来自两个向量的3D转换矩阵

Question

I have a pair of 3D points in two coordinates systems, and I need to find the transformation matrix (rotation, scale, translation) between the coordinates systems.

For example two points
p0 = (x0,y0,z0)
p1 = (x1,y1,z1)

which correspond to points in another coordinates system:
q0 = (x0', y0', z0')
q1 = (x1', y1', z1')

I need to find the transformation M (R|T) such that
q0 = M * p0
q1 = M * p1

If there is an easy way to do it using opencv or python it would be terrific.

Answer 1

We can interpret your problem in this way. You want to find a matrix M such that

    for matrix P = [p1 p2] and Q = [q1 q2], Q = MP. 

We can then solve for M:

    M = Q.dot(numpy.linalg.pinv(P))