.26041 -8.406250  561.592
## 91860  -37.26013 -8.406250  561.669
## 91861  -37.25986 -8.406250  561.217
## 91862  -37.25958 -8.406250  560.697
## 91863  -37.25930 -8.406250  559.853
## 91864  -37.25902 -8.406250  558.741
## 91865  -37.25875 -8.406250  557.648
## 91866  -37.25847 -8.406250  556.774
## 91867  -37.25819 -8.406250  556.525
## 91868  -37.25791 -8.406250  556.533
## 91869  -37.25763 -8.406250  556.687
## 91870  -37.25736 -8.406250  556.832
## 91871  -37.25708 -8.406250  557.114
## 91872  -37.25680 -8.406250  557.681
## 91873  -37.25652 -8.406250  558.520
## 91874  -37.25625 -8.406250  559.425
## 91875  -37.25597 -8.406250  560.201
## 91876  -37.25569 -8.406250  560.298
## 91877  -37.25541 -8.406250  560.272
## 91878  -37.25513 -8.406250  560.299
## 91879  -37.25486 -8.406250  560.685
## 91880  -37.25458 -8.406250  561.274
## 91881  -37.25430 -8.406250  562.068
## 91882  -37.25402 -8.406250  562.984
## 91883  -37.25375 -8.406250  563.979
## 91884  -37.25347 -8.406250  564.908
## 91885  -37.25319 -8.406250  565.406
## 91886  -37.25291 -8.406250  565.820
## 91887  -37.25263 -8.406250  566.128
## 91888  -37.25236 -8.406250  566.851
## 91889  -37.25208 -8.406250  567.639
## 91890  -37.25180 -8.406250  568.926
## 91891  -37.25152 -8.406250  569.813
## 91892  -37.25125 -8.406250  571.060
## 91893  -37.25097 -8.406250  572.407
## 91894  -37.25069 -8.406250  573.276
## 91895  -37.25041 -8.406250  574.033
## 91896  -37.25013 -8.406250  574.514
## 91897  -37.24986 -8.406250  574.733
## 91898  -37.24958 -8.406250  574.675
## 91899  -37.24930 -8.406250  574.208
## 91900  -37.24902 -8.406250  573.619
## 91901  -37.24875 -8.406250  573.019
## 91902  -37.24847 -8.406250  572.583
## 91903  -37.24819 -8.406250  573.193
## 91904  -37.24791 -8.406250  573.831
## 91905  -37.24763 -8.406250  574.308
## 91906  -37.24736 -8.406250  574.263
## 91907  -37.24708 -8.406250  574.172
## 91908  -37.24680 -8.406250  574.457
## 91909  -37.24652 -8.406250  575.131
## 91910  -37.24625 -8.406250  576.008
## 91911  -37.24597 -8.406250  576.675
## 91912  -37.24569 -8.406250  577.078
## 91913  -37.24541 -8.406250  577.416
## 91914  -37.24513 -8.406250  578.076
## 91915  -37.24486 -8.406250  579.443
## 91916  -37.24458 -8.406250  581.109
## 91917  -37.24430 -8.406250  583.022
## 91918  -37.24402 -8.406250  584.554
## 91919  -37.24375 -8.406250  586.042
## 91920  -37.24347 -8.406250  587.252
## 91921  -37.24319 -8.406250  587.949
## 91922  -37.24291 -8.406250  588.376
## 91923  -37.24263 -8.406250  588.620
## 91924  -37.24236 -8.406250  588.810
## 91925  -37.24208 -8.406250  588.947
## 91926  -37.24180 -8.406250  589.004
## 91927  -37.24152 -8.406250  589.178
## 91928  -37.24125 -8.406250  589.328
## 91929  -37.24097 -8.406250  589.583
## 91930  -37.24069 -8.406250  589.762
## 91931  -37.24041 -8.406250  589.818
## 91932  -37.24013 -8.406250  589.479
## 91933  -37.23986 -8.406250  588.514
## 91934  -37.23958 -8.406250  587.284
## 91935  -37.23930 -8.406250  586.105
## 91936  -37.23902 -8.406250  584.888
## 91937  -37.23875 -8.406250  583.894
## 91938  -37.23847 -8.406250  583.002
## 91939  -37.23819 -8.406250  582.499
## 91940  -37.23791 -8.406250  581.873
## 91941  -37.23763 -8.406250  580.991
## 91942  -37.23736 -8.406250  579.652
## 91943  -37.23708 -8.406250  578.197
## 91944  -37.23680 -8.406250  576.823
## 91945  -37.23652 -8.406250  575.742
## 91946  -37.23625 -8.406250  574.981
## 91947  -37.23597 -8.406250  574.719
## 91948  -37.23569 -8.406250  574.675
## 91949  -37.23541 -8.406250  574.792
## 91950  -37.23513 -8.406250  574.652
## 91951  -37.23486 -8.406250  573.900
## 91952  -37.23458 -8.406250  572.891
## 91953  -37.23430 -8.406250  571.810
## 91954  -37.23402 -8.406250  571.011
## 91955  -37.23375 -8.406250  570.337
## 91956  -37.23347 -8.406250  569.609
## 91957  -37.23319 -8.406250  569.102
## 91958  -37.23291 -8.406250  568.862
## 91959  -37.23263 -8.406250  569.140
## 91960  -37.23236 -8.406250  570.871
## 91961  -37.23208 -8.406250  572.713
## 91962  -37.23180 -8.406250  574.295
## 91963  -37.23152 -8.406250  575.035
## 91964  -37.23125 -8.406250  575.449
## 91965  -37.23097 -8.406250  575.866
## 91966  -37.23069 -8.406250  576.122
## 91967  -37.23041 -8.406250  576.358
## 91968  -37.23013 -8.406250  576.252
## 91969  -37.22986 -8.406250  575.599
## 91970  -37.22958 -8.406250  574.846
## 91971  -37.22930 -8.406250  574.255
## 91972  -37.22902 -8.406250  574.224
## 91973  -37.22875 -8.406250  574.326
## 91974  -37.22847 -8.406250  574.484
## 91975  -37.22819 -8.406250  574.535
## 91976  -37.22791 -8.406250  574.567
## 91977  -37.22763 -8.406250  574.574
## 91978  -37.22736 -8.406250  574.566
## 91979  -37.22708 -8.406250  574.641
## 91980  -37.22680 -8.406250  574.934
## 91981  -37.22652 -8.406250  575.353
## 91982  -37.22625 -8.406250  575.801
## 91983  -37.22597 -8.406250  575.945
## 91984  -37.22569 -8.406250  575.561
## 91985  -37.22541 -8.406250  574.904
## 91986  -37.22513 -8.406250  574.097
## 91987  -37.22486 -8.406250  573.879
## 91988  -37.22458 -8.406250  573.325
## 91989  -37.22430 -8.406250  572.150
## 91990  -37.22402 -8.406250  570.258
## 91991  -37.22375 -8.406250  568.518
## 92845  -37.36291 -8.406528  524.728
## 92846  -37.36263 -8.406528  524.187
## 92847  -37.36236 -8.406528  523.996
## 92848  -37.36208 -8.406528  524.278
## 92849  -37.36180 -8.406528  524.731
## 92850  -37.36152 -8.406528  525.589
## 92851  -37.36125 -8.406528  526.308
## 92852  -37.36097 -8.406528  526.586
## 92853  -37.36069 -8.406528  526.022
## 92854  -37.36041 -8.406528  525.433
## 92855  -37.36013 -8.406528  525.249
## 92856  -37.35986 -8.406528  525.412
## 92857  -37.35958 -8.406528  525.809
## 92858  -37.35930 -8.406528  526.141
## 92859  -37.35902 -8.406528  526.739
## 92860  -37.35875 -8.406528  527.228
## 92861  -37.35847 -8.406528  527.299
## 92862  -37.35819 -8.406528  526.620
## 92863  -37.35791 -8.406528  525.824
## 92864  -37.35763 -8.406528  525.261
## 92865  -37.35736 -8.406528  524.900
## 92866  -37.35708 -8.406528  524.707
## 92867  -37.35680 -8.406528  524.777
## 92868  -37.35652 -8.406528  524.915
## 92869  -37.35625 -8.406528  525.276
## 92870  -37.35597 -8.406528  525.846
## 92871  -37.35569 -8.406528  526.588
## 92872  -37.35541 -8.406528  527.538
## 92873  -37.35513 -8.406528  528.748
## 92874  -37.35486 -8.406528  530.053
## 92875  -37.35458 -8.406528  531.154
## 92876  -37.35430 -8.406528  531.966
## 92877  -37.35402 -8.406528  532.089
## 92878  -37.35375 -8.406528  532.031
## 92879  -37.35347 -8.406528  532.176
## 92880  -37.35319 -8.406528  532.968
## 92881  -37.35291 -8.406528  534.054
## 92882  -37.35263 -8.406528  535.013
## 92883  -37.35236 -8.406528  535.124
## 92884  -37.35208 -8.406528  534.900
## 92885  -37.35180 -8.406528  534.290
## 92886  -37.35152 -8.406528  533.162
## 92887  -37.35125 -8.406528  532.247
## 92888  -37.35097 -8.406528  531.867
## 92889  -37.35069 -8.406528  532.643
## 92890  -37.35041 -8.406528  533.700
## 92891  -37.35013 -8.406528  535.100
## 92892  -37.34986 -8.406528  535.959
## 92893  -37.34958 -8.406528  536.643
## 92894  -37.34930 -8.406528  537.066
## 92895  -37.34902 -8.406528  537.171
## 92896  -37.34875 -8.406528  537.061
## 92897  -37.34847 -8.406528  536.844
## 92898  -37.34819 -8.406528  536.313
## 92899  -37.34791 -8.406528  535.963
## 92900  -37.34763 -8.406528  535.848
## 92901  -37.34736 -8.406528  536.139
## 92902  -37.34708 -8.406528  536.346
## 92903  -37.34680 -8.406528  536.323
## 92904  -37.34652 -8.406528  535.935
## 92905  -37.34625 -8.406528  535.381
## 92906  -37.34597 -8.406528  534.791
## 92907  -37.34569 -8.406528  534.263
## 92908  -37.34541 -8.406528  534.161
## 92909  -37.34513 -8.406528  534.330
## 92910  -37.34486 -8.406528  534.854
## 92911  -37.34458 -8.406528  535.109
## 92912  -37.34430 -8.406528  535.279
## 92913  -37.34402 -8.406528  534.566
## 92914  -37.34375 -8.406528  533.797
## 92915  -37.34347 -8.406528  533.365
## 92916  -37.34319 -8.406528  533.867
## 92917  -37.34291 -8.406528  534.648
## 92918  -37.34263 -8.406528  535.328
## 92919  -37.34236 -8.406528  535.489
## 92920  -37.34208 -8.406528  535.479
## 92921  -37.34180 -8.406528  535.478
## 92922  -37.34152 -8.406528  535.309
## 92923  -37.34125 -8.406528  535.130
## 92924  -37.34097 -8.406528  534.968
## 92925  -37.34069 -8.406528  534.986
## 92926  -37.34041 -8.406528  535.056
## 92927  -37.34013 -8.406528  535.293
## 92928  -37.33986 -8.406528  535.918
## 92929  -37.33958 -8.406528  536.423
## 92930  -37.33930 -8.406528  537.169
## 92931  -37.33902 -8.406528  537.411
## 92932  -37.33875 -8.406528  537.007
## 92933  -37.33847 -8.406528  536.701
## 92934  -37.33819 -8.406528  536.617
## 92935  -37.33791 -8.406528  536.853
## 92936  -37.33763 -8.406528  536.846
## 92937  -37.33736 -8.406528  536.881
## 92938  -37.33708 -8.406528  537.113
## 92939  -37.33680 -8.406528  537.647
## 92940  -37.33652 -8.406528  538.441
## 92941  -37.33625 -8.406528  539.078
## 92942  -37.33597 -8.406528  539.496
## 92943  -37.33569 -8.406528  539.633
## 92944  -37.33541 -8.406528  539.601
## 92945  -37.33513 -8.406528  539.355
## 92946  -37.33486 -8.406528  539.283
## 92947  -37.33458 -8.406528  539.289
## 92948  -37.33430 -8.406528  539.506
## 92949  -37.33402 -8.406528  539.959
## 92950  -37.33375 -8.406528  540.512
## 92951  -37.33347 -8.406528  541.313
## 92952  -37.33319 -8.406528  542.270
## 92953  -37.33291 -8.406528  543.115
## 92954  -37.33263 -8.406528  543.639
## 92955  -37.33236 -8.406528  543.548
## 92956  -37.33208 -8.406528  543.256
## 92957  -37.33180 -8.406528  542.627
## 92958  -37.33152 -8.406528  542.160
## 92959  -37.33125 -8.406528  541.484
## 92960  -37.33097 -8.406528  540.672
## 92961  -37.33069 -8.406528  539.379
## 92962  -37.33041 -8.406528  538.464
## 92963  -37.33013 -8.406528  538.201
## 92964  -37.32986 -8.406528  539.291
## 92965  -37.32958 -8.406528  540.711
## 92966  -37.32930 -8.406528  541.985
## 92967  -37.32902 -8.406528  542.101
## 92968  -37.32875 -8.406528  541.795
## 92969  -37.32847 -8.406528  541.520
## 92970  -37.32819 -8.406528  541.639
## 92971  -37.32791 -8.406528  541.989
## 92972  -37.32763 -8.406528  542.542
## 92973  -37.32736 -8.406528  543.243
## 92974  -37.32708 -8.406528  544.120
## 92975  -37.32680 -8.406528  544.683
## 92976  -37.32652 -8.406528  545.163
## 92977  -37.32625 -8.406528  545.423
## 92978  -37.32597 -8.406528  545.548
## 92979  -37.32569 -8.406528  545.769
## 92980  -37.32541 -8.406528  545.634
## 92981  -37.32513 -8.406528  545.565
## 92982  -37.32486 -8.406528  544.748
## 92983  -37.32458 -8.406528  544.005
## 92984  -37.32430 -8.406528  543.376
## 92985  -37.32402 -8.406528  543.343
## 92986  -37.32375 -8.406528  543.929
## 92987  -37.32347 -8.406528  544.739
## 92988  -37.32319 -8.406528  545.605
## 92989  -37.32291 -8.406528  546.551
## 92990  -37.32263 -8.406528  547.598
## 92991  -37.32236 -8.406528  548.562
## 92992  -37.32208 -8.406528  549.173
## 92993  -37.32180 -8.406528  549.253
## 92994  -37.32152 -8.406528  548.802
## 92995  -37.32125 -8.406528  548.385
## 92996  -37.32097 -8.406528  548.434
## 92997  -37.32069 -8.406528  549.551
## 92998  -37.32041 -8.406528  550.901
## 92999  -37.32013 -8.406528  552.423
## 93000  -37.31986 -8.406528  553.101
## 93001  -37.31958 -8.406528  553.431
## 93002  -37.31930 -8.406528  552.854
## 93003  -37.31902 -8.406528  552.044
## 93004  -37.31875 -8.406528  551.224
## 93005  -37.31847 -8.406528  550.527
## 93006  -37.31819 -8.406528  550.528
## 93007  -37.31791 -8.406528  550.928
## 93008  -37.31763 -8.406528  551.631
## 93009  -37.31736 -8.406528  552.117
## 93010  -37.31708 -8.406528  552.762
## 93011  -37.31680 -8.406528  553.459
## 93012  -37.31652 -8.406528  554.749
## 93013  -37.31625 -8.406528  555.684
## 93014  -37.31597 -8.406528  555.549
## 93015  -37.31569 -8.406528  554.160
## 93016  -37.31541 -8.406528  552.473
## 93017  -37.31513 -8.406528  551.249
## 93018  -37.31486 -8.406528  551.166
## 93019  -37.31458 -8.406528  551.297
## 93020  -37.31430 -8.406528  552.003
## 93021  -37.31402 -8.406528  552.540
## 93022  -37.31375 -8.406528  552.623
## 93023  -37.31347 -8.406528  551.835
## 93024  -37.31319 -8.406528  550.593
## 93025  -37.31291 -8.406528  549.296
## 93026  -37.31263 -8.406528  547.754
## 93027  -37.31236 -8.406528  546.615
## 93028  -37.31208 -8.406528  545.300
## 93029  -37.31180 -8.406528  544.898
## 93030  -37.31152 -8.406528  544.460
## 93031  -37.31125 -8.406528  544.083
## 93032  -37.31097 -8.406528  543.849
## 93033  -37.31069 -8.406528  543.548
## 93034  -37.31041 -8.406528  543.590
## 93035  -37.31013 -8.406528  543.843
## 93036  -37.30986 -8.406528  544.880
## 93037  -37.30958 -8.406528  546.170
## 93038  -37.30930 -8.406528  547.464
## 93039  -37.30902 -8.406528  548.432
## 93040  -37.30875 -8.406528  549.395
## 93041  -37.30847 -8.406528  550.128
## 93042  -37.30819 -8.406528  550.893
## 93043  -37.30791 -8.406528  551.049
## 93044  -37.30763 -8.406528  551.070
## 93045  -37.30736 -8.406528  550.173
## 93046  -37.30708 -8.406528  548.937
## 93047  -37.30680 -8.406528  547.721
## 93048  -37.30652 -8.406528  547.393
## 93049  -37.30625 -8.406528  547.501
## 93050  -37.30597 -8.406528  547.836
## 93051  -37.30569 -8.406528  547.666
## 93052  -37.30541 -8.406528  547.607
## 93053  -37.30513 -8.406528  547.926
## 93054  -37.30486 -8.406528  549.110
## 93055  -37.30458 -8.406528  550.441
## 93056  -37.30430 -8.406528  552.169
## 93057  -37.30402 -8.406528  553.603
## 93058  -37.30375 -8.406528  555.350
## 93059  -37.30347 -8.406528  556.952
## 93060  -37.30319 -8.406528  558.060
## 93061  -37.30291 -8.406528  558.566
## 93062  -37.30263 -8.406528  558.849
## 93063  -37.30236 -8.406528  558.967
## 93064  -37.30208 -8.406528  558.892
## 93065  -37.30180 -8.406528  558.531
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## 93075  -37.29902 -8.406528  555.850
## 93076  -37.29875 -8.406528  555.203
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## 93078  -37.29819 -8.406528  553.551
## 93079  -37.29791 -8.406528  552.951
## 93080  -37.29763 -8.406528  552.578
## 93081  -37.29736 -8.406528  552.286
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## 93083  -37.29680 -8.406528  552.625
## 93084  -37.29652 -8.406528  553.362
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## 93089  -37.29513 -8.406528  555.005
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## 93091  -37.29458 -8.406528  555.604
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## 95651  -37.33625 -8.407083  541.084
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## 95653  -37.33569 -8.407083  541.575
## 95654  -37.33541 -8.407083  541.749
## 95655  -37.33513 -8.407083  541.891
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## 95670  -37.33097 -8.407083  541.939
## 95671  -37.33069 -8.407083  540.109
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## 95900  -37.26708 -8.407083  568.255
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## 95902  -37.26652 -8.407083  567.703
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## 95915  -37.26291 -8.407083  558.484
## 95916  -37.26263 -8.407083  558.242
## 95917  -37.26236 -8.407083  558.893
## 95918  -37.26208 -8.407083  559.931
## 95919  -37.26180 -8.407083  561.165
## 95920  -37.26152 -8.407083  562.113
## 95921  -37.26125 -8.407083  562.946
## 95922  -37.26097 -8.407083  563.622
## 95923  -37.26069 -8.407083  564.210
## 95924  -37.26041 -8.407083  564.441
## 95925  -37.26013 -8.407083  564.117
## 95926  -37.25986 -8.407083  563.020
## 95927  -37.25958 -8.407083  561.717
## 95928  -37.25930 -8.407083  560.655
## 95929  -37.25902 -8.407083  560.199
## 95930  -37.25875 -8.407083  560.004
## 95931  -37.25847 -8.407083  559.911
## 95932  -37.25819 -8.407083  559.751
## 95933  -37.25791 -8.407083  559.466
## 95934  -37.25763 -8.407083  558.952
## 95935  -37.25736 -8.407083  558.060
## 95936  -37.25708 -8.407083  557.250
## 95937  -37.25680 -8.407083  556.849
## 95938  -37.25652 -8.407083  557.122
## 95939  -37.25625 -8.407083  557.574
## 95940  -37.25597 -8.407083  557.926
## 95941  -37.25569 -8.407083  557.631
## 95942  -37.25541 -8.407083  557.454
## 95943  -37.25513 -8.407083  557.817
## 95944  -37.25486 -8.407083  559.268
## 95945  -37.25458 -8.407083  561.109
## 95946  -37.25430 -8.407083  562.878
## 95947  -37.25402 -8.407083  564.401
## 95948  -37.25375 -8.407083  565.455
## 95949  -37.25347 -8.407083  566.206
## 95950  -37.25319 -8.407083  566.734
## 95951  -37.25291 -8.407083  567.158
## 95952  -37.25263 -8.407083  567.623
## 95953  -37.25236 -8.407083  568.207
## 95954  -37.25208 -8.407083  569.037
## 95955  -37.25180 -8.407083  570.234
## 95956  -37.25152 -8.407083  571.859
## 95957  -37.25125 -8.407083  573.532
## 95958  -37.25097 -8.407083  574.983
## 95959  -37.25069 -8.407083  575.870
## 95960  -37.25041 -8.407083  576.481
## 95961  -37.25013 -8.407083  576.957
## 95962  -37.24986 -8.407083  577.457
## 95963  -37.24958 -8.407083  577.817
## 95964  -37.24930 -8.407083  577.969
## 95965  -37.24902 -8.407083  577.909
## 95966  -37.24875 -8.407083  577.823
## 95967  -37.24847 -8.407083  577.881
## 95968  -37.24819 -8.407083  578.235
## 95969  -37.24791 -8.407083  578.640
## 95970  -37.24763 -8.407083  578.870
## 95971  -37.24736 -8.407083  578.754
## 95972  -37.24708 -8.407083  578.489
## 95973  -37.24680 -8.407083  578.222
## 95974  -37.24652 -8.407083  578.059
## 95975  -37.24625 -8.407083  578.066
## 95976  -37.24597 -8.407083  578.293
## 95977  -37.24569 -8.407083  578.860
## 95978  -37.24541 -8.407083  579.614
## 95979  -37.24513 -8.407083  580.492
## 95980  -37.24486 -8.407083  581.357
## 95981  -37.24458 -8.407083  582.383
## 