Geometría analítica para el plano
library(ggplot2)
library(plotly)
##
## Adjuntando el paquete: 'plotly'
## The following object is masked from 'package:ggplot2':
##
## last_plot
## The following object is masked from 'package:stats':
##
## filter
## The following object is masked from 'package:graphics':
##
## layout
library(dplyr)
##
## Adjuntando el paquete: 'dplyr'
## The following objects are masked from 'package:stats':
##
## filter, lag
## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, union
x_vals=seq(-10,10,length.out = 100)
y_vals=seq(-10,10,length.out = 100)
plane=expand.grid(x=x_vals,y=y_vals)
plane$z=5-plane$x-2*plane$y
t_vals=seq(-10,10,length.out = 100)
linea=data.frame(x=1+2*t_vals,y=3-t_vals,z=2+t_vals)
linea
## x y z
## 1 -19.00000000 13.00000000 -8.00000000
## 2 -18.59595960 12.79797980 -7.79797980
## 3 -18.19191919 12.59595960 -7.59595960
## 4 -17.78787879 12.39393939 -7.39393939
## 5 -17.38383838 12.19191919 -7.19191919
## 6 -16.97979798 11.98989899 -6.98989899
## 7 -16.57575758 11.78787879 -6.78787879
## 8 -16.17171717 11.58585859 -6.58585859
## 9 -15.76767677 11.38383838 -6.38383838
## 10 -15.36363636 11.18181818 -6.18181818
## 11 -14.95959596 10.97979798 -5.97979798
## 12 -14.55555556 10.77777778 -5.77777778
## 13 -14.15151515 10.57575758 -5.57575758
## 14 -13.74747475 10.37373737 -5.37373737
## 15 -13.34343434 10.17171717 -5.17171717
## 16 -12.93939394 9.96969697 -4.96969697
## 17 -12.53535354 9.76767677 -4.76767677
## 18 -12.13131313 9.56565657 -4.56565657
## 19 -11.72727273 9.36363636 -4.36363636
## 20 -11.32323232 9.16161616 -4.16161616
## 21 -10.91919192 8.95959596 -3.95959596
## 22 -10.51515152 8.75757576 -3.75757576
## 23 -10.11111111 8.55555556 -3.55555556
## 24 -9.70707071 8.35353535 -3.35353535
## 25 -9.30303030 8.15151515 -3.15151515
## 26 -8.89898990 7.94949495 -2.94949495
## 27 -8.49494949 7.74747475 -2.74747475
## 28 -8.09090909 7.54545455 -2.54545455
## 29 -7.68686869 7.34343434 -2.34343434
## 30 -7.28282828 7.14141414 -2.14141414
## 31 -6.87878788 6.93939394 -1.93939394
## 32 -6.47474747 6.73737374 -1.73737374
## 33 -6.07070707 6.53535354 -1.53535354
## 34 -5.66666667 6.33333333 -1.33333333
## 35 -5.26262626 6.13131313 -1.13131313
## 36 -4.85858586 5.92929293 -0.92929293
## 37 -4.45454545 5.72727273 -0.72727273
## 38 -4.05050505 5.52525253 -0.52525253
## 39 -3.64646465 5.32323232 -0.32323232
## 40 -3.24242424 5.12121212 -0.12121212
## 41 -2.83838384 4.91919192 0.08080808
## 42 -2.43434343 4.71717172 0.28282828
## 43 -2.03030303 4.51515152 0.48484848
## 44 -1.62626263 4.31313131 0.68686869
## 45 -1.22222222 4.11111111 0.88888889
## 46 -0.81818182 3.90909091 1.09090909
## 47 -0.41414141 3.70707071 1.29292929
## 48 -0.01010101 3.50505051 1.49494949
## 49 0.39393939 3.30303030 1.69696970
## 50 0.79797980 3.10101010 1.89898990
## 51 1.20202020 2.89898990 2.10101010
## 52 1.60606061 2.69696970 2.30303030
## 53 2.01010101 2.49494949 2.50505051
## 54 2.41414141 2.29292929 2.70707071
