An interpolant based on line segment voronoi diagrams

Abstract

This paper considers the interpolation for multi-dimensionaldata using Voronoi diagrams. Sibson’s interpolant is well-known as aninterpolation method for discrete data using Voronoi diagrams. Recently,Gross and Farin extended Sibson’s interpolant to continuous data distributedover polygons and circles. On the other hand, the authors recentlyfound another interpolation method for discrete data. This paperoutlines the authors’ interpolation method briefly, and extends it to datadistributed over line segments. For this purpose, we utilize line segmentVoronoi diagrams. The resulting interpolant is expressed in terms of theintegrations of the data function over the given line segments.