Improving the Global Continuity of the Natural Neighbor Interpolation

  • Hisamoto Hiyoshi
  • Kokichi Sugihara
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3045)


The natural neighbor interpolation is a potential interpolation method for multidimensional data. However, only globally C1 interpolants have been known so far. This paper proposes a globally C2 interpolant, and write it in an explicit form. When the data are supplied to the interpolant from a third-degree polynomial, the interpolant can reproduce that polynomial exactly. The idea used to derive the interpolant is applicable to obtain a globally Ck interpolant for an arbitrary non-negative integer k. Hence, this paper gets rid of the continuity limitation of the natural neighbor interpolation, and thus leads it to a new research stage.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Hisamoto Hiyoshi
    • 1
  • Kokichi Sugihara
    • 2
  1. 1.Department of Computer Science, Faculty of EngineeringGunma UniversityGunmaJapan
  2. 2.Department of Mathematical Informatics, Graduate School of Information Science and TechnologyUniversity of TokyoTokyoJapan

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