问题
I am trying to write a little unwrapper for meshes. This uses a finite-element-method to solve for minimal linear stress between flattened and the raw surface. At the moment there are some vertices pinned to get a result. Without this the triangles are rotated and translated randomly...
But as this pinning isn't necessary for the problem, the better solution would be to directly solve the singular matrix. Petsc does provide some methodes to solve a singular system by providing some information on the nullspace. http://www.mcs.anl.gov/petsc/petsc-current/docs/manual.pdf#section.4.6 I wonder if there is any alternative for this in Eigen. If not, are there any other possibilities to solve this problem without fixing/pinning vertices.
thanks, nice regards
see also this link for further informaton: dev history
回答1:
Eigen provides an algorithm for SVD decomposition: Jacobi SVD.
The SVD decomposition gives the null-space. Following the notations of the wikipedia article, let M = U D V be the SVD decomposition of M, where D is a diagonal matrix of the singular values. Then, from the Range, null space and rank:
The right-singular vectors [V] corresponding to vanishing singular values of M span the null space of M
来源：https://stackoverflow.com/questions/40594803/solving-a-singular-matrix