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Differentials-Based Segmentation and Parameterization for Point-Sampled Surfaces

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Abstract

Efficient parameterization of point-sampled surfaces is a fundamental problem in the field of digital geometry processing. In order to parameterize a given point-sampled surface for minimal distance distortion, a differentials-based segmentation and parameterization approach is proposed in this paper. Our approach partitions the point-sampled geometry based on two criteria: variation of Euclidean distance between sample points, and angular difference between surface differential directions. According to the analysis of normal curvatures for some specified directions, a new projection approach is adopted to estimate the local surface differentials. Then a k-means clustering (k-MC) algorithm is used for partitioning the model into a set of charts based on the estimated local surface attributes. Finally, each chart is parameterized with a statistical method — multidimensional scaling (MDS) approach, and the parameterization results of all charts form an atlas for compact storage.

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Authors and Affiliations

  1. State Key Laboratory of CAD & CG, Zhejiang University, Hangzhou, 310027, China

    Yong-Wei Miao, Jie-Qing Feng, Chun-Xia Xiao & Qun-Sheng Peng

  2. College of Science, Zhejiang University of Technology, Hangzhou, 310032, China

    Yong-Wei Miao

  3. School of Computing Sciences, University of East Anglia, Norwich, NR4 7TJ, U.K.

    A. R. Forrest

Authors
  1. Yong-Wei Miao
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  2. Jie-Qing Feng
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  3. Chun-Xia Xiao
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  4. Qun-Sheng Peng
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  5. A. R. Forrest
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Corresponding author

Correspondence to Yong-Wei Miao.

Additional information

This work is supported by the National Grand Fundamental Research 973 Program of China under Grant No. 2002CB312101, the National Natural Science Foundation of China (NSFC) under Grant Nos. 60503056, 60333010, and the Natural Science Foundation of Zhejiang Province under Grant No. R106449.

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Miao, YW., Feng, JQ., Xiao, CX. et al. Differentials-Based Segmentation and Parameterization for Point-Sampled Surfaces. J Comput Sci Technol 22, 749–760 (2007). https://doi.org/10.1007/s11390-007-9088-5

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  • DOI: https://doi.org/10.1007/s11390-007-9088-5

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