Exercise 1 - Answer
clear
close all
% create box
% first row is horizontal coordinates; second row is vertical coordinates
my_pts = [2 2 3 3 2;2 3 3 2 2];
% display the original box
figure(1)
plot(my_pts(1,1:end),my_pts(2,1:end),'b*-');
% write code here to create your 2D rotation matrix my_rot
xita=pi/6;
my_rot = [cos(xita) sin(xita);-sin(xita) cos(xita)];
% write code to perform rotation using my_rot and my_pts and store the result in my_rot_pts
my_rot_pts = my_rot*my_pts;
% Plot output
hold on;
plot(my_rot_pts(1,1:end),my_rot_pts(2,1:end),'r*-');
axis([1.5 4.5 0 3.5]);Exercise 2 - Answer
d_x = 1; % howmuchever you want to translate in horizontal direction
d_y = 3; % howmuchever you want to translate in vertical direction
% create the original box
% first row has horizontal coordinates, second row has vertical coordinates
my_points = [1 1 2 2 1;1 2 2 1 1];
% Plot the original box
figure(1)
plot(my_points(1,1:end),my_points(2,1:end),'b*-');
% write code to create your Homogeneous 2D Translation matrix my_trans using d_x and d_y
my_trans = [1 0 d_x;0 1 d_y;0 0 1];
% Next, we perform the translation
% write code to convert my_points to the homogeneous system and store the result in hom_my_points
hom_my_points = [my_points;ones(1,5)];
% write code to perform translation in the homogeneous system using my_trans and hom_my_points and store the result in trans_my_points
trans_my_points = my_trans*hom_my_points;
% Plot the Translated box (output) which has to be done in Cartesian, so...
% cut out the X, Y points and ignore the 3rd dimension
hold on
plot(trans_my_points(1,1:end),trans_my_points(2,1:end),'r*-');
axis([0.5 3.5 0.5 5.5]); % just to make the plot nicely visible
Exercise 3 - Answer
% we will perform a rotation followed by a translation, and then in reverse
% order and compare the results, both using the homogeneous system
d_x = 1; % howmuchever you want to translate in horizontal direction
d_y = 1; % howmuchever you want to translate in vertical direction
% create original box
% first row is horizontal and second row is vertical coordinates
my_pts = [3 3 4 4 3;3 4 4 3 3]; % Plot the box
% Plot the box
figure(1)
plot(my_pts(1,1:end),my_pts(2,1:end),'b*-');
% write code here to create your 2D rotation matrix my_rot
xita=pi/6;
my_rot = [cos(xita) sin(xita);-sin(xita) cos(xita)];
% write code to create your Homogeneous 2D Translation matrix hom_trans using d_x & d_y
hom_trans = [1 0 d_x;0 1 d_y;0 0 1];
% Perform Compound transformation
% write code to construct your 2D Homogeneous Rotation Matrix using my_rot and storethe result in hom_rot
% HINT: start with a 3x3 identity matrix and replace a part of it with my_rot to create hom_rot
hom_rot = [my_rot [0;0];[0 0 1]];
% write code to convert my_pts to the homogeneous system and store the result in hom_my_pts
hom_my_pts = [my_points;ones(1,5)];
% write code to perform in a single compound transformation: translation (hom_trans) followed by rotation (hom_rot) on hom_my_pts, and store the result in trans_my_pts
trans_my_pts = hom_trans*hom_rot*hom_my_pts;
% Plot the transformed box (output) which has to be done in Cartesian, so...
% cut out the X, Y points and ignore the 3rd dimension
hold on
plot(trans_my_pts(1,1:end),trans_my_pts(2,1:end),'r*-');
axis([2 8 -2 5]); % just to make the plot nicely visible
% Now, let us reverse the order of rotation and translation and compare
figure(2);
plot(my_pts(1,1:end),my_pts(2,1:end),'b*-');
% write code to perform in a single compound transformation: rotation followed by translation, and store the result in trans_my_pts
trans_my_pts = hom_rot*hom_trans*hom_my_pts;
% Plot the Transformed box (output) which has to be done in Cartesian, so...
% cut out the X, Y points and ignore the 3rd dimension
hold on
plot(trans_my_pts(1,1:end),trans_my_pts(2,1:end),'r*-');
axis([2 8 -2 5]); % just to make the plot nicely visible