Example $9$

In this example we first translate the square horizontally $12$ units using increments of $0\mathrm{.}4.$ We then

rotate the resulting square clockwise pi$//2$ radians around the vertex $(13,0)$ using increments of pi$//10$

radians.

clf

S$=[0,1,1,0,0$;$0,0,1,1,0$;$1,1,1,1,1]$; $\%$ square in homogeneous coordinates

M$1=[1,0,0\mathrm{.}4$;$0,1,0$;$0,0,1]$; $\%$ first translation matrix

theta $=$ pi$/10$; $\%$ define the angle theta

Q $=[$cos$($theta$),-$sin$($theta$),0$;sin$($theta$),$ cos$($theta$),0$;$0,0,1]$; $\%$ rotation matrix about $(0,0)$

QP $=[1,0,13$;$0,1,0$;$0,0,1]$Q$\text{'}[1,0,-13$;$0,1,0$;$0,0,1]$; $\%$ rotation matrix about $(13,0)$

p $=$ plot$($S$(1,$:$),$S$(2,$:$))$; $\%$ plot the original square

axis equal, axis$([-0\mathrm{.}5,15,-2,5]),$ grid on

for i $=1$:$30$

S $=$ M$1*$S; $\%$ compute the translated square

set$($p$,$'xdata',S$(1,$:$),$'ydata',S$(2,$:$))$; $\%$ plot the translated square

pause$(0\mathrm{.}1)$

end

for i $=1$:$5$

S$=$QP$*$S; $\%$ compute the rotated square

set$($p$,$'xdata',S$(1,$:$),$'ydata',S$(2,$:$))$; $\%$ plot the rotated square

pause $(0\mathrm{.}1)$

end

EXERCISES

Consider the square in EXAMPLE $9.$ The goal of this exercise is to bring back the square to its

original position by first translating it horizontally to the left $12$ units using $30$ iterations, and

then rotating it counterclockwise pi$//2$ radians around the point $(1,0)$ using $5$ iterations. This

can be done by modifying the code in EXAMPLE $9$ by adding two for loops. The first loop

should translate the square while the second should rotate it around the point $(1,0).$ Note that

the rotation is counterclockwise, while in EXAMPLE $9$ it was clockwise. Include the M$-$file.

You do not need to include the figure.