95982  -37.24430 -8.407083  583.682
## 95983  -37.24402 -8.407083  585.303
## 95984  -37.24375 -8.407083  586.871
## 95985  -37.24347 -8.407083  588.160
## 95986  -37.24319 -8.407083  588.827
## 95987  -37.24291 -8.407083  589.212
## 95988  -37.24263 -8.407083  589.461
## 95989  -37.24236 -8.407083  589.752
## 95990  -37.24208 -8.407083  590.068
## 95991  -37.24180 -8.407083  590.459
## 95992  -37.24152 -8.407083  590.927
## 95993  -37.24125 -8.407083  591.398
## 95994  -37.24097 -8.407083  591.801
## 95995  -37.24069 -8.407083  592.091
## 95996  -37.24041 -8.407083  592.095
## 95997  -37.24013 -8.407083  591.674
## 95998  -37.23986 -8.407083  590.701
## 95999  -37.23958 -8.407083  589.460
## 96000  -37.23930 -8.407083  588.155
## 96001  -37.23902 -8.407083  587.013
## 96002  -37.23875 -8.407083  585.955
## 96003  -37.23847 -8.407083  584.981
## 96004  -37.23819 -8.407083  583.997
## 96005  -37.23791 -8.407083  583.036
## 96006  -37.23763 -8.407083  582.075
## 96007  -37.23736 -8.407083  581.110
## 96008  -37.23708 -8.407083  580.192
## 96009  -37.23680 -8.407083  579.407
## 96010  -37.23652 -8.407083  578.845
## 96011  -37.23625 -8.407083  578.547
## 96012  -37.23597 -8.407083  578.523
## 96013  -37.23569 -8.407083  578.822
## 96014  -37.23541 -8.407083  579.088
## 96015  -37.23513 -8.407083  579.034
## 96016  -37.23486 -8.407083  578.386
## 96017  -37.23458 -8.407083  577.413
## 96018  -37.23430 -8.407083  576.242
## 96019  -37.23402 -8.407083  575.279
## 96020  -37.23375 -8.407083  574.420
## 96021  -37.23347 -8.407083  573.792
## 96022  -37.23319 -8.407083  573.407
## 96023  -37.23291 -8.407083  573.437
## 96024  -37.23263 -8.407083  573.997
## 96025  -37.23236 -8.407083  575.170
## 96026  -37.23208 -8.407083  576.345
## 96027  -37.23180 -8.407083  576.974
## 96028  -37.23152 -8.407083  576.631
## 96029  -37.23125 -8.407083  575.942
## 96030  -37.23097 -8.407083  575.253
## 96031  -37.23069 -8.407083  575.067
## 96032  -37.23041 -8.407083  575.197
## 96033  -37.23013 -8.407083  575.679
## 96034  -37.22986 -8.407083  576.621
## 96035  -37.22958 -8.407083  577.628
## 96036  -37.22930 -8.407083  578.379
## 96037  -37.22902 -8.407083  578.618
## 96038  -37.22875 -8.407083  578.584
## 96039  -37.22847 -8.407083  578.350
## 96040  -37.22819 -8.407083  578.027
## 96041  -37.22791 -8.407083  577.631
## 96042  -37.22763 -8.407083  577.248
## 96043  -37.22736 -8.407083  576.983
## 96044  -37.22708 -8.407083  576.799
## 96045  -37.22680 -8.407083  576.753
## 96046  -37.22652 -8.407083  576.688
## 96047  -37.22625 -8.407083  576.704
## 96048  -37.22597 -8.407083  576.742
## 96049  -37.22569 -8.407083  576.837
## 96050  -37.22541 -8.407083  576.822
## 96051  -37.22513 -8.407083  576.620
## 96052  -37.22486 -8.407083  576.166
## 96053  -37.22458 -8.407083  575.233
## 96054  -37.22430 -8.407083  573.524
## 96055  -37.22402 -8.407083  570.937
## 96056  -37.22375 -8.407083  568.654
## 96908  -37.36347 -8.407361  524.487
## 96909  -37.36319 -8.407361  523.343
## 96910  -37.36291 -8.407361  522.540
## 96911  -37.36263 -8.407361  522.525
## 96912  -37.36236 -8.407361  523.916
## 96913  -37.36208 -8.407361  525.829
## 96914  -37.36180 -8.407361  527.552
## 96915  -37.36152 -8.407361  528.944
## 96916  -37.36125 -8.407361  529.389
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## 96918  -37.36069 -8.407361  529.019
## 96919  -37.36041 -8.407361  528.305
## 96920  -37.36013 -8.407361  527.838
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## 96928  -37.35791 -8.407361  528.701
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## 96931  -37.35708 -8.407361  529.431
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## 96942  -37.35402 -8.407361  531.044
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## 96944  -37.35347 -8.407361  530.977
## 96945  -37.35319 -8.407361  532.203
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## 96988  -37.34125 -8.407361  539.857
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## 96992  -37.34013 -8.407361  541.461
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## 97000  -37.33791 -8.407361  541.058
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## 97002  -37.33736 -8.407361  541.067
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## 97004  -37.33680 -8.407361  541.855
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## 97009  -37.33541 -8.407361  542.774
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## 97013  -37.33430 -8.407361  543.876
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## 97026  -37.33069 -8.407361  540.518
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## 97030  -37.32958 -8.407361  541.183
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## 97035  -37.32819 -8.407361  545.473
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## 97037  -37.32763 -8.407361  546.306
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## 97040  -37.32680 -8.407361  549.292
## 97041  -37.32652 -8.407361  549.952
## 97042  -37.32625 -8.407361  550.103
## 97043  -37.32597 -8.407361  550.072
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## 97047  -37.32486 -8.407361  547.252
## 97048  -37.32458 -8.407361  546.494
## 97049  -37.32430 -8.407361  546.205
## 97050  -37.32402 -8.407361  546.828
## 97051  -37.32375 -8.407361  547.573
## 97052  -37.32347 -8.407361  548.779
## 97053  -37.32319 -8.407361  550.102
## 97054  -37.32291 -8.407361  551.191
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## 97056  -37.32236 -8.407361  553.059
## 97057  -37.32208 -8.407361  553.775
## 97058  -37.32180 -8.407361  554.261
## 97059  -37.32152 -8.407361  554.038
## 97060  -37.32125 -8.407361  553.751
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## 97062  -37.32069 -8.407361  554.042
## 97063  -37.32041 -8.407361  554.791
## 97064  -37.32013 -8.407361  555.716
## 97065  -37.31986 -8.407361  556.815
## 97066  -37.31958 -8.407361  557.647
## 97067  -37.31930 -8.407361  557.963
## 97068  -37.31902 -8.407361  557.346
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## 97070  -37.31847 -8.407361  554.969
## 97071  -37.31819 -8.407361  554.402
## 97072  -37.31791 -8.407361  554.312
## 97073  -37.31763 -8.407361  554.520
## 97074  -37.31736 -8.407361  554.963
## 97075  -37.31708 -8.407361  555.852
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## 97077  -37.31652 -8.407361  556.609
## 97078  -37.31625 -8.407361  556.896
## 97079  -37.31597 -8.407361  556.859
## 97080  -37.31569 -8.407361  555.613
## 97081  -37.31541 -8.407361  554.786
## 97082  -37.31513 -8.407361  553.648
## 97083  -37.31486 -8.407361  553.878
## 97084  -37.31458 -8.407361  554.172
## 97085  -37.31430 -8.407361  553.858
## 97086  -37.31402 -8.407361  553.175
## 97087  -37.31375 -8.407361  552.505
## 97088  -37.31347 -8.407361  552.197
## 97089  -37.31319 -8.407361  552.226
## 97090  -37.31291 -8.407361  552.010
## 97091  -37.31263 -8.407361  551.768
## 97092  -37.31236 -8.407361  550.319
## 97093  -37.31208 -8.407361  548.767
## 97094  -37.31180 -8.407361  546.682
## 97095  -37.31152 -8.407361  545.493
## 97096  -37.31125 -8.407361  544.896
## 97097  -37.31097 -8.407361  544.841
## 97098  -37.31069 -8.407361  544.995
## 97099  -37.31041 -8.407361  545.517
## 97100  -37.31013 -8.407361  546.301
## 97101  -37.30986 -8.407361  547.041
## 97102  -37.30958 -8.407361  547.820
## 97103  -37.30930 -8.407361  548.576
## 97104  -37.30902 -8.407361  549.619
## 97105  -37.30875 -8.407361  550.808
## 97106  -37.30847 -8.407361  552.357
## 97107  -37.30819 -8.407361  554.066
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## 97109  -37.30763 -8.407361  556.135
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## 97111  -37.30708 -8.407361  553.995
## 97112  -37.30680 -8.407361  552.989
## 97113  -37.30652 -8.407361  552.587
## 97114  -37.30625 -8.407361  552.408
## 97115  -37.30597 -8.407361  552.622
## 97116  -37.30569 -8.407361  552.807
## 97117  -37.30541 -8.407361  552.995
## 97118  -37.30513 -8.407361  552.973
## 97119  -37.30486 -8.407361  552.399
## 97120  -37.30458 -8.407361  551.958
## 97121  -37.30430 -8.407361  552.332
## 97122  -37.30402 -8.407361  553.622
## 97123  -37.30375 -8.407361  555.495
## 97124  -37.30347 -8.407361  557.650
## 97125  -37.30319 -8.407361  559.893
## 97126  -37.30291 -8.407361  561.693
## 97127  -37.30263 -8.407361  562.812
## 97128  -37.30236 -8.407361  562.148
## 97129  -37.30208 -8.407361  561.040
## 97130  -37.30180 -8.407361  559.576
## 97131  -37.30152 -8.407361  559.043
## 97132  -37.30125 -8.407361  558.753
## 97133  -37.30097 -8.407361  558.654
## 97134  -37.30069 -8.407361  558.519
## 97135  -37.30041 -8.407361  558.588
## 97136  -37.30013 -8.407361  558.940
## 97137  -37.29986 -8.407361  559.501
## 97138  -37.29958 -8.407361  559.770
## 97139  -37.29930 -8.407361  559.888
## 97140  -37.29902 -8.407361  559.006
## 97141  -37.29875 -8.407361  558.137
## 97142  -37.29847 -8.407361  556.923
## 97143  -37.29819 -8.407361  555.731
## 97144  -37.29791 -8.407361  554.684
## 97145  -37.29763 -8.407361  553.770
## 97146  -37.29736 -8.407361  553.325
## 97147  -37.29708 -8.407361  553.199
## 97148  -37.29680 -8.407361  553.861
## 97149  -37.29652 -8.407361  554.953
## 97150  -37.29625 -8.407361  556.179
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## 97159  -37.29375 -8.407361  553.583
