(HW=Homework!) One of the most useful applications for linear algebra in data science is image manipulation. We often need to compress, expand, warp, skew, etc. images. To do so, we left multiply a transformation matrix by each of the point vectors.
For this assignment, build the first letters for both your first and last name using point plots in R.

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 a .RMD file. I will know if your assignment is correct if the animation runs. correctly

library(gifski)
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(plotly)
## Loading required package: ggplot2
## 
## Attaching package: '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(anim.plots)

Plot initial characters of my name Shwe, Lwin

# Plot SL 
x = c(sin(seq(-pi*.3,pi*2.3,length.out=2000))/2-1,seq(0,1,length.out=1000),c(rep(0,200)),c(rep(0,200)),seq(0,1,length.out=1000))
y = c(seq(-1,1,length.out=2000),rep(0,1000),seq(0,2,length.out=200),seq(0,2,length.out=200),rep(0,1000))

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

Note that the echo = FALSE parameter was added to the code chunk to prevent printing of the R code that generated the plot.

write R code that will left multiply (%>%) a square matrix (x) against each of the vectors of points (y)

leftMultiply  <- function(x,y){
   x %*% y
}
leftMultiply(matrix(rep(seq(1,3, length.out=3),3), nrow = 3, ncol = 3),diag(3))
##      [,1] [,2] [,3]
## [1,]    1    1    1
## [2,]    2    2    2
## [3,]    3    3    3

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

for (i in seq(0,2,length.out=10)) {
  shear <- leftMultiply(matrix(c(1,0,i,1),byrow=T,nrow=2), z)
  plot(shear[2,]~shear[1,], xlim=c(-3,2), ylim=c(-5,3))
}

for (i in seq(.5,1.5,length.out=10)) {
  scale <- leftMultiply(matrix(c(i,0,0,i),byrow=T,nrow=2), z)
  plot(scale[2,]~scale[1,], xlim=c(-3,2), ylim=c(-3,3))
}

for (i in seq(0,2*pi,length.out=10)) {
  rotate <- leftMultiply(matrix(c(cos(i),sin(i),-sin(i),cos(i)),byrow=T,nrow=2), z)
  plot(rotate[2,]~rotate[1,], xlim=c(-3,2), ylim=c(-3,3))
}

project_z <- rbind(z, rep(0, ncol(z)))

for (i in seq(0,2*pi,length.out=5)) {
  project <- leftMultiply(matrix(c(1,0,0,0,cos(i),sin(i),0,-sin(i),cos(i)),byrow=T,nrow=3), project_z)
  plot(project[2,]~project[1,], xlim=c(-3,2), ylim=c(-3,3))
}