How to build A matrix for the argmin E=∑||N×(v_i-v_j)||^2 by solving it in a least square sense?
this energy is designed for constrainting vertex symmetrically distributed in both sides of the symmetric plane of a mesh, where N(a,b,c) is the normal of the plane (N is given), and "×" is the cross product. v_i and v_j is a pair of symmetric vertices.
To solve the energy minimization in a least square sense, E should be written as ||Ax-B||^2, where x is mesh vertex matrix(n vertices).
The question is I cannot find a proper A to build the Ax-B.
Similar as a Laplace matrix (n*n), I think the size of A should be ?*n, since in some cases we also need to minimize E=||L(v)||^2 to keep smoothness, and the Laplace matrix will link with this A matrix which obtains something like (LT*L+AT*A)X=AT*b in final code of Eigen to solve the problem.
I want to know how to build A matrix. I cannot figure it out.