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Construction of Subdivision Surfaces by Fourth-Order Geometric Flows with G1 Boundary Conditions

  • Guoliang Xu
  • Qing Pan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6130)

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.

Keywords

Subdivision Surface Geometric Partial Differential Equations G1 continuity 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Guoliang Xu
    • 1
  • Qing Pan
    • 2
  1. 1.LSEC, Institute of Computational Mathematics, Academy of Mathematics and System SciencesChinese Academy of SciencesBeijingChina
  2. 2.College of Mathematics and Computer ScienceHunan Normal UniversityChangshaChina

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