data 605 hw 1

library(animation)

Create My Initials

# Initials NC
x <- c(rep(-1, 500), 
       seq(-1, 0, length.out = 500), 
       rep(0, 500),
       rep(0.5, 500),
       seq(1, 1.75,length.out=500),
       seq(1, 1.75,length.out=500),
       seq(0.5,1,length.out=500),
       seq(0.5,1,length.out=500))

y <- c(seq(-2,2,length.out=500), 
       seq(2,-2,length.out=500), 
       seq(-2,2,length.out=500),
       seq(-1.5,1.5,length.out=500),
       rep(2,500),
       rep(-2,500),
       seq(-1.5,-2,length.out=500),
       seq(1.5,2,length.out=500))

z <- rbind(x, y)
z <-data.frame(z)
plot(y~x, xlim=c(-5,5), ylim=c(-5,5))

Shear

a <- diag(2) 
ani.options(interval = 1/20)
for (i in seq(-3,3,length.out=100)){
  
  a[1,2] <- i
  new_x <- apply(z,2,function(x) a%*%x)
  plot(new_x[2,] ~ new_x[1,], xlim=c(-5,5), ylim=c(-5,5))
}

Scaling

a <- diag(2)
ani.options(interval = 1/20)
for (i in seq(-3,3, length.out=100)){
    a[1,1] <- i
    a[2,2] <- i
    new_x <- apply(z,2,function(x) a%*%x)
    plot(new_x[2,] ~ new_x[1,],  xlim=c(-5,5), ylim=c(-5,5))
}

Rotation

a <- diag(2)
ani.options(interval = 1/20)
for (i in seq(-3, 3, length.out = 100)) {
    a[1, 1] = i
    newmat = apply(z, 2, function(x) a %*% x)
    plot(newmat[2, ] ~ newmat[1, ],  xlim=c(-5,5), ylim=c(-5,5))
}

Projection

myf = function(x) { matrix(c(cos(x), -sin(x), sin(x), cos(x)), byrow = TRUE, nrow = 2) }
ani.options(interval = 1/20)
for (i in seq(-3,3, length.out = 100)) {
    a = myf(i)
    a[1,1] <- i
    newmat = apply(z, 2, function(x) a %*% x)
    plot(newmat[2, ] ~ newmat[1, ],  xlim=c(-5,5), ylim=c(-5,5))
}