We explore the construction of parametric surfaces which interpolate p
rescribed 3D scattered data using spaces of parametric splines defined
on a 2D triangulation. The method is based on minimizing certain natu
ral energy expressions. Several examples involving Ailing holes and cr
owning 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 gen
eralized triangulations.