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A C 1 Globally Interpolatory Spline of Arbitrary Topology

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Variational, Geometric, and Level Set Methods in Computer Vision (VLSM 2005)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 3752))

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Abstract

Converting point samples and/or triangular meshes to a more compact spline representation for arbitrarily topology is both desirable and necessary for computer vision and computer graphics. This paper presents a C 1 manifold interpolatory spline that can exactly pass through all the vertices and interpolate their normals for data input of complicated topological type. Starting from the Powell-Sabin spline as a building block, we integrate the concepts of global parametrization, affine atlas, and splines defined over local, open domains to arrive at an elegant, easy-to-use spline solution for complicated datasets. The proposed global spline scheme enables the rapid surface reconstruction and facilitates the shape editing and analysis functionality.

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Author information

Authors and Affiliations

  1. Center for Visual Computing (CVC) and Department of Computer Science, Stony Brook University, NY, Stony Brook, 11794-4400, USA

    Ying He, Miao Jin, Xianfeng Gu & Hong Qin

Authors
  1. Ying He
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  2. Miao Jin
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  3. Xianfeng Gu
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  4. Hong Qin
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Editor information

Editors and Affiliations

  1. MAS - Ecole Centrale Paris, Grande Voie des Vignes, 92295, Chatenay-Malabry, France

    Nikos Paragios

  2. I.N.R.I.A, 2004 route des lucioles,, 06902, Sophia-Antipolis, France

    Olivier Faugeras

  3. Department of Mathematics, UCLA,  

    Tony Chan

  4. Image and Pattern Analysis Group, Heidelberg Collaboratory for Image Processing, University of Heidelberg, Germany

    Christoph Schnörr

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© 2005 Springer-Verlag Berlin Heidelberg

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He, Y., Jin, M., Gu, X., Qin, H. (2005). A C 1 Globally Interpolatory Spline of Arbitrary Topology. In: Paragios, N., Faugeras, O., Chan, T., Schnörr, C. (eds) Variational, Geometric, and Level Set Methods in Computer Vision. VLSM 2005. Lecture Notes in Computer Science, vol 3752. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11567646_25

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  • DOI: https://doi.org/10.1007/11567646_25

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-29348-4

  • Online ISBN: 978-3-540-32109-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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