Issues and Implementation of C1 and C2 Natural Neighbor Interpolation

  • T. Bobach
  • M. Bertram
  • G. Umlauf
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4292)


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 C 2 local coordinates. The globally C 2 interpolant that Hiyoshi and Sugihara presented in 2004 is then compared to Sibson’s and Farin’s C 1 interpolants when applied to scattered data interpolation.


Voronoi Diagram Digital Terrain Modelling Data Site Derivative Estimation Natural Neighbor 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • T. Bobach
    • 1
  • M. Bertram
    • 2
  • G. Umlauf
    • 1
  1. 1.IRTG, Geometric Algorithms GroupTU KaiserslauternGermany
  2. 2.Computer Graphics GroupTU KaiserslauternGermany

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