2d coordinate transformation specified origin matlab

I asked this question sometime ago but i realised I did not ask it well due to me being new to matlab, I have a cordinate point I want to rotate 45 degrees clock wise but has a different origin other than 0,0. My origin is [start_x = 24.000;start_y = 16.000] and the cordinate I want to rotate about the origin is [target_x = 27.000,target_y = 16.000]

This what I have attempted so far.

theta = pi/4 ;

R = [cos(theta) -sin(theta); sin(theta) cos(theta)];

p = [target_x target_y]';

New_Target = p * R;

Any Ideas?

Answer 1

[Brian Hart]

Hi Reuben,

You're almost there.

The basic idea is to subtract the rotation point value from the target point, so that you ARE rotating about the origin. Then do the rotation, and add the offset back.

target_x = 27.000;
target_y = 16.000;
start_x = 24.000;
start_y = 16.000;

p = [target_x target_y]';
rotPt = [start_x start_y]';

theta = pi/4 ;
R = [cos(theta) -sin(theta); sin(theta) cos(theta)];
pTmp = p - rotPt;
pRotTmp = R * pTmp; %this is the proper multiplication order
pRot = pRotTmp + rotPt;

With this you get

pRot =

   26.1213
   18.1213

[Reuben Addison]

Thank you, this has been very helpful to me.