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

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Advances in Geometric Modeling and Processing (GMP 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4975))

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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.

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Authors and Affiliations

  1. Grenoble INP, Laboratoire Jean Kuntzmann, CNRS UMR 5224, BP. 53, F-38041, Grenoble Cedex 9, France

    Stefanie Hahmann & Baptiste Caramiaux

  2. Université Joseph Fourier, INRIA, Laboratoire Jean Kuntzmann, CNRS UMR 5224, BP. 53, F-38041, Grenoble Cedex 9, France

    Georges-Pierre Bonneau

Authors
  1. Stefanie Hahmann
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  2. Georges-Pierre Bonneau
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  3. Baptiste Caramiaux
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Falai Chen Bert Jüttler

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© 2008 Springer-Verlag Berlin Heidelberg

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Hahmann, S., Bonneau, GP., Caramiaux, B. (2008). Bicubic G1 Interpolation of Irregular Quad Meshes Using a 4-Split. In: Chen, F., Jüttler, B. (eds) Advances in Geometric Modeling and Processing. GMP 2008. Lecture Notes in Computer Science, vol 4975. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79246-8_2

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  • DOI: https://doi.org/10.1007/978-3-540-79246-8_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-79245-1

  • Online ISBN: 978-3-540-79246-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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