## 97160  -37.29347 -8.407361  553.480
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## 97162  -37.29291 -8.407361  551.934
## 97163  -37.29263 -8.407361  551.810
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## 97212  -37.27902 -8.407361  566.892
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## 98285  -37.35736 -8.407639  531.028
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## 98287  -37.35680 -8.407639  531.773
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## 98290  -37.35597 -8.407639  531.501
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## 98301  -37.35291 -8.407639  533.256
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## 98320  -37.34763 -8.407639  540.749
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## 98343  -37.34125 -8.407639  541.776
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## 98351  -37.33902 -8.407639  543.700
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## 98376  -37.33208 -8.407639  545.855
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## 98379  -37.33125 -8.407639  544.030
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## 98381  -37.33069 -8.407639  541.433
## 98382  -37.33041 -8.407639  540.304
## 98383  -37.33013 -8.407639  539.969
## 98384  -37.32986 -8.407639  540.643
## 98385  -37.32958 -8.407639  541.790
## 98386  -37.32930 -8.407639  543.551
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## 98388  -37.32875 -8.407639  545.817
## 98389  -37.32847 -8.407639  546.321
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## 98391  -37.32791 -8.407639  547.109
## 98392  -37.32763 -8.407639  547.554
## 98393  -37.32736 -8.407639  548.581
## 98394  -37.32708 -8.407639  549.588
## 98395  -37.32680 -8.407639  550.808
## 98396  -37.32652 -8.407639  551.304
## 98397  -37.32625 -8.407639  551.248
## 98398  -37.32597 -8.407639  551.007
## 98399  -37.32569 -8.407639  550.668
## 98400  -37.32541 -8.407639  550.216
## 98401  -37.32513 -8.407639  549.251
## 98402  -37.32486 -8.407639  548.351
## 98403  -37.32458 -8.407639  547.609
## 98404  -37.32430 -8.407639  547.473
## 98405  -37.32402 -8.407639  548.228
## 98406  -37.32375 -8.407639  549.239
## 98407  -37.32347 -8.407639  550.516
## 98408  -37.32319 -8.407639  551.589
## 98409  -37.32291 -8.407639  552.595
## 98410  -37.32263 -8.407639  553.530
## 98411  -37.32236 -8.407639  554.362
## 98412  -37.32208 -8.407639  554.989
## 98413  -37.32180 -8.407639  555.432
## 98414  -37.32152 -8.407639  555.565
## 98415  -37.32125 -8.407639  555.698
## 98416  -37.32097 -8.407639  555.628
## 98417  -37.32069 -8.407639  555.716
## 98418  -37.32041 -8.407639  556.090
## 98419  -37.32013 -8.407639  556.730
## 98420  -37.31986 -8.407639  557.955
## 98421  -37.31958 -8.407639  558.890
## 98422  -37.31930 -8.407639  559.400
## 98423  -37.31902 -8.407639  558.988
## 98424  -37.31875 -8.407639  557.771
## 98425  -37.31847 -8.407639  556.737
## 98426  -37.31819 -8.407639  555.794
## 98427  -37.31791 -8.407639  555.105
## 98428  -37.31763 -8.407639  554.952
## 98429  -37.31736 -8.407639  555.755
## 98430  -37.31708 -8.407639  556.771
## 98431  -37.31680 -8.407639  557.781
## 98432  -37.31652 -8.407639  557.819
## 98433  -37.31625 -8.407639  557.551
## 98434  -37.31597 -8.407639  557.221
## 98435  -37.31569 -8.407639  556.739
## 98436  -37.31541 -8.407639  555.919
## 98437  -37.31513 -8.407639  555.596
## 98438  -37.31486 -8.407639  554.968
## 98439  -37.31458 -8.407639  554.264
## 98440  -37.31430 -8.407639  553.480
## 98441  -37.31402 -8.407639  552.932
## 98442  -37.31375 -8.407639  552.590
## 98443  -37.31347 -8.407639  552.498
## 98444  -37.31319 -8.407639  552.785
## 98445  -37.31291 -8.407639  552.814
## 98446  -37.31263 -8.407639  552.768
## 98447  -37.31236 -8.407639  551.475
## 98448  -37.31208 -8.407639  550.029
## 98449  -37.31180 -8.407639  547.938
## 98450  -37.31152 -8.407639  546.565
## 98451  -37.31125 -8.407639  545.688
## 98452  -37.31097 -8.407639  545.613
## 98453  -37.31069 -8.407639  545.800
## 98454  -37.31041 -8.407639  546.275
## 98455  -37.31013 -8.407639  547.070
## 98456  -37.30986 -8.407639  547.923
## 98457  -37.30958 -8.407639  548.932
## 98458  -37.30930 -8.407639  549.877
## 98459  -37.30902 -8.407639  550.797
## 98460  -37.30875 -8.407639  551.863
## 98461  -37.30847 -8.407639  553.323
## 98462  -37.30819 -8.407639  555.202
## 98463  -37.30791 -8.407639  556.620
## 98464  -37.30763 -8.407639  557.258
## 98465  -37.30736 -8.407639  556.567
## 98466  -37.30708 -8.407639  555.349
## 98467  -37.30680 -8.407639  554.493
## 98468  -37.30652 -8.407639  554.122
## 98469  -37.30625 -8.407639  554.156
## 98470  -37.30597 -8.407639  554.396
## 98471  -37.30569 -8.407639  554.662
## 98472  -37.30541 -8.407639  554.965
## 98473  -37.30513 -8.407639  554.899
## 98474  -37.30486 -8.407639  553.963
## 98475  -37.30458 -8.407639  553.378
## 98476  -37.30430 -8.407639  552.952
## 98477  -37.30402 -8.407639  554.367
## 98478  -37.30375 -8.407639  556.672
## 98479  -37.30347 -8.407639  559.041
## 98480  -37.30319 -8.407639  560.957
## 98481  -37.30291 -8.407639  562.193
## 98482  -37.30263 -8.407639  563.001
## 98483  -37.30236 -8.407639  562.408
## 98484  -37.30208 -8.407639  561.103
## 98485  -37.30180 -8.407639  559.614
## 98486  -37.30152 -8.407639  559.233
## 98487  -37.30125 -8.407639  559.247
## 98488  -37.30097 -8.407639  559.437
## 98489  -37.30069 -8.407639  559.809
## 98490  -37.30041 -8.407639  560.204
## 98491  -37.30013 -8.407639  560.753
## 98492  -37.29986 -8.407639  560.616
## 98493  -37.29958 -8.407639  560.261
## 98494  -37.29930 -8.407639  559.510
## 98495  -37.29902 -8.407639  559.022
## 98496  -37.29875 -8.407639  558.072
## 98497  -37.29847 -8.407639  556.911
## 98498  -37.29819 -8.407639  555.746
## 98499  -37.29791 -8.407639  554.782
## 98500  -37.29763 -8.407639  554.013
## 98501  -37.29736 -8.407639  553.465
## 98502  -37.29708 -8.407639  553.466
## 98503  -37.29680 -8.407639  553.826
## 98504  -37.29652 -8.407639  555.412
## 98505  -37.29625 -8.407639  557.202
## 98506  -37.29597 -8.407639  558.550
## 98507  -37.29569 -8.407639  558.636
## 98508  -37.29541 -8.407639  558.237
## 98509  -37.29513 -8.407639  557.058
## 98510  -37.29486 -8.407639  555.941
## 98511  -37.29458 -8.407639  555.000
## 98512  -37.29430 -8.407639  554.370
## 98513  -37.29402 -8.407639  554.222
## 98514  -37.29375 -8.407639  554.001
## 98515  -37.29347 -8.407639  553.796
## 98516  -37.29319 -8.407639  553.160
## 98517  -37.29291 -8.407639  552.848
## 98518  -37.29263 -8.407639  552.712
## 98519  -37.29236 -8.407639  553.641
## 98520  -37.29208 -8.407639  554.948
## 98521  -37.29180 -8.407639  556.086
## 98522  -37.29152 -8.407639  556.939
## 98523  -37.29125 -8.407639  557.070
## 98524  -37.29097 -8.407639  556.928
## 98525  -37.29069 -8.407639  556.650
## 98526  -37.29041 -8.407639  556.267
## 98527  -37.29013 -8.407639  556.144
## 98528  -37.28986 -8.407639  556.201
## 98529  -37.28958 -8.407639  556.420
## 98530  -37.28930 -8.407639  556.207
## 98531  -37.28902 -8.407639  555.399
## 98532  -37.28875 -8.407639  554.827
## 98533  -37.28847 -8.407639  554.418
## 98534  -37.28819 -8.407639  554.645
## 98535  -37.28791 -8.407639  555.122
## 98536  -37.28763 -8.407639  555.885
## 98537  -37.28736 -8.407639  556.349
## 98538  -37.28708 -8.407639  556.674
## 98539  -37.28680 -8.407639  556.753
## 98540  -37.28652 -8.407639  557.048
## 98541  -37.28625 -8.407639  557.294
## 98542  -37.28597 -8.407639  557.300
## 98543  -37.28569 -8.407639  556.984
## 98544  -37.28541 -8.407639  556.567
## 98545  -37.28513 -8.407639  556.212
## 98546  -37.28486 -8.407639  555.800
## 98547  -37.28458 -8.407639  555.450
## 98548  -37.28430 -8.407639  554.968
## 98549  -37.28402 -8.407639  554.866
## 98550  -37.28375 -8.407639  555.068
## 98551  -37.28347 -8.407639  555.410
## 98552  -37.28319 -8.407639  555.881
## 98553  -37.28291 -8.407639  556.371
## 98554  -37.28263 -8.407639  556.807
## 98555  -37.28236 -8.407639  557.182
## 98556  -37.28208 -8.407639  557.592
## 98557  -37.28180 -8.407639  558.472
## 98558  -37.28152 -8.407639  559.805
## 98559  -37.28125 -8.407639  561.316
## 98560  -37.28097 -8.407639  562.835
## 98561  -37.28069 -8.407639  563.784
## 98562  -37.28041 -8.407639  564.465
## 98563  -37.28013 -8.407639  564.870
## 98564  -37.27986 -8.407639  