Quadrilateral Meshing for Hexahedral Mesh Generation Based on Facet Normal Matching

Hiroshi Kawaharada; Yusuke Imai; Hiroyuki Hiraoka

doi:10.20965/ijat.2014.p0356

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IJAT Vol.8 No.3 pp. 356-364

doi: 10.20965/ijat.2014.p0356

(2014)

Paper:

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Quadrilateral Meshing for Hexahedral Mesh Generation Based on Facet Normal Matching

Hiroshi Kawaharada, Yusuke Imai, and Hiroyuki Hiraoka

Department of Precision Mechanics, Chuo University, 1-13-27 Kasuga, Bunkyo-ku, Tokyo 112-8551, Japan

Received:

November 28, 2013

Accepted:

March 5, 2014

Published:

May 5, 2014

Keywords:

CAD, volume mesh, sharp feature, fitting, voxel

Abstract

Because performance testing using actual products is costly, manufacturers use lower-cost Computer-Aided Design (CAD) simulations. In this paper, we focus on hexahedral meshes, which are more accurate than tetrahedral meshes, for finite element analysis. Our final objective is automatic hexahedral mesh generation with sharp features to precisely represent the corresponding features of a target shape. Our hexahedral mesh is generated using a voxel-based algorithm. In our previous works, we fitted the surface of the voxels to the target surface using Laplacian energy minimization and used normal vectors in the fitting to preserve sharp features. However, we were unable to precisely represent sharp concave features using the method. In this proposal, we improve the previously used Laplacian energy minimization by adding a term that depends on facet normalmatching for multi-normal vectors, instead of using normal vector matching.

Cite this article as:

H. Kawaharada, Y. Imai, and H. Hiraoka, “Quadrilateral Meshing for Hexahedral Mesh Generation Based on Facet Normal Matching,” Int. J. Automation Technol., Vol.8 No.3, pp. 356-364, 2014.

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References

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[2] H. Date, S. Kanai, T. Kishinami, and I. Nishigaki, “Mesh Simplification and Adaptive LOD for Finite Element mesh Generation,” Int. J. of CAD/CAM, Vol.6, No.1, Paper No.8, 2006.
[3] H. Date, S. Noguchi, M. Onosato, and S. Kanai, “Flexible Control of Multimaterial Tetrahedra Mesh Properties by Using Multiresolution Techniques,” IEEE Trans. on Magnetics, Vol.45, Issue 3, pp. 1352-1355, 2009.
[4] H. Kawaharada and H. Hiraoka, “Boundary Stencils of Volume Subdivision for Simulations,” Proc. of the ACDDE2011, 3-8.
[5] H. Kawaharada and K. Sugihara, “Hexahedral Mesh Generation Using Subdivision,” Computational Engineering, Vol.16, No.2, pp. 12-15, 2011.
[6] R. Schneiders, R. Schindler, and F. Weiler, “Octree-based Generation of Hexahedral Element Meshes,” The 5th Int. Meshing Roundtable, 205-215, 1996.
[7] M. Loic, “A New Approach to Octree-based Hexahedral Meshing,” The 10th Int. Meshing Roundtable, 209-221, 2001.
[8] M. L. Saten, S. J. Owen, and T. D. Blacker, “Unconstrained Paving and Plastering: A New Idea for All Hexahedral Mesh Generation,” The 14th Int. Meshing Roundtable, 399-416, 2005.
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[14] S. Jason, S. A. Mitchell, P. Knupp, and D. White, “Methods for Multisweep Automation,” The 9th Int. Meshing Roundtable, 77-87, 2000.
[15] R. Xevi and J. Sarrate, “An Automatic and General Least-squares Projection Procedure for Sweep Meshing,” The 15th Int. Meshing Roundtable, 487-506, 2006.
[16] M. Nieser, U. Reitebuch, and K. Polthier, “CubeCover-Parameterization of 3D Volumes,” Computer Graphics Forum, Vol.30, Issue 5, pp. 1397-1406, 2011.
[17] S. Moriya, H. Hiraoka, and H. Kawaharada, “Replication of Sharp Features Hexahedral Meshes Using Modified Laplacian Energy Minimization,” In the Proc. of ACDDE2012.
[18] Y. Imai, S. Moriya, H. Hiraoka, and H. Kawaharada, “Quadrilateral Mesh Fitting that Preserves Sharp features based on Multi-normals for Laplacian Energy,” In the Proc. of ACDDE2013.
[19] Y. Li, Y. Liu, W. Xu, W. Wang, and B. Guo, “All-hex meshing using singularity-restricted field,” ACM Trans. on Graphics, Vol.31, Issue 6, Article No.177, 2012.
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Available from: http://shapes.aimatshape.net/
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This article is published under a Creative Commons Attribution-NoDerivatives 4.0 Internationa License.

