Bicubic G1 Interpolation of Irregular Quad Meshes Using a 4-Split

  • Stefanie Hahmann
  • Georges-Pierre Bonneau
  • Baptiste Caramiaux
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4975)

Abstract

We present a piecewise bi-cubic parametric G1 spline surface interpolating the vertices of any irregular quad mesh of arbitrary topological type. While tensor product surfaces need a chess boarder parameterization they are not well suited to model surfaces of arbitrary topology without introducing singularities. Our spline surface consists of tensor product patches, but they can be assembled with G1-continuity to model any non-tensor-product configuration. At common patch vertices an arbitrary number of patches can meet. The parametric domain is built by 4-splitting one unit square for each input quadrangular face. This key idea of our method enables to define a very low degree surface, that interpolates the input vertices and results from an explicit and local procedure : no global linear system has to be solved.

Keywords

G1 continuity arbitrary topology interpolation quad meshes Bézier surfaces 4-split 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Stefanie Hahmann
    • 1
  • Georges-Pierre Bonneau
    • 2
  • Baptiste Caramiaux
    • 1
  1. 1.Grenoble INP, Laboratoire Jean Kuntzmann, CNRS UMR 5224Grenoble Cedex 9France
  2. 2.Université Joseph Fourier, INRIA, Laboratoire Jean Kuntzmann, CNRS UMR 5224Grenoble Cedex 9France

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