## 55 2.81818182 2.09090909 2.90909091
## 56 3.22222222 1.88888889 3.11111111
## 57 3.62626263 1.68686869 3.31313131
## 58 4.03030303 1.48484848 3.51515152
## 59 4.43434343 1.28282828 3.71717172
## 60 4.83838384 1.08080808 3.91919192
## 61 5.24242424 0.87878788 4.12121212
## 62 5.64646465 0.67676768 4.32323232
## 63 6.05050505 0.47474747 4.52525253
## 64 6.45454545 0.27272727 4.72727273
## 65 6.85858586 0.07070707 4.92929293
## 66 7.26262626 -0.13131313 5.13131313
## 67 7.66666667 -0.33333333 5.33333333
## 68 8.07070707 -0.53535354 5.53535354
## 69 8.47474747 -0.73737374 5.73737374
## 70 8.87878788 -0.93939394 5.93939394
## 71 9.28282828 -1.14141414 6.14141414
## 72 9.68686869 -1.34343434 6.34343434
## 73 10.09090909 -1.54545455 6.54545455
## 74 10.49494949 -1.74747475 6.74747475
## 75 10.89898990 -1.94949495 6.94949495
## 76 11.30303030 -2.15151515 7.15151515
## 77 11.70707071 -2.35353535 7.35353535
## 78 12.11111111 -2.55555556 7.55555556
## 79 12.51515152 -2.75757576 7.75757576
## 80 12.91919192 -2.95959596 7.95959596
## 81 13.32323232 -3.16161616 8.16161616
## 82 13.72727273 -3.36363636 8.36363636
## 83 14.13131313 -3.56565657 8.56565657
## 84 14.53535354 -3.76767677 8.76767677
## 85 14.93939394 -3.96969697 8.96969697
## 86 15.34343434 -4.17171717 9.17171717
## 87 15.74747475 -4.37373737 9.37373737
## 88 16.15151515 -4.57575758 9.57575758
## 89 16.55555556 -4.77777778 9.77777778
## 90 16.95959596 -4.97979798 9.97979798
## 91 17.36363636 -5.18181818 10.18181818
## 92 17.76767677 -5.38383838 10.38383838
## 93 18.17171717 -5.58585859 10.58585859
## 94 18.57575758 -5.78787879 10.78787879
## 95 18.97979798 -5.98989899 10.98989899
## 96 19.38383838 -6.19191919 11.19191919
## 97 19.78787879 -6.39393939 11.39393939
## 98 20.19191919 -6.59595960 11.59595960
## 99 20.59595960 -6.79797980 11.79797980
## 100 21.00000000 -7.00000000 12.00000000
p = ggplot() +
geom_tile(data = plane, aes(x = x, y = y, fill = z), alpha = 0.3) +
geom_line(data = linea, aes(x = x, y = y, color = z)) +
labs(title = "Plano y Recta en el Espacio",
x = "X",
y = "Y",
fill = "Z (Plano)",
color = "Z (Recta)") +
theme_minimal()
p
p1 = plot_ly() %>%
add_surface(
x = matrix(plane$x,nrow=100),
y = matrix(plane$y,nrow=100),
z = matrix(plane$z,nrow=100),
colorscale="Viridis",
showscale=FALSE,
name="Plano",
contours = list(
x = list(show = TRUE, color = "black"),
y = list(show = TRUE, color = "black"),
z = list(show = TRUE, color = "black"))) %>%
add_trace(
x = linea$x, y = linea$y, z = linea$z,
mode = 'lines', type = 'scatter3d', line = list(color = 'red', width = 4), name= "Linea recta"
) %>% add_trace(
x = c(-7), y = c(7), z = c(-2),
mode = 'markers', type = 'scatter3d',
marker = list(color = 'yellow', size = 5),
name = "Intersección"
) %>%
layout(
title = "Plano y Recta en el Espacio",
scene = list(
xaxis = list(title = "X",range=c(-10,10),dtick=1),
yaxis = list(title = "Y",range=c(-10,10),dtick=1),
zaxis = list(title = "Z",range=c(-10,10),dtick=1)
)
)
p1