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Mesh parameterization by minimizing the synthesized distortion metric with the coefficient-optimizing algorithm.

Jingqi Yan1, Xin Yang, Pengfei Shi

  • 1Institute of Image Processing and Pattern Recognition, Shanghai Jiao Tong University, Shanghai, China. jqyan@sjtu.edu.cn

IEEE Transactions on Visualization and Computer Graphics
|December 31, 2005
PubMed
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This study introduces a new metric and algorithm for 3D mesh parameterization, reducing local deformations for better postprocessing. The new method ensures more uniform area and angle distributions in planar domains.

Area of Science:

  • Computer Graphics
  • Geometric Modeling
  • Computational Geometry

Background:

  • 3D mesh parameterization maps 3D surfaces to 2D domains.
  • Existing methods often minimize average distortions but overlook local deformations.
  • High local deformations negatively impact texture mapping and remeshing.

Purpose of the Study:

  • To introduce a novel distortion metric for 3D mesh parameterization.
  • To develop an iterative algorithm for minimizing this new metric.
  • To improve the uniformity of area and angle deformations in parameterization.

Main Methods:

  • A new metric synthesizing average distortions and deformation variances (area and angle).
  • The coefficient-optimizing algorithm for iterative minimization.

Related Experiment Videos

  • Global position updates via solving the Laplace system after coefficient optimization.

    • Main Results:

    • The new metric and algorithm yield satisfactory average area and angle deformations.
    • Deformations are distributed more uniformly across the mesh.
    • The coefficient-optimizing algorithm demonstrates high performance in experiments.

    Conclusions:

    • The proposed synthesized distortion metric effectively addresses limitations of previous metrics.
    • The coefficient-optimizing algorithm provides an efficient and effective minimization process.
    • This work enhances the quality of 3D mesh parameterization for downstream applications.