Discrete Harmonic Functions from Local Coordinates

Abstract

In this work we focus on approximations of continuous harmonic functions by discrete harmonic functions based on the discrete Laplacian in a triangulation of a point set. We show how the choice of edge weights based on generalized barycentric coordinates influences the approximation quality of discrete harmonic functions. Furthermore, we consider a varying point set to demonstrate that generalized barycentric coordinates based on natural neighbors admit discrete harmonic functions that continuously depend on the point set.KeywordsHarmonic FunctionRoot Mean SquareVoronoi DiagramDelaunay TriangulationNatural NeighborThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.