math - How to calculate the conversion matrix of two meshes

Question

I have two identical mesh objects, but their positions and rotation directions are different; I know the position information of the two mesh vertices, how can I get the relative transformation matrix between them

question from:https://stackoverflow.com/questions/66060613/how-to-calculate-the-conversion-matrix-of-two-meshes

Answer 1

1. obtain or construct homogenuous transform matrix for each object

   lets call them a,b corresponding to meshes A,B

2. compute the difference matrix d

   for example you want to go from A to B then its just matter of solving:

              a*d = b
   Inverse(a)*a*d = Inverse(a)*b
                d = Inverse(a)*b
   

   Beware in case you use different notations (like reverse order of multiplication and or inverse matrices instead of direct ones the equation might get inverted and or transposed)