565.285
## 98565  -37.27958 -8.407639  565.759
## 98566  -37.27930 -8.407639  566.231
## 98567  -37.27902 -8.407639  566.697
## 98568  -37.27875 -8.407639  567.232
## 98569  -37.27847 -8.407639  567.951
## 98570  -37.27819 -8.407639  568.806
## 98571  -37.27791 -8.407639  569.680
## 98572  -37.27763 -8.407639  570.460
## 98573  -37.27736 -8.407639  571.309
## 98574  -37.27708 -8.407639  571.950
## 98575  -37.27680 -8.407639  572.430
## 98576  -37.27652 -8.407639  572.294
## 98577  -37.27625 -8.407639  572.100
## 98578  -37.27597 -8.407639  572.227
## 98579  -37.27569 -8.407639  572.947
## 98580  -37.27541 -8.407639  573.740
## 98581  -37.27513 -8.407639  574.050
## 98582  -37.27486 -8.407639  573.973
## 98583  -37.27458 -8.407639  573.678
## 98584  -37.27430 -8.407639  573.370
## 98585  -37.27402 -8.407639  573.118
## 98586  -37.27375 -8.407639  572.904
## 98587  -37.27347 -8.407639  572.857
## 98588  -37.27319 -8.407639  573.034
## 98589  -37.27291 -8.407639  573.137
## 98590  -37.27263 -8.407639  572.977
## 98591  -37.27236 -8.407639  572.442
## 98592  -37.27208 -8.407639  571.838
## 98593  -37.27180 -8.407639  571.656
## 98594  -37.27152 -8.407639  571.830
## 98595  -37.27125 -8.407639  571.855
## 98596  -37.27097 -8.407639  571.556
## 98597  -37.27069 -8.407639  570.138
## 98598  -37.27041 -8.407639  568.327
## 98599  -37.27013 -8.407639  566.113
## 98600  -37.26986 -8.407639  564.195
## 98601  -37.26958 -8.407639  562.764
## 98602  -37.26930 -8.407639  562.300
## 98603  -37.26902 -8.407639  562.911
## 98604  -37.26875 -8.407639  564.246
## 98605  -37.26847 -8.407639  566.127
## 98606  -37.26819 -8.407639  567.391
## 98607  -37.26791 -8.407639  568.286
## 98608  -37.26763 -8.407639  568.722
## 98609  -37.26736 -8.407639  568.813
## 98610  -37.26708 -8.407639  568.706
## 98611  -37.26680 -8.407639  568.007
## 98612  -37.26652 -8.407639  567.724
## 98613  -37.26625 -8.407639  567.591
## 98614  -37.26597 -8.407639  567.588
## 98615  -37.26569 -8.407639  567.144
## 98616  -37.26541 -8.407639  566.229
## 98617  -37.26513 -8.407639  565.191
## 98618  -37.26486 -8.407639  563.823
## 98619  -37.26458 -8.407639  562.411
## 98620  -37.26430 -8.407639  561.398
## 98621  -37.26402 -8.407639  560.791
## 98622  -37.26375 -8.407639  560.910
## 98623  -37.26347 -8.407639  560.961
## 98624  -37.26319 -8.407639  560.285
## 98625  -37.26291 -8.407639  559.690
## 98626  -37.26263 -8.407639  559.380
## 98627  -37.26236 -8.407639  559.935
## 98628  -37.26208 -8.407639  560.896
## 98629  -37.26180 -8.407639  562.003
## 98630  -37.26152 -8.407639  562.915
## 98631  -37.26125 -8.407639  563.700
## 98632  -37.26097 -8.407639  564.313
## 98633  -37.26069 -8.407639  564.913
## 98634  -37.26041 -8.407639  565.129
## 98635  -37.26013 -8.407639  564.999
## 98636  -37.25986 -8.407639  563.951
## 98637  -37.25958 -8.407639  562.794
## 98638  -37.25930 -8.407639  561.722
## 98639  -37.25902 -8.407639  561.876
## 98640  -37.25875 -8.407639  562.372
## 98641  -37.25847 -8.407639  562.801
## 98642  -37.25819 -8.407639  562.326
## 98643  -37.25791 -8.407639  561.698
## 98644  -37.25763 -8.407639  560.415
## 98645  -37.25736 -8.407639  559.230
## 98646  -37.25708 -8.407639  558.103
## 98647  -37.25680 -8.407639  556.995
## 98648  -37.25652 -8.407639  556.327
## 98649  -37.25625 -8.407639  556.422
## 98650  -37.25597 -8.407639  556.845
## 98651  -37.25569 -8.407639  556.922
## 98652  -37.25541 -8.407639  557.321
## 98653  -37.25513 -8.407639  558.097
## 98654  -37.25486 -8.407639  559.553
## 98655  -37.25458 -8.407639  561.383
## 98656  -37.25430 -8.407639  563.078
## 98657  -37.25402 -8.407639  564.259
## 98658  -37.25375 -8.407639  565.342
## 98659  -37.25347 -8.407639  566.413
## 98660  -37.25319 -8.407639  566.994
## 98661  -37.25291 -8.407639  567.549
## 98662  -37.25263 -8.407639  567.764
## 98663  -37.25236 -8.407639  568.682
## 98664  -37.25208 -8.407639  569.716
## 98665  -37.25180 -8.407639  571.495
## 98666  -37.25152 -8.407639  573.397
## 98667  -37.25125 -8.407639  575.282
## 98668  -37.25097 -8.407639  577.204
## 98669  -37.25069 -8.407639  578.356
## 98670  -37.25041 -8.407639  579.102
## 98671  -37.25013 -8.407639  579.305
## 98672  -37.24986 -8.407639  579.829
## 98673  -37.24958 -8.407639  580.218
## 98674  -37.24930 -8.407639  580.637
## 98675  -37.24902 -8.407639  580.450
## 98676  -37.24875 -8.407639  580.061
## 98677  -37.24847 -8.407639  579.766
## 98678  -37.24819 -8.407639  580.031
## 98679  -37.24791 -8.407639  580.154
## 98680  -37.24763 -8.407639  580.508
## 98681  -37.24736 -8.407639  580.254
## 98682  -37.24708 -8.407639  579.946
## 98683  -37.24680 -8.407639  579.889
## 98684  -37.24652 -8.407639  579.920
## 98685  -37.24625 -8.407639  580.127
## 98686  -37.24597 -8.407639  580.470
## 98687  -37.24569 -8.407639  580.970
## 98688  -37.24541 -8.407639  581.687
## 98689  -37.24513 -8.407639  582.365
## 98690  -37.24486 -8.407639  583.109
## 98691  -37.24458 -8.407639  583.888
## 98692  -37.24430 -8.407639  584.857
## 98693  -37.24402 -8.407639  585.925
## 98694  -37.24375 -8.407639  586.908
## 98695  -37.24347 -8.407639  588.072
## 98696  -37.24319 -8.407639  588.973
## 98697  -37.24291 -8.407639  589.732
## 98698  -37.24263 -8.407639  590.196
## 98699  -37.24236 -8.407639  590.618
## 98700  -37.24208 -8.407639  591.171
## 98701  -37.24180 -8.407639  591.558
## 98702  -37.24152 -8.407639  592.271
## 98703  -37.24125 -8.407639  593.022
## 98704  -37.24097 -8.407639  593.514
## 98705  -37.24069 -8.407639  593.746
## 98706  -37.24041 -8.407639  593.555
## 98707  -37.24013 -8.407639  593.178
## 98708  -37.23986 -8.407639  592.782
## 98709  -37.23958 -8.407639  591.984
## 98710  -37.23930 -8.407639  591.517
## 98711  -37.23902 -8.407639  590.373
## 98712  -37.23875 -8.407639  589.058
## 98713  -37.23847 -8.407639  587.965
## 98714  -37.23819 -8.407639  587.276
## 98715  -37.23791 -8.407639  586.763
## 98716  -37.23763 -8.407639  585.637
## 98717  -37.23736 -8.407639  584.362
## 98718  -37.23708 -8.407639  583.160
## 98719  -37.23680 -8.407639  582.327
## 98720  -37.23652 -8.407639  581.738
## 98721  -37.23625 -8.407639  581.244
## 98722  -37.23597 -8.407639  581.183
## 98723  -37.23569 -8.407639  581.706
## 98724  -37.23541 -8.407639  582.100
## 98725  -37.23513 -8.407639  582.210
## 98726  -37.23486 -8.407639  581.472
## 98727  -37.23458 -8.407639  580.365
## 98728  -37.23430 -8.407639  579.128
## 98729  -37.23402 -8.407639  577.838
## 98730  -37.23375 -8.407639  576.576
## 98731  -37.23347 -8.407639  575.859
## 98732  -37.23319 -8.407639  575.633
## 98733  -37.23291 -8.407639  575.900
## 98734  -37.23263 -8.407639  576.423
## 98735  -37.23236 -8.407639  576.671
## 98736  -37.23208 -8.407639  576.903
## 98737  -37.23180 -8.407639  576.745
## 98738  -37.23152 -8.407639  576.321
## 98739  -37.23125 -8.407639  575.789
## 98740  -37.23097 -8.407639  575.169
## 98741  -37.23069 -8.407639  575.303
## 98742  -37.23041 -8.407639  575.773
## 98743  -37.23013 -8.407639  576.910
## 98744  -37.22986 -8.407639  578.019
## 98745  -37.22958 -8.407639  579.120
## 98746  -37.22930 -8.407639  580.198
## 98747  -37.22902 -8.407639  581.359
## 98748  -37.22875 -8.407639  581.787
## 98749  -37.22847 -8.407639  581.530
## 98750  -37.22819 -8.407639  580.843
## 98751  -37.22791 -8.407639  580.071
## 98752  -37.22763 -8.407639  579.492
## 98753  -37.22736 -8.407639  579.379
## 98754  -37.22708 -8.407639  579.359
## 98755  -37.22680 -8.407639  579.252
## 98756  -37.22652 -8.407639  578.933
## 98757  -37.22625 -8.407639  578.664
## 98758  -37.22597 -8.407639  578.467
## 98759  -37.22569 -8.407639  578.405
## 98760  -37.22541 -8.407639  578.213
## 98761  -37.22513 -8.407639  577.809
## 98762  -37.22486 -8.407639  576.837
## 98763  -37.22458 -8.407639  575.409
## 98764  -37.22430 -8.407639  572.886
## 98765  -37.22402 -8.407639  570.281
## 98766  -37.22375 -8.407639  568.359
## 99617  -37.36375 -8.407917  523.190
## 99618  -37.36347 -8.407917  522.995
## 99619  -37.36319 -8.407917  522.236
## 99620  -37.36291 -8.407917  521.894
## 99621  -37.36263 -8.407917  522.368
## 99622  -37.36236 -8.407917  524.535
## 99623  -37.36208 -8.407917  527.144
## 99624  -37.36180 -8.407917  529.527
## 99625  -37.36152 -8.407917  530.776
## 99626  -37.36125 -8.407917  531.410
## 99627  -37.36097 -8.407917  531.520
## 99628  -37.36069 -8.407917  531.421
## 99629  -37.36041 -8.407917  531.133
## 99630  -37.36013 -8.407917  530.934
## 99631  -37.35986 -8.407917  530.627
## 99632  -37.35958 -8.407917  530.571
## 99633  -37.35930 -8.407917  530.512
## 99634  -37.35902 -8.407917  530.933
## 99635  -37.35875 -8.407917  531.285
## 99636  -37.35847 -8.407917  531.622
## 99637  -37.35819 -8.407917  531.861
## 99638  -37.35791 -8.407917  532.075
## 99639  -37.35763 -8.407917  532.432
## 99640  -37.35736 -8.407917  532.808
## 99641  -37.35708 -8.407917  