A Transfinite Form of Sibson's Interpolant

Sibson’s interpolant uses Voronoi diagrams in the plane to interpolate a set of scattered data points. This paper presents an extension of this method to handle the interpolation of a set of functional curves (transfinite surface interpolation). We derive a simple formula for this new surface type which can interpolate to any number of boundary curves. In addition, a unique surface may be created from a set of discontinuous curves. Finally, we present a form of the interpolant which uses convex or concave polygonal domains. @ 1999 Published by Elsevier Science B.V. All rights reserved.