Data 605 HW 1

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library(ggplot2)
library(gganimate)
library(gifski)

Instructions

Then, write R code that will left multiply (%*%) a square matrix (x) against each of the vectors of points (y). Initially, that square matrix will be the Identity matrix.

Use a loop that changes the transformation matrix incrementally to demonstrate 1) shear, 2) scaling, 3) rotation , and 4) projection in animated fashion.

Hint: Use x11() to open a new plotting window in R.

Upload your document as an .RMD file. I will know if your assignment is correct if the animation runs. correctly.

Creating my initials

x=c(rep(-2,500),
    seq(-2,-1,length.out=500),
    seq(-1,0,length.out=500), 
    rep(0,500), rep(1,500),
    seq(1,2,length.out=500),
    seq(1,2,length.out=500),
    rep(2,500),rep(2,500),
    seq(2,1.5,length.out=500),
    seq(2,1.5,length.out=500),
    seq(1.5,1,length.out=500) )

y=c(seq(-1,1,length.out=500),
    seq(1,-1,length.out=500),
    seq(-1,1,length.out=500), 
    seq(-1,1,length.out=500),
    seq(-1,1,length.out=500),
    rep(1,500),rep(-1,500),
    seq(0.5,1,length.out=500),
    seq(-0.5,-1,length.out=500),
    seq(0.5,0,length.out=500),
    seq(-0.5,0,length.out=500),
    rep(0,500) )

z=rbind(x,y)
 

plot(y~x, xlim=c(-2,3), ylim=c(-2,3))

Shearing

Creating the shearing animation by updating the transformation matrix.

scale <- as.numeric(seq(0, 5, by = 0.2 ))

x11()
for (val in scale) {
  t_matrix <- matrix(c(1, 0, val, 1), nrow=2, ncol=2)
  shearing <- apply(z, 2, function(x) x %*% t_matrix)
    plot(shearing[2,] ~ shearing[1,], xlim=c(-3, 3), ylim=c(-3, 3))
}

Scaling

Creating the scaling animation by updating the transformation matrix.

x11()
for (val in scale) {
  ext_z <- rbind(z, numeric(3000))
  trans_matrix <- matrix(c(cos(val), sin(val), 0, -sin(val), cos(val), 0, 0, 0, 1), nrow=3, ncol=3)
  scaling <- apply(ext_z, 2, function(x) x %*% trans_matrix)
  plot(scaling[2,] ~ scaling[1,], xlim=c(-3,3), ylim=c(-3,3))
}

Rotation

Creating the rotation animation by updating the transformation matrix.

x11()
for (val in scale) {
  rot_z <- rbind(z, numeric(3000))
  trans_matrix <- matrix(c(cos(val), sin(val), 0, -sin(val), cos(val), 0, 0, 0, 1), nrow=3, ncol=3)
  rotation <- apply(rot_z, 2, function(x) x %*% trans_matrix)
  plot(rotation[2,] ~ rotation[1,], xlim=c(-3,3), ylim=c(-3,3))
}

Projection

Creating the projection animation by updating the transformation matrix.

x11()
for (val in  seq(-3,3,length.out=50)) {
  proj_z <- rbind(z, numeric(3000))
  trans_matrix <- matrix(c(val,0,0,0,1,0,0,0,1), nrow=3, ncol=3)
  projection <- apply(proj_z, 2, function(x) x %*% trans_matrix)
  plot(projection [2,] ~ projection [1,], xlim=c(-3,3), ylim=c(-3,3))
}