MATLAB: Rotation about a point

homeworkMATLABmatricesprogramming

Hi there I have been given a problem:
"A triangle is defined by the points (1, 1), (2, 4) and (7, 2). Using the three constituent simple transformations, transform the triangle with a rotation about the point (1, 3) by 60◦ anti-clockwise".
If I am being honest I have no idea how to start this
Any help would be great
Daniel

Best Answer

If you want the equations they are as follows;
X = [1 2 7 1];
Y = [1 4 2 1];
ang = -60  % degrees

Xc = 1;  % X cener of rotation
Yc = 3;  % Y center of rotation
% Shift X/Y to the rotation center
Xshift = X - Xc;        
Yshift = Y - Yc;
% Rotate the coordinates
Xsrot =  Xshift*cosd(ang) + Yshift*sind(ang);
Ysrot = -Xshift*sind(ang) + Yshift*cosd(ang);
% Shift the rotated coordinates back to the original reference center
Xrot = Xsrot + Xc;
Yrot = Ysrot + Yc;
Now X,Y is the original triangle and Xrot,Yrot is the rotated triangle
This can be shortened to:
X = [1 2 7 1];
Y = [1 4 2 1];
ang = -60;  % degrees
Xc = 1;
Yc = 3;
Xrot =  (X-Xc)*cosd(ang) + (Y-Yc)*sind(ang) + Xc;
Yrot = -(X-Xc)*sind(ang) + (Y-Yc)*cosd(ang) + Yc;
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