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A computational approach to joint line detection on triangular meshes

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Abstract

In this paper, we present formulae for evaluating differential quantities at vertices of triangular meshes that may approximate potential piecewise smooth surfaces with discontinuous normals or discontinuous curvatures at the joint lines. We also define the C 1 and C 2 discontinuity measures for surface meshes using changing rates of one-sided curvatures or changing rates of curvatures across mesh edges. The curvatures are computed discretely as of local interpolating surfaces that lie within a tolerance to the mesh. Together with proper estimation of local shape parameters, the obtained discontinuity measures own properties like sensitivity to salient joint lines and being scale invariant. A simple algorithm is finally developed for detection of C 1 or C 2 discontinuity joint lines on triangular meshes with even highly non-uniform triangulations. Several examples are provided to demonstrate the effectiveness of the proposed method.

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Acknowledgments

We owe thanks to anonymous referees for their helpful comments on an earlier version of the paper. This work is supported by Natural Science Foundation of China Grants (60970077, 11290142), the ARC 9/09 Grant (MOE2008-T2-1-075), MOE RG 59/08 (M52110092), NRF 2007IDM-IDM002-010 of Singapore.

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang University, Hangzhou, China

    Xunnian Yang

  2. School of Computer Engineering, Nanyang Technological University, Singapore, Singapore

    Jianmin Zheng

  3. Division of Mathematics, SPMS, Nanyang Technological University, Singapore, Singapore

    Desheng Wang

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  1. Xunnian Yang
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  2. Jianmin Zheng
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  3. Desheng Wang
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Correspondence to Xunnian Yang.

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Yang, X., Zheng, J. & Wang, D. A computational approach to joint line detection on triangular meshes. Engineering with Computers 30, 583–597 (2014). https://doi.org/10.1007/s00366-012-0303-9

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  • DOI: https://doi.org/10.1007/s00366-012-0303-9

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