Rotating a rectangle about a point other than the origin

This is a homework assignment that ive been working on in matlab for a few days but and ive done everything ive needed to do accept that the second rectangle needs to be rotated about an end point on the end of the first rectangle. my professor for this class doesnt care how we do this just as long as we get the right result and since i know literally nothing about matlab and linear algebra ive managed to find some stuff on here that lets me get the job done but i havent found out how to rotate about a point other than the origin. so please keep in mind i have zero matlab experience.

thanks

axis([-1 10 -5 4]);
%first rectangle along x axis
rect.Vertices=[0 0;4 0;4 .5;0 .5];
rect.faces=[1 2 3 4];
theta = pi/9;
R=[cos(theta) sin(theta);-sin(theta) cos(theta)];
patch(rect,'Vertices',rect.Vertices,'FaceColor',[0 .5 0]);

%second rectangle along x axis
rect.Vertices=[4 0;8 0;8 .5;4 .5];
rect.faces=[1 2 3 4];
theta = pi/9;
R=[cos(theta) sin(theta);-sin(theta) cos(theta)];
patch(rect,'Vertices',rect.Vertices,'FaceColor',[0 .5 .5]);

%rotates second rectangle
rect.Vertices=[4 0;8 0;8 .5;4 .5];
rect.faces=[1 2 3 4];
theta = pi/9;
R=[cos(theta) sin(theta);-sin(theta) cos(theta)];
patch(rect,'Vertices',rect.Vertices*R,'FaceColor',[0 .5 .5]);

%rotates first rectangle
rect.Vertices=[0 0;4 0;4 .5;0 .5];
rect.faces=[1 2 3 4];
theta = pi/9;
R=[cos(theta) sin(theta);-sin(theta) cos(theta)];
patch(rect,'Vertices',rect.Vertices*R,'FaceColor',[0 0 .5]);

%rotates second rectangle -30 degrees
rect.Vertices=[4 0;8 0;8 .5;4 .5];
rect.faces=[1 2 3 4];
theta = -pi/6;
R=[cos(theta) sin(theta);-sin(theta) cos(theta)];
patch(rect,'Vertices',rect.Vertices*R,'FaceColor',[0 .5 .5]);

%rotates object 10 degrees
rect.Vertices=[4 0;8 0;8 .5;4 .5];
rect.faces=[1 2 3 4];
theta = -pi/18;
R=[cos(theta) sin(theta);-sin(theta) cos(theta)];
patch(rect,'Vertices',rect.Vertices*R,'FaceColor',[0 .5 .5]);

rect.Vertices=[0 0;4 0;4 .5;0 .5];
rect.faces=[1 2 3 4];
theta = -pi/18;
R=[cos(theta) sin(theta);-sin(theta) cos(theta)];
patch(rect,'Vertices',rect.Vertices*R,'FaceColor',[0 0 .5]);

%rotates second rectangle -30 degrees
rect.Vertices=[4 0;8 0;8 .5;4 .5];
rect.faces=[1 2 3 4];
theta = -2*pi/9;
R=[cos(theta) sin(theta);-sin(theta) cos(theta)];
patch(rect,'Vertices',rect.Vertices*R,'FaceColor',[0 .5 .5]);

Answer 1

[bym]

you have to do a composite rotation, consisting of:

• translate your rotation point to the origin
• perform rotation
• reverse translate to original coordinates

I will try to dig up something in my old files, but in the mean time you might want to do some research on homogeneous coordinates