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An Optimization-Based Iterative Approach to Tetrahedral Mesh Smoothing

  • Chapter
Image-Based Geometric Modeling and Mesh Generation

Part of the book series: Lecture Notes in Computational Vision and Biomechanics ((LNCVB,volume 3))

Abstract

The optimal Delaunay triangulation (ODT) is an effective approach in improving the quality of inner vertices of a tetrahedral mesh. Recently it had been extended boundary-optimized Delaunay triangulation (B-ODT), in which both inner and boundary vertices are repositioned by analytically minimizing the \(\mathcal{L}^{1}\) error between a paraboloid function and its piecewise linear interpolation over the neighborhood of each vertex. In the present work, we describe a smoothing method that is based on the B-ODT method but has better performance. We smooth the mesh in an edge-by-edge fashion by adjusting each pair of vertices of every edge. This method has the volume-preserving and sharp-feature-preserving properties. A number of experiments are included to demonstrate the performance of our method.

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Acknowledgements

The work described was supported in part by an NIH Award (Number R15HL103497) from the National Heart, Lung, and Blood Institute (NHLBI) and by a subcontract from the National Biomedical Computation Resource (NIH Award Number P41 RR08605). The content is solely the responsibility of the authors and does not necessarily represent the official views of the sponsors.

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Authors and Affiliations

  1. Department of Computer Science, University of Wisconsin-Milwaukee, 3200 N. Cramer St, Milwaukee, WI, 53211, USA

    Zhanheng Gao, Zeyun Yu & Jun Wang

  2. College of Computer Science and Technology, Jilin University, 2699 Qianjin St, Changchun, Jilin, 130012, China

    Zhanheng Gao

Authors
  1. Zhanheng Gao
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  2. Zeyun Yu
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  3. Jun Wang
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Corresponding author

Correspondence to Zeyun Yu .

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Editors and Affiliations

  1. Department of Mechanical Engineering, Carnegie Mellon University, Forbes Avenue 5000, Pittsburgh, 15213, Pennsylvania, USA

    Yongjie (Jessica) Zhang

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Gao, Z., Yu, Z., Wang, J. (2013). An Optimization-Based Iterative Approach to Tetrahedral Mesh Smoothing. In: Zhang, Y. (eds) Image-Based Geometric Modeling and Mesh Generation. Lecture Notes in Computational Vision and Biomechanics, vol 3. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-4255-0_8

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  • DOI: https://doi.org/10.1007/978-94-007-4255-0_8

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-007-4254-3

  • Online ISBN: 978-94-007-4255-0

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