Insight for Practical Subdivision Modeling with Discrete Gauss-Bonnet Theorem

  • Ergun Akleman
  • Jianer Chen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4077)


In this paper, we introduce an insight for practical subdivision modeling to improve the quality of control mesh structures. Our approach is based on a discrete version of Gaussian-Bonnet theorem on piecewise planar manifold meshes and vertex angle deflections that determines local geometric behavior. Based on discrete Gaussian-Bonnet theorem, summation of angle deflections of all vertices is independent of mesh structure and it depends on only the topology of the mesh surface. Based on this result, it can be possible to improve organization of mesh structure of a shape according to its intended geometric structure.


Saddle Point Discrete Version Subdivision Scheme Mesh Structure Subdivision Surface 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Ergun Akleman
    • 1
  • Jianer Chen
    • 2
  1. 1.Visualization Sciences Program, Department of ArchitectureTexas A&M UniversityCollege StationUSA
  2. 2.Computer Science DepartmentTexas A&M UniversityCollege StationUSA

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