A transfinite form of Sibson's interpolant

Sibson's interpolant uses Voronoi diagrams in the plane to interpolate a se t of scattered data points. This paper presents an extension of this method to handle the interpolation of a set of functional curves (transfinite sur face interpolation). We derive a simple formula for this new surface type w hich can interpolate to any number of boundary curves. In addition, a uniqu e surface may be created from a set of discontinuous curves. Finally, we pr esent a form of the interpolant which uses convex or concave polygonal doma ins. (C) 1999 Published by Elsevier Science B.V. All rights reserved.