Question

The square below undergoes 2-D geometric transformation and is shown in the sketch below in its original position. The coordinates of the vertices are given as (x, y) below and labeled. The square is rotated about the z-axis 45° CW about Point A and then uniformly scaled about point B to be 3/2 of its original size. Determine the final transformed coordinates of the vertices: A’, B’, C', and D'. Initial Coordinates: | A (1, 1), B (1, 3), C (3, 3), D (3, 1)

How can I solve this using MATLAB?

Answer 1

CODE

LL LLL LLL LLL %% We will use homogeneous coordinate system A-[1 1 1]; % first two value denote x and y coordinate of vertice B=[1 3 1]; C=[3 3 1]; D=[3 1 1]; T1=[1 0 -1;0 1 -1;0 0 1]; %translate A to origin R=[cosd(45) sind (45) 0; -sind (45) cosd (45) ; 0 1]; S=[3/2 0 0;0 3/2 0;0 1]; T2=[1 1; 1 1;0 1];% translate back to final position AT= A*T1*R*S*T2; BT= B*T1*R*S*T2; CT= (*11*R*5*T2; DT= D*T1*R*S*T2; fprintf('The transformed coordinates are') AT(:,1:2) BT(:,1:2) CT(:,1:2) DT(1,132) 16 -

OUTPUT

>> TRANS The transformed coordinates are ans = © 2.1213 ans = -2.1213 4.2426 ans = 0 6.3640 ans = 2.1213 4.2426