Abstract
This paper presents a new quality improvement algorithm for segmented quadrilateral/hexahedral meshes which are generated from multiple materials. The proposed algorithm combines mesh pillowing, curve and surface fairing driven by geometric flows, and optimization-based mesh regularization. The pillowing technique for quadrilateral/hexahedral meshes is utilized to eliminate doublets with two or more edges/faces located on boundary curves/surfaces. The non-manifold boundary for multiple materials is divided into several surface patches with common curves. Then curve vertices, surface vertices, and interior vertices are optimized via different strategies. Various geometric flows for surface smoothing are compared and discussed as well. Finally, the proposed algorithm is applied to three mesh datasets, the resulting quadrilateral meshes are well smoothed with volume and feature preserved, and hexahedral meshes have desirable Jacobians.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bobenko E, Schröder P, Caltech T (2005) Discrete Willmore flow. In: Eurographics symposium on geometry processing, pp 101–110
Bryant R (1984) A duality theorem for Willmore surfaces. J Differ Geom 20:23–53
Canann A (1991) Plastering and optismoothing: new approaches to automated, 3D hexahedral mesh generation and mesh smoothing. PhD dissertation, Brigham Young University, Provo, UT
Desbrun M, Meyer M, Schröder P, Barr AH (1999) Implicit fairing of irregular meshes using diffusion and curvature flow. In: SIGGRAPH’99 proceedings of the 26th annual conference on computer graphics and interactive techniques, Los Angeles, USA, pp 317–324
Escher J, Simonett G (1998) The volume preserving mean curvature flow near spheres. Proc Am Math Soc 126(9):2789–2796
Field D (1988) Laplacian smoothing and Delaunay triangulation. Commun Appl Numer Methods 4:709–712
Freitag LA, Knupp PM (2002) Tetrahedral mesh improvement via optimization of the element condition number. Int J Numer Methods Eng 53:1377–1391
Freitag L, Plassmann P (2000) Local optimization-based simplicial mesh untangling and improvement. Int J Numer Methods Eng 49:109–125
Ito Y, Shih A, Soni B (2009) Octree-based reasonable-quality hexahedral mesh generation using a new set of refinement templates. Int J Numer Methods Eng 77:1809–1833
Knupp P (2000) Hexahedral mesh untangling and algebraic mesh quality metrics. In: Proceedings of 9th international meshing roundtable, pp 173–183
Knupp P (2001) Hexahedral and tetrahedral mesh untangling. Eng Comput 17:261–268
Leng J, Zhang Y, Xu G (2011) A novel geometric flow-driven approach for quality improvement of segmented tetrahedral meshes. In: Proceedings of the 20th international meshing roundtable, pp 327–344
Li T, McKeag R, Armstrong C (1995) Hexahedral meshing using midpoint subdivision and integer programming. Comput Methods Appl Mech Eng 124:171–193
Mitchell S, Tautges T (1995) Pillowing doublets: refining a mesh to ensure that faces share at most one edge. In: Proceedings of the 4th international meshing roundtable, pp 231–240
Owen S (1998) A survey of unstructured mesh generation technology. In: Proceedings of the 7th international meshing roundtable, pp 239–267
Qian J, Zhang Y, Wang W, Lewis A, Siddiq Qidwai M, Geltmacher A (2010) Quality improvement of non-manifold hexahedral meshes for critical feature determination of microstructure materials. Int J Numer Methods Eng 82:1406–1423
Sapiro G (2001) Geometric partial differential equations and image analysis. Cambridge University Press, Cambridge
Schneiders R (1996) A grid-based algorithm for the generation of hexahedral element meshes. Eng Comput 12:168–177
Tautges T, Blacker T, Mitchell S (1996) The whisker-weaving algorithm: a connectivity based method for constructing all-hexahedral finite element meshes. Int J Numer Methods Eng 39:3327–3349
Xu G (2008) Geometric partial differential equation methods in computational geometry. Science Press of China, Beijing
Zhang Y, Bajaj C (2006) Adaptive and quality quadrilateral/hexahedral meshing from volumetric data. Comput Methods Appl Mech Eng 195:942–960
Zhang Y, Bajaj C, Sohn B (2005) 3D finite element meshing from imaging data. Comput Methods Appl Mech Eng 194:5083–5106
Zhang Y, Bajaj C, Xu G (2005) Surface smoothing and quality improvement of quadrilateral/hexahedral meshes with geometric flow. In: Proceedings of the 14th international meshing roundtable, pp 449–468
Zhang Y, Hughes T, Bajaj C (2010) An automatic 3D mesh generation method for domains with multiple material. Comput Methods Appl Mech Eng 199:405–415
Acknowledgements
The work in this paper was done when J. Leng was a visiting student at the Department of Mechanical Engineering, Carnegie Mellon University. J. Leng, Y. Zhang and J. Qian were supported in part by Y. Zhang’s ONR-YIP award N00014-10-1-0698, an ONR grant N00014-08-1-0653, an AFOSR grant FA9550-11-1-0346, and a NSF/DoD-MRSEC seed grant. J. Leng and G. Xu were supported in part by NSFC key project under the grant 10990013 and Funds for Creative Research Groups of China (grant No. 11021101).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Leng, J., Xu, G., Zhang, Y., Qian, J. (2013). Quality Improvement of Segmented Hexahedral Meshes Using Geometric Flows. 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_11
Download citation
DOI: https://doi.org/10.1007/978-94-007-4255-0_11
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-007-4254-3
Online ISBN: 978-94-007-4255-0
eBook Packages: EngineeringEngineering (R0)