DATA 605 HW1-YINA QIAO

library(dplyr)

## 
## Attaching package: 'dplyr'

## The following objects are masked from 'package:stats':
## 
##     filter, lag

## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union

library(gifski)

HW Outline

1. Part 1: Draw Initials ‘Y’ and ‘Q’
   • Creation of ‘Y’
   • Creation of ‘Q’
2. Part 2: Transformation
   • Application of Transformations to ‘Y’ and ‘Q’

Part 1 Draw Initials Y Q

• Create Y

# Diagonal line 1 (left branch of Y)
x_1_y <- seq(-3, -2, length.out = 500)
y_1_y <- seq(2, 0, length.out = 500)

# Diagonal line 2 (right branch of Y)
x_2_y <- seq(-1, -2, length.out = 500)
y_2_y <- seq(2, 0, length.out = 500)

# Vertical line (stem of Y)
x_3_y <- rep(-2, 500)
y_3_y <- seq(0, -2, length.out = 500)

# Combine x and y coordinates for Y
x_y <- c(x_1_y, x_2_y, x_3_y)
y_y <- c(y_1_y, y_2_y, y_3_y)

plot(y_y~x_y, xlim=c(-3,4),ylim=c(-3,3))

• Create Q

# Circle for Q
r = 1  # Radius
h = 2  # x-coordinate of center
k = 0  # y-coordinate of center
theta <- seq(0, 2 * pi, length.out = 1000)
x_q_circle <- h + r * cos(theta)  
y_q_circle <- k + r * sin(theta)  

# Plot the circle
plot(x_q_circle, y_q_circle, type = "l", xlim = c(-3, 4), ylim = c(-3, 3), aspect = 1, lwd = 6)

## Warning in plot.window(...): "aspect" is not a graphical parameter

## Warning in plot.xy(xy, type, ...): "aspect" is not a graphical parameter

## Warning in axis(side = side, at = at, labels = labels, ...): "aspect" is not a
## graphical parameter

## Warning in axis(side = side, at = at, labels = labels, ...): "aspect" is not a
## graphical parameter

## Warning in box(...): "aspect" is not a graphical parameter

## Warning in title(...): "aspect" is not a graphical parameter

# Tail
x1 <- 2
y1 <- -0.5
x2 <- 2.5
y2 <- -1.5
m <- (y2 - y1) / (x2 - x1)
b <- y1 - m * x1
x_2_q <- seq(2, 2.5, length.out = 100)
y_2_q <- m * x_2_q + b

# Add the tail to the plot
lines(x_2_q, y_2_q, lwd = 6)

• Combined YQ

# Combine x and y coordinates for Y and Q
x <- c(x_y, x_q_circle, x_2_q)
y <- c(y_y, y_q_circle, y_2_q)
yq <- rbind(x, y)
plot(y~x, xlim=c(-3,4),ylim=c(-3,3))

Part 2 Transformation

• Use a loop that changes the transformation matrix incrementally to demonstrate 1) shear, 2) scaling, 3) rotation , and 4) projection in animated fashion
• A Pop up window will open to demonstrate the animation

# Transformation types
trans_type <- c("identity", "shear", "scale", "rotate", "project")

# Open a new plotting window
x11()

# Loop through transformation types
for (t in trans_type) {
  for (i in seq(0, pi*2, length.out = 60)) {
    if (t == "identity") {
      trans_matrix <- diag(2)
    } else if (t == "shear") {
      trans_matrix <- matrix(c(1, 0, i, 1), nrow = 2, ncol = 2)
    } else if (t == "scale") {
      trans_matrix <- diag(c(1 + i/10, 1 + i/10))
    } else if (t == "rotate") {
      trans_matrix <- matrix(c(cos(i), sin(i), -sin(i), cos(i)), nrow = 2, ncol = 2)
    } else if (t == "project") {
      trans_matrix <- matrix(c(1, 0, 0, 0), nrow = 2, ncol = 2)
    }

    # Apply the transformation to YQ and plot
    tyq <- apply(yq, 2, function(z) trans_matrix %*% z)
    plot(tyq[1,] ~ tyq[2,], xlim = c(-3, 4), ylim = c(-3, 3), xlab = "x", ylab = "y", main = paste(t, "transformation at i =", round(i, 2)))
    Sys.sleep(0.1)
  }
}