t=0.5
theta<-seq(0,4*pi,0.001)
theta<-theta[(cos(2.5*theta)+1.9)<=(cos(2.5*pi/5)+1.9)]
x<-c((cos(2.5*theta)+1.9)*cos(theta),-.4,-.18)
y<-c((cos(2.5*theta)+1.9)*sin(theta),.6,.87)

par(mfrow=c(2,3),pty="s")

plot(x=c(-3,3),y=c(-3,3),type="n",main="star",xlab=NULL,ylab=NULL)
abline(h=0)
abline(v=0)
points(x,y,col=2)



a<-x
b<-0*y

plot(x=c(-3,3),y=c(-3,3),type="n",main="projection")
abline(h=0)
abline(v=0)
points(a,b,col=5)





a<-1.6*x
b<-1.6*y

plot(x=c(-3,3),y=c(-3,3),type="n",main="scaling (dilation or contraction)")
abline(h=0)
abline(v=0)
points(a,b,col=3)


a<-x+y
b<-y

plot(x=c(-3,3),y=c(-3,3),type="n",main="shearing")
abline(h=0)
abline(v=0)
points(a,b,col=6)

a<-x+y
b<-y

plot(x=c(-3,3),y=c(-3,3),type="n",main="shearing+reflection")
abline(h=0)
abline(v=0)
points(-a,b,col=4)


a<-cos(t*pi)*x-sin(t*pi)*y
b<-sin(t*pi)*x+cos(t*pi)*y

plot(x=c(-3,3),y=c(-3,3),type="n",main="rotation")
abline(h=0)
abline(v=0)
points(a,b,col="brown")


#-----------------------------------------------
t=0.5
theta<-seq(0,4*pi,0.001)
theta<-theta[(cos(2.5*theta)+1.9)<=(cos(2.5*pi/5)+1.9)]
x<-c((cos(2.5*theta)+1.9)*cos(theta),-.4,-.18)
y<-c((cos(2.5*theta)+1.9)*sin(theta),.6,.87)

par(mfrow=c(1,3),pty="s")

plot(x=c(-3,3),y=c(-3,3),type="n",main="star",xlab=NULL,ylab=NULL)
abline(h=0)
abline(v=0)
points(x,y,col=2)


i=1/3
j=1/4

a<-cos(2*i*pi)*x+sin(2*i*pi)*y
b<-sin(2*i*pi)*x-cos(2*i*pi)*y

plot(x=c(-3,3),y=c(-3,3),type="n",main="reflection once")
abline(h=0)
abline(v=0)
abline(0,tan(i*pi),col="green")
points(a,b,col="brown")

c<-cos(2*j*pi)*a+sin(2*j*pi)*b
d<-sin(2*j*pi)*a-cos(2*j*pi)*b

plot(x=c(-3,3),y=c(-3,3),type="n",main="reflection twice")
abline(h=0)
abline(v=0)

abline(0,tan(j*pi),col="green")
points(c,d,col="blue")