Compact feature-aware Hermite-style high-order surface reconstruction
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. Here 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 G0 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.
- Authors:
-
[3];
[1]
- Stony Brook Univ., NY (United States). Dept. of Applied Mathematics
- Stony Brook Univ., NY (United States). Dept. of Applied Mathematics; Google Inc., Mountain View (United States)
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Publication Date:
- Research Org.:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)
- OSTI Identifier:
- 1557760
- Report Number(s):
- LA-UR-19-20389
Journal ID: ISSN 0177-0667
- Grant/Contract Number:
- 89233218CNA000001; AC02-06CH11357
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Engineering with Computers
- Additional Journal Information:
- Journal Name: Engineering with Computers; Journal ID: ISSN 0177-0667
- Publisher:
- Springer
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 42 ENGINEERING; Computer Science; Mathematics; high-order methods; surface reconstruction; weighted least squares; Hermite approximations; geometric discontinuities; finite element methods
Citation Formats
Li, Yipeng, Zhao, Xinglin, Ray, Navamita, and Jiao, XIangmin. Compact feature-aware Hermite-style high-order surface reconstruction. United States: N. p., 2019.
Web. doi:10.1007/s00366-019-00815-z.
Li, Yipeng, Zhao, Xinglin, Ray, Navamita, & Jiao, XIangmin. Compact feature-aware Hermite-style high-order surface reconstruction. United States. https://doi.org/10.1007/s00366-019-00815-z
Li, Yipeng, Zhao, Xinglin, Ray, Navamita, and Jiao, XIangmin. Wed .
"Compact feature-aware Hermite-style high-order surface reconstruction". United States. https://doi.org/10.1007/s00366-019-00815-z. https://www.osti.gov/servlets/purl/1557760.
@article{osti_1557760,
title = {Compact feature-aware Hermite-style high-order surface reconstruction},
author = {Li, Yipeng and Zhao, Xinglin and Ray, Navamita and Jiao, XIangmin},
abstractNote = {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. Here 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 G0 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.},
doi = {10.1007/s00366-019-00815-z},
journal = {Engineering with Computers},
number = ,
volume = ,
place = {United States},
year = {2019},
month = {7}
}
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Works referenced in this record:
Automated low-order to high-order mesh conversion
journal, March 2018
- Ims, Jeremy; Wang, Z. J.
- Engineering with Computers, Vol. 35, Issue 1
Reconstructing high-order surfaces for meshing
journal, September 2011
- Jiao, Xiangmin; Wang, Duo
- Engineering with Computers, Vol. 28, Issue 4
A triangular G1 patch from boundary curves
journal, February 1996
- Walton, Dj; Meek, Ds
- Computer-Aided Design, Vol. 28, Issue 2
Higher-Order Mesh Generation Using Linear Meshes [EM Programmer's Notebook]
journal, April 2019
- Young, John C.
- IEEE Antennas and Propagation Magazine, Vol. 61, Issue 2
Robust moving least-squares fitting with sharp features
journal, July 2005
- Fleishman, Shachar; Cohen-Or, Daniel; Silva, Cláudio T.
- ACM Transactions on Graphics, Vol. 24, Issue 3
Curved PN triangles
conference, January 2001
- Vlachos, Alex; Peters, Jörg; Boyd, Chas
- Proceedings of the 2001 symposium on Interactive 3D graphics - SI3D '01
Gmsh: A 3-D finite element mesh generator with built-in pre- and post-processing facilities
journal, September 2009
- Geuzaine, Christophe; Remacle, Jean-François
- International Journal for Numerical Methods in Engineering, Vol. 79, Issue 11
Optimal Isoparametric Finite Elements and Error Estimates for Domains Involving Curved Boundaries
journal, June 1986
- Lenoir, M.
- SIAM Journal on Numerical Analysis, Vol. 23, Issue 3
NURBS-enhanced finite element method (NEFEM)
journal, October 2008
- Sevilla, Ruben; Fernández-Méndez, Sonia; Huerta, Antonio
- International Journal for Numerical Methods in Engineering, Vol. 76, Issue 1
Anisotropic mesh adaptation for evolving triangulated surfaces
journal, December 2009
- Jiao, Xiangmin; Colombi, Andrew; Ni, Xinlai
- Engineering with Computers, Vol. 26, Issue 4
On the generation of symmetric Lebesgue-like points in the triangle
journal, December 2012
- Rapetti, Francesca; Sommariva, Alvise; Vianello, Marco
- Journal of Computational and Applied Mathematics, Vol. 236, Issue 18
Consistent computation of first- and second-order differential quantities for surface meshes
conference, January 2008
- Jiao, Xiangmin; Zha, Hongyuan
- Proceedings of the 2008 ACM symposium on Solid and physical modeling - SPM '08
Identification of and discontinuities for surface meshes in CAD
journal, February 2008
- Jiao, Xiangmin; Bayyana, Narasimha R.
- Computer-Aided Design, Vol. 40, Issue 2
Interpolation theory over curved elements, with applications to finite element methods
journal, August 1972
- Ciarlet, P. G.; Raviart, P. -A.
- Computer Methods in Applied Mechanics and Engineering, Vol. 1, Issue 2
A novel cubic-order algorithm for approximating principal direction vectors
journal, January 2004
- Goldfeather, Jack; Interrante, Victoria
- ACM Transactions on Graphics, Vol. 23, Issue 1
Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement
journal, October 2005
- Hughes, T. J. R.; Cottrell, J. A.; Bazilevs, Y.
- Computer Methods in Applied Mechanics and Engineering, Vol. 194, Issue 39-41
Condition numbers and equilibration of matrices
journal, December 1969
- van der Sluis, A.
- Numerische Mathematik, Vol. 14, Issue 1
Accuracy-preserving source term quadrature for third-order edge-based discretization
journal, September 2017
- Nishikawa, Hiroaki; Liu, Yi
- Journal of Computational Physics, Vol. 344
Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree
journal, December 1995
- Wendland, Holger
- Advances in Computational Mathematics, Vol. 4, Issue 1
Works referencing / citing this record:
Surface reconstruction based on CAD model driven priori templates
journal, December 2019
- Hao, Long; Huang, Xiang; Li, ShuangGao
- Review of Scientific Instruments, Vol. 90, Issue 12