Parallel implementation of surface reconstruction from noisy samples

Abstra t We onsider the problem of re onstru ting a surfa e from noisy samples by approximating the point set with non-uniform rational B-spline surfa es. We fo us on the fa t that the knot sequen es should also be part of the unknown variables that in lude the ontrol points and the weights in order to nd their optimal positions. We show how to set up the free knot problem su h that onstrained nonlinear optimization an be applied eÆ iently. We des ribe in detail a parallel implementation of our approa h that give almost linear speedup. Finally, we provide numeri al results obtained on the Chemnitzer Linux Cluster super omputer.