Please provide solutions to 5a and 5b. Also please explain. Answer must be in MA

Question

Please provide solutions to 5a and 5b. Also please explain. Answer must be in MATLAB code.

6 MATLAB sessions: Laboratory 4 EXAMPLE 6 Consider the matrix T representing the triangle in the previous problems. In homogeneous coordinates the matrix becomes -0.5 0 0.5-0.5 In the following M-file we translate the triangle using c.1 and c2-1 for 20 times. We then translate the triangle horizontally using ci--.1 and c20 and 40 iterations. clf Tw [-0 . 5 ,0 , 0 . 5 ,-0 . 5 ;-1 , 1 ,-1 ,-1; 1 , 1 , 1 , 1); % define the triangle in homogeneous coordinates MI [1 ,0 , c 1:0, 1,c2:0,0,11; % define the first translation matrix M2· [1,0,-c1 ; 0,1,0:0,0,1] ; % define the second translation matrix p-plot (T(1, :),T(2, :)); % plot the original triangle axis([-7,7,-7,7) axis square figure(gcf) for i -1:20 T-M1*T; % compute the translated triangle set (p,'xdata ,,T(1, :) ,'ydata,,T(2, :)); % plot pause (0-1) the translated triangle end for i 1:40 TwM2*T; % compute the translated triangle set (p,'xdata ,,T(1, :),'ydata,,T(2, :)); % plot pause (0-1) the translated triangle end EXERCISES 5. (a) Modify the M-file in EXAMPLE 6 adding translations that bring the triangle to its original position using 20 iterations. (b) Write down a rotation matrix Q that rotates a vector in homogeneous coordinates /40 radians in the counterclockwise direction. Then modify the M-file in part (a) adding to each iteration (for all three loops) a rotation defined by the matrix Q Note that the triangle should NOT end up in its original location like it should for 5(a). You might need to change the axes to see where it "lands."

Explanation / Answer

% 5 (a)

c1 = .1;
c2 = .1;
M1 = [1,0,c1; 0,1,c2; 0,0,1];
M2 = [1,0,-c1; 0,1,0; 0,0,1];

for i = 1:20
   T = T./M2;
   T = T./M2;
end

for i = 1:20
   T = T./M1;
end

% 5 (b)

% Rotate vector M1 in homogeneous coordinates
theta = pi/40;
update_M1 = M1*[1;1i]*exp(-1i*theta*pi/180);

% We got original T in 5 (a), so Rotate it by theta

axis([-7,7,-7,7])
axis square
figure(gcf);
for i = 1:20
   T = M1*T;
   set(p,'xdata',T(1,:),'ydata',T(2:))
   pause(0.1)
end

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