533.245
## 99642  -37.35680 -8.407917  533.471
## 99643  -37.35652 -8.407917  533.490
## 99644  -37.35625 -8.407917  533.264
## 99645  -37.35597 -8.407917  532.915
## 99646  -37.35569 -8.407917  532.396
## 99647  -37.35541 -8.407917  531.918
## 99648  -37.35513 -8.407917  531.648
## 99649  -37.35486 -8.407917  531.507
## 99650  -37.35458 -8.407917  531.507
## 99651  -37.35430 -8.407917  531.360
## 99652  -37.35402 -8.407917  531.047
## 99653  -37.35375 -8.407917  530.837
## 99654  -37.35347 -8.407917  531.023
## 99655  -37.35319 -8.407917  532.119
## 99656  -37.35291 -8.407917  533.346
## 99657  -37.35263 -8.407917  534.084
## 99658  -37.35236 -8.407917  533.883
## 99659  -37.35208 -8.407917  533.248
## 99660  -37.35180 -8.407917  532.820
## 99661  -37.35152 -8.407917  532.820
## 99662  -37.35125 -8.407917  533.430
## 99663  -37.35097 -8.407917  534.276
## 99664  -37.35069 -8.407917  535.386
## 99665  -37.35041 -8.407917  536.437
## 99666  -37.35013 -8.407917  537.316
## 99667  -37.34986 -8.407917  537.901
## 99668  -37.34958 -8.407917  538.341
## 99669  -37.34930 -8.407917  538.581
## 99670  -37.34902 -8.407917  539.423
## 99671  -37.34875 -8.407917  540.085
## 99672  -37.34847 -8.407917  540.737
## 99673  -37.34819 -8.407917  541.390
## 99674  -37.34791 -8.407917  541.826
## 99675  -37.34763 -8.407917  542.060
## 99676  -37.34736 -8.407917  541.434
## 99677  -37.34708 -8.407917  540.757
## 99678  -37.34680 -8.407917  540.091
## 99679  -37.34652 -8.407917  539.707
## 99680  -37.34625 -8.407917  539.545
## 99681  -37.34597 -8.407917  539.644
## 99682  -37.34569 -8.407917  540.031
## 99683  -37.34541 -8.407917  540.475
## 99684  -37.34513 -8.407917  540.804
## 99685  -37.34486 -8.407917  540.700
## 99686  -37.34458 -8.407917  540.446
## 99687  -37.34430 -8.407917  540.265
## 99688  -37.34402 -8.407917  539.909
## 99689  -37.34375 -8.407917  539.902
## 99690  -37.34347 -8.407917  540.193
## 99691  -37.34319 -8.407917  541.038
## 99692  -37.34291 -8.407917  541.989
## 99693  -37.34263 -8.407917  542.823
## 99694  -37.34236 -8.407917  543.183
## 99695  -37.34208 -8.407917  543.361
## 99696  -37.34180 -8.407917  543.487
## 99697  -37.34152 -8.407917  543.718
## 99698  -37.34125 -8.407917  544.010
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## 99700  -37.34069 -8.407917  544.702
## 99701  -37.34041 -8.407917  545.038
## 99702  -37.34013 -8.407917  545.288
## 99703  -37.33986 -8.407917  545.501
## 99704  -37.33958 -8.407917  545.577
## 99705  -37.33930 -8.407917  545.615
## 99706  -37.33902 -8.407917  545.401
## 99707  -37.33875 -8.407917  545.183
## 99708  -37.33847 -8.407917  544.989
## 99709  -37.33819 -8.407917  544.784
## 99710  -37.33791 -8.407917  544.703
## 99711  -37.33763 -8.407917  544.759
## 99712  -37.33736 -8.407917  544.904
## 99713  -37.33708 -8.407917  545.121
## 99714  -37.33680 -8.407917  545.296
## 99715  -37.33652 -8.407917  545.201
## 99716  -37.33625 -8.407917  545.124
## 99717  -37.33597 -8.407917  545.083
## 99718  -37.33569 -8.407917  545.356
## 99719  -37.33541 -8.407917  545.713
## 99720  -37.33513 -8.407917  546.201
## 99721  -37.33486 -8.407917  546.694
## 99722  -37.33458 -8.407917  547.167
## 99723  -37.33430 -8.407917  547.569
## 99724  -37.33402 -8.407917  547.445
## 99725  -37.33375 -8.407917  547.361
## 99726  -37.33347 -8.407917  547.275
## 99727  -37.33319 -8.407917  547.479
## 99728  -37.33291 -8.407917  547.669
## 99729  -37.33263 -8.407917  547.690
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## 99731  -37.33208 -8.407917  547.317
## 99732  -37.33180 -8.407917  546.787
## 99733  -37.33152 -8.407917  545.987
## 99734  -37.33125 -8.407917  545.047
## 99735  -37.33097 -8.407917  544.122
## 99736  -37.33069 -8.407917  543.008
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## 99742  -37.32902 -8.407917  545.639
## 99743  -37.32875 -8.407917  546.670
## 99744  -37.32847 -8.407917  547.526
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## 99749  -37.32708 -8.407917  550.874
## 99750  -37.32680 -8.407917  551.515
## 99751  -37.32652 -8.407917  551.942
## 99752  -37.32625 -8.407917  551.968
## 99753  -37.32597 -8.407917  551.923
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## 99757  -37.32486 -8.407917  549.995
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## 99759  -37.32430 -8.407917  549.515
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## 99821  -37.30708 -8.407917  556.858
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## 99866  -37.29458 -8.407917  555.917
## 99867  -37.29430 -8.407917  555.066
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## 99869  -37.29375 -8.407917  554.625
## 99870  -37.29347 -8.407917  554.531
## 99871  -37.29319 -8.407917  554.051
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## 99873  -37.29263 -8.407917  553.894
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## 99878  -37.29125 -8.407917  557.023
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## 99881  -37.29041 -8.407917  556.477
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## 99883  -37.28986 -8.407917  556.452
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## 99886  -37.28902 -8.407917  556.078
## 99887  -37.28875 -8.407917  555.441
## 99888  -37.28847 -8.407917  554.849
## 99889  -37.28819 -8.407917  554.882
## 99890  -37.28791 -8.407917  555.067
## 99891  -37.28763 -8.407917  555.384
## 99892  -37.28736 -8.407917  555.696
## 99893  -37.28708 -8.407917  556.053
## 99894  -37.28680 -8.407917  556.631
## 99895  -37.28652 -8.407917  557.045
## 99896  -37.28625 -8.407917  557.535
## 99897  -37.28597 -8.407917  557.832
## 99898  -37.28569 -8.407917  557.838
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## 99901  -37.28486 -8.407917  556.609
## 99902  -37.28458 -8.407917  556.052
## 99903  -37.28430 -8.407917  555.663
## 99904  -37.28402 -8.407917  555.564
## 99905  -37.28375 -8.407917  555.673
## 99906  -37.28347 -8.407917  555.936
## 99907  -37.28319 -8.407917  556.280
## 99908  -37.28291 -8.407917  556.656
## 99909  -37.28263 -8.407917  556.994
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## 99911  -37.28208 -8.407917  557.557
## 99912  -37.28180 -8.407917  558.108
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## 99917  -37.28041 -8.407917  563.884
## 99918  -37.28013 -8.407917  564.496
## 99919  -37.27986 -8.407917  565.079
## 99920  -37.27958 -8.407917  565.623
## 99921  -37.27930 -8.407917  566.303
## 99922  -37.27902 -8.407917  566.784
## 99923  -37.27875 -8.407917  567.507
## 99924  -37.27847 -8.407917  568.337
## 99925  -37.27819 -8.407917  569.420
## 99926  -37.27791 -8.407917  570.511
## 99927  -37.27763 -8.407917  571.551
## 99928  -37.27736 -8.407917  572.455
## 99929  -37.27708 -8.407917  573.105
## 99930  -37.27680 -8.407917  573.244
## 99931  -37.27652 -8.407917  573.143
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## 99933  -37.27597 -8.407917  572.871
## 99934  -37.27569 -8.407917  573.532
## 99935  -37.27541 -8.407917  574.328
## 99936  -37.27513 -8.407917  574.910
## 99937  -37.27486 -8.407917  574.911
## 99938  -37.27458 -8.407917  574.609
## 99939  -37.27430 -8.407917  574.066
## 99940  -37.27402 -8.407917  573.738
## 99941  -37.27375 -8.407917  573.355
## 99942  -37.27347 -8.407917  573.018
## 99943  -37.27319 -8.407917  572.969
## 99944  -37.27291 -8.407917  572.840
## 99945  -37.27263 -8.407917  572.518
## 99946  -37.27236 -8.407917  571.800
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## 99948  -37.27180 -8.407917  570.477
## 99949  -37.27152 -8.407917  570.457
## 99950  -37.27125 -8.407917  570.327
## 99951  -37.27097 -8.407917  569.917
## 99952  -37.27069 -8.407917  568.650
## 99953  -37.27041 -8.407917  567.105
## 99954  -37.27013 -8.407917  565.472
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## 99960  -37.26847 -8.407917  565.570
## 99961  -37.26819 -8.407917  566.824
## 99962  -37.26791 -8.407917  567.838
## 99963  -37.26763 -8.407917  568.680
## 99964  -37.26736 -8.407917  568.927
## 99965  -37.26708 -8.407917  569.007
## 99966  -37.26680 -8.407917  569.015
## 99967  -37.26652 -8.407917  568.731
## 99968  -37.26625 -8.407917  568.414
## 99969  -37.26597 -8.407917  567.736
## 99970  -37.26569 -8.407917  567.195
## 99971  -37.26541 -8.407917  566.285
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## 99973  -37.26486 -8.407917  564.048
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## 99975  -37.26430 -8.407917  562.229
## 99976  -37.26402 -8.407917  561.893
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## 99981  -37.26263 -8.407917  559.995
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## 99984  -37.26180 -8.407917  562.793
## 99985  -37.26152 -8.407917  563.665
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## 99987  -37.26097 -8.407917  564.869
