I have 3D points of my model. And I have 2D points - projection of these 3D points of my model on plane. I want to find 3d-affine transformation (translation, rotation and scale) of 3D-model so that projection of this 3D-model give me 2D points on plane the same as I have.
How can I find 3d-affine transformation of my 3D model if I have 2D points of its projection?
Just find the null space to your projection matrix, e.g. in matlab you can use u=null(P) (or Python (NumPy, SciPy), finding the null space of a matrix in numpy). This will be a single vector, as P is projecting one dimension down from 3D space.
An affine transformation satisfying P*A=P (where P is the projection and A is the affine transformation) would be A=([u u ... u]+I), where you form a matrix from the nullspace vector u to match the dimension of A (likely 4x4 to include translation).
