MATLAB: Vector projection on rotated coordinate system

coordinate system rotationvector projection

I have to vectors: red (XR, YR, ZR) and blue (XB, YB, ZB) in XYZ coordinate
system. I would like to calculate projection of these two vectors on X'Y', X'Z' and Y'Z' planes
where X'Y'Z' is rotaded, along Z (angle 'alpha') and Y (angle 'beta') axises, coordinate system XYZ.
Vectors stay in old XYZ system (are not rotated). Only system is rotaded along two axisies.
Any suggestions how this could be done?
rotation.jpg

Best Answer

I'll assume your given vectors are in a 3x2 matrix called columnVectors, that your angles are in degrees, and that rotations are done in Z first and Y second.
Rz=@(x) [cosd(x),-sind(x),0 ; ...
        sind(x),cosd(x),0 ;...
        0 0 1];
    
Ry = @(x) [cosd(x), 0, sind(x); 0 1 0; -sind(x), 0, cosd(x) ];
R=Ry(beta)*Rz(alpha); %ANGLES ARE IN DEGREES!!
[XpYp,XpZp,YpZp]=deal(R.'*columnVectors);
XpYp(3,:)=0; %X'Y'
XpZp(2,:)=0; %X'Z'
YpZp(1,:)=0; %Y'Z'
XpYp=R*XpYp;
XpZp=R*XpZp;
YpZp=R*YpZp;
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