Issues and implementation of C1 and C2 natural neighbor interpolation

Authors:
T. Bobach;M. Bertram;G. Umlauf
Affiliations:
IRTG, Geometric Algorithms Group, TU Kaiserslautern, Germany;Computer Graphics Group, TU Kaiserslautern, Germany;IRTG, Geometric Algorithms Group, TU Kaiserslautern, Germany
Venue:
ISVC'06 Proceedings of the Second international conference on Advances in Visual Computing - Volume Part II
Year:
2006

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Abstract

Smooth local coordinates have been proposed by Hiyoshi and Sugihara 2000 to improve the classical Sibson's and Laplace coordinates. These smooth local coordinates are computed by integrating geometric quantities over weights in the power diagram. In this paper we describe how to efficiently implement the Voronoi based C2 local coordinates. The globally C2 interpolant that Hiyoshi and Sugihara presented in 2004 is then compared to Sibson's and Farin's C1 interpolants when applied to scattered data interpolation.