Discrete Coons patches

We investigate surfaces which interpolate given boundary curves. We show that the discrete bilinearly blended Coons patch can be defined as the solution of a linear system. With the goal of producing better shape than the Coons patch, this idea is generalized, resulting in a new method based on a blend of variational principles. We show that no single blend of variational principles can produce “good” shape for all boundary curve geometries. We also discuss triangular Coons patches and point out the connections to the rectangular case.  1999 Elsevier Science B.V. All rights reserved.