Manifold Parameterization

  • Lei Zhang
  • Ligang Liu
  • Zhongping Ji
  • Guojin Wang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4035)


Manifold parameterization considers the problem of parameterizing a given triangular mesh onto another mesh surface, which could be particularly plane or sphere surfaces. In this paper we propose a unified framework for manifold parameterization between arbitrary meshes with identical genus. Our approach does this task by directly mapping the connectivity of the source mesh onto the target mesh surface without any intermediate domain and partition of the meshes. The connectivity graph of source mesh is used to approximate the geometry of target mesh using least squares meshes. A subset of user specified vertices are constrained to have the geometry information of the target mesh. The geometry of the mesh vertices is reconstructed while approximating the known geometry of the subset by positioning each vertex approximately at the center of its immediate neighbors. This leads to a sparse linear system which can be effectively solved. Our approach is simple and fast with less user interactions. Many experimental results and applications are presented to show the applicability and flexibility of the approach.


Surface parameterization compatible meshes least squares mesh morphing 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Lei Zhang
    • 1
    • 2
  • Ligang Liu
    • 1
    • 2
  • Zhongping Ji
    • 1
    • 2
  • Guojin Wang
    • 1
    • 2
  1. 1.Department of MathematicsZhejiang UniversityHangzhouChina
  2. 2.State Key Lab of CAD&CGZhejiang UniversityHangzhouChina

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