## 99988  -37.26069 -8.407917  565.319
## 99989  -37.26041 -8.407917  565.380
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## 110762 -37.27902 -8.410139  566.778
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## 110765 -37.27819 -8.410139  569.899
## 110766 -37.27791 -8.410139  570.527
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## 110768 -37.27736 -8.410139  572.040
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## 110771 -37.27652 -8.410139  575.922
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## 110773 -37.27597 -8.410139  577.900
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## 110780 -37.27402 -8.410139  574.638
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## 110785 -37.27263 -8.410139  571.913
## 110786 -37.27236 -8.410139  571.588
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## 110788 -37.27180 -8.410139  570.801
## 110789 -37.27152 -8.410139  570.133
## 110790 -37.27125 -8.410139  569.683
## 110791 -37.27097 -8.410139  569.453
## 110792 -37.27069 -8.410139  569.669
## 110793 -37.27041 -8.410139  569.742
## 110794 -37.27013 -8.410139  569.689
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## 110796 -37.26958 -8.410139  567.497
## 110797 -37.26930 -8.410139  566.218
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## 110801 -37.26819 -8.410139  566.440
## 110802 -37.26791 -8.410139  568.024
## 110803 -37.26763 -8.410139  569.286
## 110804 -37.26736 -8.410139  569.797
## 110805 -37.26708 -8.410139  569.953
## 110806 -37.26680 -8.410139  569.974
## 110807 -37.26652 -8.410139  570.229
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## 111919 -37.33402 -8.410417  556.791
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## 111939 -37.32847 -8.410417  555.551
## 111940 -37.32819 -8.410417  555.971
## 111941 -37.32791 -8.410417  556.583
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## 111948 -37.32597 -8.410417  560.763
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## 111953 -37.32458 -8.410417  562.584
## 111954 -37.32430 -8.410417  562.522
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## 111957 -37.32347 -8.410417  563.647
## 111958 -37.32319 -8.410417  564.063
## 111959 -37.32291 -8.410417  564.299
## 111960 -37.32263 -8.410417  564.251
## 111961 -37.32236 -8.410417  563.685
## 111962 -37.32208 -8.410417  563.095
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## 111965 -37.32125 -8.410417  563.992
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## 111967 -37.32069 -8.410417  564.561
## 111968 -37.32041 -8.410417  564.469
## 111969 -37.32013 -8.410417  564.407
## 111970 -37.31986 -8.410417  564.990
## 111971 -37.31958 -8.410417  565.659
## 111972 -37.31930 -8.410417  566.319
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## 111975 -37.31847 -8.410417  567.889
## 111976 -37.31819 -8.410417  567.304
## 111977 -37.31791 -8.410417  566.598
## 111978 -37.31763 -8.410417  566.033
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## 111980 -37.31708 -8.410417  565.483
## 111981 -37.31680 -8.410417  565.862
## 111982 -37.31652 -8.410417  566.977
## 111983 -37.31625 -8.410417  568.226
## 111984 -37.31597 -8.410417  569.064
## 111985 -37.31569 -8.410417  569.491
## 111986 -37.31541 -8.410417  569.342
## 111987 -37.31513 -8.410417  568.780
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## 111989 -37.31458 -8.410417  568.449
## 111990 -37.31430 -8.410417  568.237
## 111991 -37.31402 -8.410417  567.651
## 111992 -37.31375 -8.410417  567.211
## 111993 -37.31347 -8.410417  566.795
## 111994 -37.31319 -8.410417  566.590
## 111995 -37.31291 -8.410417  566.324
## 111996 -37.31263 -8.410417  565.929
## 111997 -37.31236 -8.410417  565.340
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## 112000 -37.31152 -8.410417  560.401
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## 112002 -37.31097 -8.410417  555.686
## 112003 -37.31069 -8.410417  553.798
## 112004 -37.31041 -8.410417  552.845
## 112005 -37.31013 -8.410417  552.740
## 112006 -37.30986 -8.410417  553.862
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## 112009 -37.30902 -8.410417  558.844
## 112010 -37.30875 -8.410417  560.243
## 112011 -37.30847 -8.410417  561.535
## 112012 -37.30819 -8.410417  562.409
## 112013 -37.30791 -8.410417  563.403
## 112014 -37.30763 -8.410417  564.634
## 112015 -37.30736 -8.410417  566.383
## 112016 -37.30708 -8.410417  568.006
## 112017 -37.30680 -8.410417  568.859
## 112018 -37.30652 -8.410417  568.887
## 112019 -37.30625 -8.410417  568.472
## 112020 -37.30597 -8.410417  567.940
## 112021 -37.30569 -8.410417  568.872
## 112022 -37.30541 -8.410417  569.575
## 112023 -37.30513 -8.410417  569.815
## 112024 -37.30486 -8.410417  569.021
## 112025 -37.30458 -8.410417  567.604
## 112026 -37.30430 -8.410417  565.722
## 112027 -37.30402 -8.410417  563.688
## 112028 -37.30375 -8.410417  562.030
## 112029 -37.30347 -8.410417  561.452
## 112030 -37.30319 -8.410417  562.370
## 112031 -37.30291 -8.410417  564.173
## 112032 -37.30263 -8.410417  566.117
## 112033 -37.30236 -8.410417  567.418
## 112034 -37.30208 -8.410417  568.275
## 112035 -37.30180 -8.410417  568.544
## 112036 -37.30152 -8.410417  568.582
## 112037 -37.30125 -8.410417  568.225
## 112038 -37.30097 -8.410417  567.603
## 112039 -37.30069 -8.410417  567.306
## 112040 -37.30041 -8.410417  566.805
## 112041 -37.30013 -8.410417  566.169
## 112042 -37.29986 -8.410417  565.378
## 112043 -37.29958 -8.410417  564.546
## 112044 -37.29930 -8.410417  563.847
## 112045 -37.29902 -8.410417  563.023
## 112046 -37.29875 -8.410417  562.512
## 112047 -37.29847 -8.410417  562.191
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## 139157 -37.29569 -8.415972  581.698
## 139158 -37.29541 -8.415972  581.788
## 139159 -37.29513 -8.415972  581.530
## 139160 -37.29486 -8.415972  580.482
## 139161 -37.29458 -8.415972  579.563
## 139162 -37.29430 -8.415972  578.541
## 139163 -37.29402 -8.415972  578.368
## 139164 -37.29375 -8.415972  578.531
## 139165 -37.29347 -8.415972  579.430
## 139166 -37.29319 -8.415972  580.096
## 139167 -37.29291 -8.415972  580.459
## 139168 -37.29263 -8.415972  580.037
## 139169 -37.29236 -8.415972  578.704
## 139170 -37.29208 -8.415972  577.234
## 139171 -37.29180 -8.415972  575.770
## 139172 -37.29152 -8.415972  575.303
## 139173 -37.29125 -8.415972  574.998
## 139174 -37.29097 -8.415972  575.126
## 139175 -37.29069 -8.415972  574.721
## 139176 -37.29041 -8.415972  574.198
## 139177 -37.29013 -8.415972  573.569
## 139178 -37.28986 -8.415972  572.868
## 139179 -37.28958 -8.415972  572.058
## 139180 -37.28930 -8.415972  571.143
## 139181 -37.28902 -8.415972  569.804
## 139182 -37.28875 -8.415972  568.566
## 139183 -37.28847 -8.415972  567.394
## 139184 -37.28819 -8.415972  567.435
## 139185 -37.28791 -8.415972  567.746
## 139186 -37.28763 -8.415972  567.957
## 139187 -37.28736 -8.415972  567.220
## 139188 -37.28708 -8.415972  566.245
## 139189 -37.28680 -8.415972  565.593
## 139190 -37.28652 -8.415972  564.973
## 139191 -37.28625 -8.415972  564.420
## 139192 -37.28597 -8.415972  563.833
## 139193 -37.28569 -8.415972  564.222
## 139194 -37.28541 -8.415972  564.945
## 139195 -37.28513 -8.415972  565.523
## 139196 -37.28486 -8.415972  565.568
## 139197 -37.28458 -8.415972  565.595
## 139198 -37.28430 -8.415972  565.978
## 139199 -37.28402 -8.415972  566.809
## 139200 -37.28375 -8.415972  567.486
## 139201 -37.28347 -8.415972  568.161
## 139202 -37.28319 -8.415972  568.300
## 139203 -37.28291 -8.415972  568.418
## 139204 -37.28263 -8.415972  568.146
## 139205 -37.28236 -8.415972  567.996
## 139206 -37.28208 -8.415972  567.829
## 139207 -37.28180 -8.415972  567.227
## 139208 -37.28152 -8.415972  566.441
## 139209 -37.28125 -8.415972  565.548
## 139210 -37.28097 -8.415972  565.326
## 139211 -37.28069 -8.415972  564.975
## 139212 -37.28041 -8.415972  564.871
## 139213 -37.28013 -8.415972  565.364
## 139214 -37.27986 -8.415972  566.750
## 139215 -37.27958 -8.415972  568.437
## 139216 -37.27930 -8.415972  569.729
## 139217 -37.27902 -8.415972  570.609
## 139218 -37.27875 -8.415972  571.604
## 139219 -37.27847 -8.415972  572.596
## 139220 -37.27819 -8.415972  573.373
## 139221 -37.27791 -8.415972  573.985
## 139222 -37.27763 -8.415972  574.534
## 139223 -37.27736 -8.415972  574.944
## 139224 -37.27708 -8.415972  575.342
## 139225 -37.27680 -8.415972  575.686
## 139226 -37.27652 -8.415972  576.059
## 139227 -37.27625 -8.415972  576.381
## 139228 -37.27597 -8.415972  576.987
## 139229 -37.27569 -8.415972  577.466
## 139230 -37.27541 -8.415972  577.953
## 139231 -37.27513 -8.415972  578.209
## 139232 -37.27486 -8.415972  578.418
## 139233 -37.27458 -8.415972  578.604
## 139234 -37.27430 -8.415972  578.451
## 139235 -37.27402 -8.415972  577.710
## 139236 -37.27375 -8.415972  576.832
##  [ reached 'max' / getOption("max.print") -- omitted 630149 rows ]

