Stable Computation of Natural Neighbor Interpolation

Natural neighbor interpolation is a scattered data interpolation method based on Voronoi diagrams. A class of natural neighbor interpolants are defined in an integral form which is not suitable for computation. This paper demonstrates that these interpolants can be computed solely with algebraic operations and conditional branches. In addition, it is noted that special care is required to achieve stable computation, and a procedure is proposed for stably calculating natural neighbor interpolation with computers. Its usability is ascertained by surface drawings of natural neighbor interpolation.