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Construction of Subdivision Surfaces by Fourth-Order Geometric Flows with G 1 Boundary Conditions

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Advances in Geometric Modeling and Processing (GMP 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6130))

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Abstract

In this paper, we present a method for constructing Loop’s subdivision surface patches with given G 1 boundary conditions and a given topology of control polygon, using several fourth-order geometric partial differential equations. These equations are solved by a mixed finite element method in a function space defined by the extended Loop’s subdivision scheme. The method is flexible to the shape of the boundaries, and there is no limitation on the number of boundary curves and on the topology of the control polygon. Several properties for the basis functions of the finite element space are developed.

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Author information

Authors and Affiliations

  1. LSEC, Institute of Computational Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing, 100190, China

    Guoliang Xu

  2. College of Mathematics and Computer Science, Hunan Normal University, Changsha, 410081, China

    Qing Pan

Authors
  1. Guoliang Xu
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  2. Qing Pan
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Editor information

Editors and Affiliations

  1. GALAAD, Inria Méditerannée, 2004 route des Lucioles, 06902, Sophia Antipolis Cedex, France

    Bernard Mourrain

  2. Department of Computer Science, College Station, Texas A&M University, 77843-3112, TX, USA

    Scott Schaefer

  3. Institute of Computational Mathematics and Scientific and Engineering Computing, Chinese Academy of Science, 100080, Beijing, China

    Guoliang Xu

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Xu, G., Pan, Q. (2010). Construction of Subdivision Surfaces by Fourth-Order Geometric Flows with G 1 Boundary Conditions. In: Mourrain, B., Schaefer, S., Xu, G. (eds) Advances in Geometric Modeling and Processing. GMP 2010. Lecture Notes in Computer Science, vol 6130. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13411-1_17

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  • DOI: https://doi.org/10.1007/978-3-642-13411-1_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-13410-4

  • Online ISBN: 978-3-642-13411-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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