Interpolation on surfaces using minimum norm networks

New methods for interpolating scattered data on a surface are presented. Similar to G. Nielson's minimum norm network technique, this approach is based upon a functional minimization that characterizes the restriction of the final interpolant to curves which form the edges in a triangulation of the domain surface. However, unlike the known minimum norm network methods we do not use only data points as vertices in the triangulation. We also consider minimum norm networks with tension properties. An appropriate method for extending the network data to a final C¹ interpolant is described. Both color blended contour regions on the surface and projections of the 4D graph of a function on a surface are used in illustrating examples. Finally, special cases, possible extensions and applications in surface design are addressed.