ARAP++: an extension of the local/global approach to mesh parameterization

  • Zhao Wang
  • Zhong-xuan Luo
  • Jie-lin Zhang
  • Emil Saucan


Mesh parameterization is one of the fundamental operations in computer graphics (CG) and computeraided design (CAD). In this paper, we propose a novel local/global parameterization approach, ARAP++, for singleand multi-boundary triangular meshes. It is an extension of the as-rigid-as-possible (ARAP) approach, which stitches together 1-ring patches instead of individual triangles. To optimize the spring energy, we introduce a linear iterative scheme which employs convex combination weights and a fitting Jacobian matrix corresponding to a prescribed family of transformations. Our algorithm is simple, efficient, and robust. The geometric properties (angle and area) of the original model can also be preserved by appropriately prescribing the singular values of the fitting matrix. To reduce the area and stretch distortions for high-curvature models, a stretch operator is introduced. Numerical results demonstrate that ARAP++ outperforms several state-of-the-art methods in terms of controlling the distortions of angle, area, and stretch. Furthermore, it achieves a better visualization performance for several applications, such as texture mapping and surface remeshing.


Mesh parameterization Convex combination weights Stretch operator Jacobian matrix 

CLC number




The authors would like to thank Dr. Zhao-liang MENG, Dr. Xin FAN, and Dr. Wan-feng QI for their constructive recommendations for this work.


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Copyright information

© Journal of Zhejiang University Science Editorial Office and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Zhao Wang
    • 1
  • Zhong-xuan Luo
    • 1
    • 2
  • Jie-lin Zhang
    • 1
  • Emil Saucan
    • 3
  1. 1.School of Mathematical SciencesDalian University of TechnologyDalianChina
  2. 2.School of SoftwareDalian University of TechnologyDalianChina
  3. 3.Max Planck Institute for Mathematics in the SciencesLeipzigGermany

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