[1] [1] A. Yamanaka and T. Takaki, “Simulation of Microstructure Evolution and Deformation Behavior for Dual-Phase Steel by Multi-Phase-Field Method and Elastoplastic Finite Element Method,” Int. J. of Automation Technology, Vol.7, No.1, pp. 16-23, 2013.

[2] [2] H. Date, S. Kanai, T. Kishinami, and I. Nishigaki, “Mesh Simplification and Adaptive LOD for Finite Element mesh Generation,” Int. J. of CAD/CAM, Vol.6, No.1, Paper No.8, 2006.

[3] [3] H. Date, S. Noguchi, M. Onosato, and S. Kanai, “Flexible Control of Multimaterial Tetrahedra Mesh Properties by Using Multiresolution Techniques,” IEEE Trans. on Magnetics, Vol.45, Issue 3, pp. 1352-1355, 2009.

[4] [4] H. Kawaharada and H. Hiraoka, “Boundary Stencils of Volume Subdivision for Simulations,” Proc. of the ACDDE2011, 3-8.

[5] [5] H. Kawaharada and K. Sugihara, “Hexahedral Mesh Generation Using Subdivision,” Computational Engineering, Vol.16, No.2, pp. 12-15, 2011.

[6] [6] R. Schneiders, R. Schindler, and F. Weiler, “Octree-based Generation of Hexahedral Element Meshes,” The 5th Int. Meshing Roundtable, 205-215, 1996.

[7] [7] M. Loic, “A New Approach to Octree-based Hexahedral Meshing,” The 10th Int. Meshing Roundtable, 209-221, 2001.

[8] [8] M. L. Saten, S. J. Owen, and T. D. Blacker, “Unconstrained Paving and Plastering: A New Idea for All Hexahedral Mesh Generation,” The 14th Int. Meshing Roundtable, 399-416, 2005.

[9] [9] Y. Wada, S. Yoshimura, and G. Yagawa, “Intelligent Local Approach for Automatic Hexahedral Mesh Generation,” The 2nd Symp. on Trends in Unstructured Mesh Generation, 1999.

[10] [10] T. D. Blacker and R. J. Meyers, “Seams and Wedges in Plastering: A 3D Hexahedral Mesh Generation Algorithm,” Engineering with Computers, Vol.2, Issue 9, pp. 83-93, 1993.

[11] [11] T. J. Tautges, T. Blacker, and S. A. Mitchell, “The Whisker Weaving Algorithm: A Connectivity-based Method for Constructing Allhexahedral Finite Element Meshes,” Int. J. for Numerical Methods in Engineering, Vol.39, pp. 3327-3349,1996.

[12] [12] M. Muller-Hannemann, “Hexahedral Mesh Generation by Successive Dual Cycle Elimination,” The 7th Int. Meshing Roundtable, 365-378, 1998.

[13] [13] A. Sheffer, M. Etzion, A. Rappoport, and M. Bercovier, “Hexahedral Mesh Generation Using The Embedded Voronoi Graph,” The 7th Int. Meshing Roundtable, 347-364, 1998.

[14] [14] S. Jason, S. A. Mitchell, P. Knupp, and D. White, “Methods for Multisweep Automation,” The 9th Int. Meshing Roundtable, 77-87, 2000.

[15] [15] R. Xevi and J. Sarrate, “An Automatic and General Least-squares Projection Procedure for Sweep Meshing,” The 15th Int. Meshing Roundtable, 487-506, 2006.

[16] [16] M. Nieser, U. Reitebuch, and K. Polthier, “CubeCover-Parameterization of 3D Volumes,” Computer Graphics Forum, Vol.30, Issue 5, pp. 1397-1406, 2011.

[17] [17] S. Moriya, H. Hiraoka, and H. Kawaharada, “Replication of Sharp Features Hexahedral Meshes Using Modified Laplacian Energy Minimization,” In the Proc. of ACDDE2012.

[18] [18] Y. Imai, S. Moriya, H. Hiraoka, and H. Kawaharada, “Quadrilateral Mesh Fitting that Preserves Sharp features based on Multi-normals for Laplacian Energy,” In the Proc. of ACDDE2013.

[19] [19] Y. Li, Y. Liu, W. Xu, W. Wang, and B. Guo, “All-hex meshing using singularity-restricted field,” ACM Trans. on Graphics, Vol.31, Issue 6, Article No.177, 2012.

[20] [20] Aim@Shape Project, cited Jul. 11, 2012,
Available from: http://shapes.aimatshape.net/

[21] [21] Polymender, cited Jul.11, 2012,
Available from: http://www.cs.wustl.edu/˜taoju/code/polymender.htm [Accessed Jul. 11, 2012]

[22] [22] R. Mehra, Q. Zhou, J. Long, A. Sheffer, A. Gooch, and N. J. Mitra, “Abstraction of Man-Made Shapes,” ACM Trans. on Graphics, Vol.28, Issue 5, pp. 1-10, 2009.