O primeiro passo na transformação dos dados foi recortar a área de interesse. O raster carregado não estava com a área desejada. Para isso, utilizando a função mask(), e em seguida a função crop(), ambas para o shapefile do Parque Nacional do Catimbau, foi delimitada a área de interesse. O próximo passo foi transformar o raster em um dataframe. Para isso, foi usada a função as.data.frame(), com o comando xy=TRUE, para indicar que a longitude iria para a variável x, a latitude para a variável y e seria cria uma nova variável para os dados correspondentes aos valores de altitude. Em seguida, apenas a variável com os dados de altitude foi renomeada, com a função colnames().

23.5.2 Criando o ggplot

ggplot()+
  geom_raster(data=topo_catimbau_df,aes(x,y,fill=altitude))+
  labs(x=NULL,
       y=NULL,
       fill="altitude (m)")+
  tema

Tendo agora o dataframe, é possível criar o mapa raster. Cotude, vale a pena a se atentar a um detalhe importante: arquivos raster são compostos de pixels, o que os tornam imagens, então uma resolução maiore irá exigir pixels menores e uma quantidade maior deles, o que torna o arquivo, muitas vezes, exponencialmente maior. Isso tudo consome informação e memória, não só do R, mas do próprio dispositivo. Então, ao escolher a resolução do arquivo raster, sempre é importante avaliar se vale a pena uma resolução alta ou se pode diminuir, sem perder informação e qualidade.

Mais ainda, é possível alterar a paleta de cor do gradiente.

23.5.3 Alterando o gradiente do raster

ggplot()+
  geom_raster(data=topo_catimbau_df,aes(x,y,fill=altitude))+
  labs(x=NULL,
       y=NULL,
       fill="altitude (m)")+
  scale_fill_viridis_c()+
  tema

O grupo de paletas viridis estão entre as mais utilizadas no R. É possível escolher qual tipo de paleta do grupo é desejado, através do comando option=.

ggplot()+
  geom_raster(data=topo_catimbau_df,aes(x,y,fill=altitude))+
  labs(x=NULL,
       y=NULL,
       fill="altitude (m)")+
  scale_fill_viridis_c(option="rocket")+
  tema

ggplot()+
  geom_raster(data=topo_catimbau_df,aes(x,y,fill=altitude))+
  labs(x=NULL,
       y=NULL,
       fill="altitude (m)")+
  scale_fill_viridis_c(option="inferno")+
  tema

ggplot()+
  geom_raster(data=topo_catimbau_df,aes(x,y,fill=altitude))+
  labs(x=NULL,
       y=NULL,
       fill="altitude (m)")+
  scale_fill_viridis_c(option="cividis")+
  tema

ggplot()+
  geom_raster(data=topo_catimbau_df,aes(x,y,fill=altitude))+
  labs(x=NULL,
       y=NULL,
       fill="altitude (m)")+
  scale_fill_viridis_c(option="mako")+
  tema

ggplot()+
  geom_raster(data=topo_catimbau_df,aes(x,y,fill=altitude))+
  labs(x=NULL,
       y=NULL,
       fill="altitude (m)")+
  scale_fill_viridis_c(option="turbo")+
  tema

O mapa, em termos técnicos, está pronto. Contudo, há também como combinar um arquivo raster e um arquivo shapefile.

23.6 Combinando os tipos de mapa

ggplot()+
  geom_sf(data=subset(Estados,name_region=="Nordeste"),color="black",fill="gray")+
  geom_sf(data=subset(Estados,name_state=="Pernambuco"),color="black",fill="yellow")+
  geom_raster(data=topo_catimbau_df,aes(x,y,fill=altitude))+
  geom_sf(data=Catimbau,color="black",fill=NA,linewidth=0.8)+
  labs(x=NULL,
       y=NULL,
       fill="altitude (m)")+
  scale_fill_viridis_c(option="turbo")+
  coord_sf(xlim=c(-41.15,-34.5),ylim=c(-9.5,-7.25))+
  annotation_scale(location="br",height = unit(0.3,"cm"))+
  annotation_north_arrow(style = north_arrow_nautical, location="tr",height = unit(1.85,"cm"),width = unit(1.85,"cm"))+
  tema