Mesh Parameterization by Minimizing the Synthesized Distortion Metric with the Coefficient-Optimizing Algorithm

Jingqi Yan, Xin Yang, Pengfei Shi, Dapeng Zhang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

4 Citations (Scopus)


The parameterization of a 3D mesh into a planar domain requires a distortion metric and a minimizing process. Most previous work has sought to minimize the average area distortion, the average angle distortion, or a combination of these. Typical distortion metrics can reflect the overall performance of parameterizations but discount high local deformations. This affects the performance of postprocessing operations such as uniform remeshing and texture mapping. This paper introduces a new metric that synthesizes the average distortions and the variances of both the area deformations and the angle deformations over an entire mesh. Experiments show that, when compared with previous work, the use of synthesized distortion metric performs satisfactorily in terms of both the average area deformation and the average angle deformation; furthermore, the area and angle deformations are distributed more uniformly. This paper also develops a new iterative process for minimizing the synthesized distortion, the coefficient-optimizing algorithm. At each iteration, rather than updating the positions immediately after the local optimization, the coefficient-optimizing algorithm first update the coefficients for the linear convex combination and then globally updates the positions by solving the Laplace system. The high performance of the coefficient-optimizing algorithm has been demonstrated in many experiments.
Original languageEnglish
Pages (from-to)83-92
Number of pages10
JournalIEEE Transactions on Visualization and Computer Graphics
Issue number1
Publication statusPublished - 1 Jan 2006


  • barycentric mapping
  • conformal mapping
  • harmonic mapping
  • Mesh parameterization
  • texture mapping

ASJC Scopus subject areas

  • Software
  • Signal Processing
  • Computer Vision and Pattern Recognition
  • Computer Graphics and Computer-Aided Design


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