Minimal energy surfaces using parametric splines Original Research Article

We explore the construction of parametric surfaces which interpolate prescribed 3D scattered data using spaces of parametric splines defined on a 2D triangulation. The method is based on minimizing certain natural energy expressions. Several examples involving filling holes and crowning surfaces are presented, and the role of the triangulation as a parameter is explored. The problem of creating closed surfaces is also addressed. This requires introducing spaces of splines on certain generalized triangulations.