# How to formulate 2D frames if I have the origin of the frames (x, y) and the inclination angle of the frame with respect to the x-axis?

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M on 13 May 2022
Edited: M on 16 May 2022
How to formulate 2D frames if I have the origin of the frames (x, y) and the inclination angle of the frame with respect to the x-axis? Then I need to compute the transformation matrix of the frames w.r.t the reference frame (which is normal x and y directions)??
The attached files are the origins and the corrosponding angles.

Matt J on 13 May 2022
Edited: Matt J on 13 May 2022
T=makehgtform('translate',[x,y,0],...
'zrotate',angleDegrees*pi/180, ...
'translate',[-x0,-y0,0]);
T=T([1,2,4],[1,2,4]); %transformation matrix
M on 16 May 2022
Edited: M on 16 May 2022
@Matt J Ok, but my question why did you choose the first origin in the .mat file to make it the reference, then you translate other origins to that origin ?
Also, Could you please tell me what does the fourth column in the transformation matrix represents?