Voronoi-based interpolation with higher continuity
Proceedings of the sixteenth annual symposium on Computational geometry
Improving continuity of Voronoi-based interpolation over Delaunay spheres
Computational Geometry: Theory and Applications
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This paper presents a general framework for constructing a variety of multi-dimensional interpolants based on Voronoi diagrams. This framework includes previously known methods such as Sibson's interpolant and Laplace's interpolant; moreover it contains infinitely many new interpolants. Computational experiments suggest that the smoothness can be improved by the proposed generalization. In addition, this framework also includes the piecewise linear interpolant over the Delaunay triangulation, which is a finite-element interpolant. This fact suggests that already established techniques in the finite element method might be brought into the research of the Voronoi-based approach. Hence this framework gives a new and promising direction of research on the interpolation based on Voronoi diagrams.