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Compact feature-aware Hermite-style high-order surface reconstruction

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Abstract

High-order surface reconstruction is now a commonly used technique for mesh generation and adaptation, geometric and physical modeling, and high-order numerical methods for solving partial differential equations (PDEs). However, surface reconstruction from a relatively coarse mesh remained a challenging problem, especially for surfaces with sharp features. In this paper, we introduce a new method to address this challenge by improving the previous state of the art, including continuous moving frames (CMF) and weighted averaging of local fittings (WALF) (Eng Comput 28 (2012)), in two aspects. First, we significantly improve the robustness of reconstruction from coarse meshes using a Hermite-style least squares approximation to incorporate normals of the surface and tangents of the feature curves. Second, we ensure both \(G^{0}\) continuity and high-order accuracy of the reconstruction near sharp features by generating parametric surface elements with an iterative feature-aware parameterization. We present the theoretical framework of our method and compare it against point-based methods in terms of accuracy and stability. We demonstrate the use of the proposed technique in generating high-order meshes for finite element methods, and show that it enables nearly identical solutions as using the meshes generated from exact geometry, while allowing additional flexibility.

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Acknowledgements

This work was supported in part under the SciDAC program in the US Department of Energy Office of Science, Office of Advanced Scientific Computing Research through subcontract #462974 with Los Alamos National Laboratory and under a subcontract with Argonne National Laboratory under Contract DE-AC02-06CH11357. Assigned: LA-UR-19-20389. Los Alamos National Laboratory is operated by Triad National Security, LLC for the National Nuclear Security Administration of U.S. Department of Energy under contract 89233218-CNA000001.

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Author notes

  1. Xinglin Zhao

    Present address: Google Inc., Mountain View, CA, USA

Authors and Affiliations

  1. Department of Applied Mathematics and Statistics and Institute for Advanced Computational Science, Stony Brook University, Stony Brook, NY, USA

    Yipeng Li, Xinglin Zhao & Xiangmin Jiao

  2. Los Alamos National Laboratory, Computer, Computational and Statistical Sciences, Los Alamos, NM, USA

    Navamita Ray

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  1. Yipeng Li
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  2. Xinglin Zhao
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  3. Navamita Ray
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  4. Xiangmin Jiao
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Correspondence to Xiangmin Jiao.

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Li, Y., Zhao, X., Ray, N. et al. Compact feature-aware Hermite-style high-order surface reconstruction. Engineering with Computers 37, 187–210 (2021). https://doi.org/10.1007/s00366-019-00815-z

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