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Stretch-Minimizing Volumetric Parameterization

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Abstract

Not many methods for parameterization guarantee bijectivity or local injectivity, which is essential for foldoverfree mappings. Stretch-minimizing parameterization which is widely used for surface parameterization, provides foldover-free mappings and is capable of trading off between angle and area distortions. We extend its usage to volumetric parameterization in this paper by deriving a 3D version of stretch-distortion energy and incorporating fixed boundary conditions. Our energy definition includes a natural barrier term which effectively prevents elements from collapsing and folding over. It saves the effort in other methods of formulating additional energy or constrains to ensure the local injectivity. We propose to minimize the overall energy integrated over the whole mesh with a relaxation-enhanced solver and optimize the energy globally. This is different from the conventional approach of surface parameterization where mesh nodes are optimized individually. Compared with other volumetric parameterizations, our approach bears the advantages of stretch-minimizing method, being foldover-free and offering a good trade-off between angle and volume distortions.

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Authors and Affiliations

  1. Department of Computer Science and Engineering, Zhejiang University, Hangzhou, 310027, China

    Yao Jin, Jie-Yi Zhao & Ruo-Feng Tong

  2. College of New Media, Zhejiang University of Media and Communications, Hangzhou, 310018, China

    Gui-Ping Qian

  3. National Centre for Computer Animation, Bournemouth University, Bournemouth, BH12 5BB, U.K.

    Jian Chang & Jianjun Zhang

Authors
  1. Yao Jin
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  2. Gui-Ping Qian
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  3. Jie-Yi Zhao
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  4. Jian Chang
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  5. Ruo-Feng Tong
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  6. Jianjun Zhang
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Corresponding author

Correspondence to Ruo-Feng Tong.

Additional information

This work was supported by the National Natural Science Foundation of China under Grant No. 61170141, the National High Technology Research and Development 863 Program of China under Grant No. 2013AA013903, the People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme FP7/2007-2013/ under REA Grant Agreement n° [612627]-“AniNex”, and the Zhejiang Provincal Natural Science Foundation of China under Grant No. LY13F020036.

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Jin, Y., Qian, GP., Zhao, JY. et al. Stretch-Minimizing Volumetric Parameterization. J. Comput. Sci. Technol. 30, 553–564 (2015). https://doi.org/10.1007/s11390-015-1545-y

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  • DOI: https://doi.org/10.1007/s11390-015-1545-y

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