DATA 605 HW1

Functions:

plotTransformation = function(m,X,Y){
  x_coord = c()
  y_coord = c()
  for (i in seq(length(X))){
    coord_m = matrix(c(X[i],Y[i]),nrow=2,ncol=1)
    new_coord = m %*% coord_m
    x_coord = append(x_coord,new_coord[1])
    y_coord = append(y_coord,new_coord[2])
  
  }
  plot(y_coord~x_coord,xlim=c(-4,8), ylim=c(-3,3))
}


shear = function(X,Y,X_shear=0,Y_shear=0){
  shear_m = matrix(c(1,Y_shear, X_shear,1),nrow =2,ncol = 2)
  plotTransformation(shear_m,X,Y)
}


scaling = function(X,Y,X_scale = 1, Y_scale = 1){
  scale_m = matrix(c(X_scale,0,0,Y_scale),nrow=2,ncol=2)
  plotTransformation(scale_m,X,Y)
}


rotation = function(X,Y,angle = 0){
  rotate_m = matrix(c(cos(angle),-sin(angle),sin(angle),cos(angle)),
    nrow=2,ncol=2)
  plotTransformation(rotate_m,X,Y)
}


reflectionOverXAxis= function(X,Y){
  reflection_m = matrix(c(1,0,0,-1),nrow=2,ncol=2)
  plotTransformation(reflection_m,X,Y)
}

Initials:

x=c(rep(0,500),seq(0,1,length.out=500),seq(0,1,length.out=500),
    rep(1,500),seq(0,1,length.out=500), seq(2,3,length.out=500),
    seq(2,3,length.out=500),seq(2,3,length.out=500))

y=c(seq(-1,1,length.out=500),rep(1,500),rep(0,500), 
    seq(0,1,length.out=500),seq(0,-1,length.out=500),
    rep(-1,500),seq(-1,1,length.out=500),rep(1,500))
plot(y~x,xlim=c(-4,8), ylim=c(-3,3))

shear(x,y,1.1)

1) Shear Transformation

scaling(x,y,2,2)

2) Scailing Transformation

angle = pi/2
rotation(x,y, angle)

2) Rotation Transformation

reflectionOverXAxis(x,y)

4) Reflection over X-Axis