Abstract
This work describes an automatic algorithm for unstructured mesh regeneration on arbitrarily shaped three-dimensional surfaces. The arbitrary surface may be: a triangulated mesh, a set of points, or an analytical surface (such as a collection of NURBS patches). To be generic, the algorithm works directly in Cartesian coordinates, as opposed to generating the mesh in parametric space, which might not be available in all the cases. In addition, the algorithm requires the implementation of three generic functions that abstractly represent the supporting surface. The first, given a point location, returns the desired characteristic size of a triangular element at this position. The second method, given the current edge in the boundary-contraction algorithm, locates the ideal apex point that forms a triangle with this edge. And the third method, given a point in space and a projection direction, returns the closest point on the geometrical supporting surface. This work also describes the implementation of these three methods to re-mesh an existing triangulated mesh that might present regions of high curvature. In this implementation, the only information about the surface geometry is a set of triangles. In order to test the efficiency of the proposed algorithm of surface mesh generation and implementation of the three abstract methods, results of performance and quality of generated triangular element examples are presented.
Similar content being viewed by others
References
Cavalcante Neto JB, Wawrzynek PA, Carvalho MTM, Martha LF, Ingraffea AR (2001) An algorithm for three-dimensional mesh generation for arbitrary regions with cracks. Eng Comput 17(1):75–91
Miranda ACO, Martha LF (2002) Mesh generation on high curvature surfaces based on background Quadtree structure. In: Proceedings of 11th International Meshing Roundtable 1, pp 333–341
Miranda ACO, Cavalcante Neto JB, Martha LF (1999) An algorithm for two-dimensional mesh generation for arbitrary regions with cracks, SIBGRAPI’99. In: Stolfi J, Tozzi C (eds) XII Brazilian Symposium on Computer Graphics, Image Processing and Vision, IEEE Computer Society Order Number PRO0481, ISBN 0-7695-0481-7, pp 29–38
Miranda ACO, Meggiolaro MA, Castro JTP, Martha LF, Bittencourt TN (2003) Fatigue life and crack path predictions in generic 2D structural components. Eng Fract Mech 70(10):1259–1279
Carlos J, Scheidegger E, Fleishman S, Silva CT (1996) Direct (re)meshing for efficient surface processing. Comput Graph Forum 25(3):527–536
Lohner R (1996) Regridding surface triangulations. J Comput Phys 126(1):1–10
Shostko AA, Lohner R, Sandberg WC (1999) Surface triangulation over intersecting geometries. Int J Numer Meth Eng 44:1359–1376
Nakahashi K, Sharov D (1995) Direct surface triangulation using the advancing front method. AIAA, pp 442–451
Lau TS, Lo SH (1996) Finite element mesh generation over analytical curved surfaces. Comput Struct 59(2):301–309
Lo SH, Lau TS (1998) Mesh generation over curved surfaces with explicit control on discretization error. Eng Comput Int J Comput Eng 15(3):357–373
Chan CT, Anastasiou K (1997) An automatic tetrahedral mesh generation scheme by the advancing front method. Commun Numer Methods Eng 13:33–46
Jin H, Tanner RI (1993) Generation of unstructured tetrahedral meshes by advancing front technique. Int J Numer Methods Eng 36:1805–1823
Lo SH (1985) A new mesh generation scheme for arbitrary planar domains. Int J Numer Methods Eng 21:1403–1426
Lohner R, Parikh P (1988) Generation of three-dimensional unstructured grids by the advancing-front method. Int J Numer Methods Fluids 8:1135–1149
Moller P, Hansbo P (1995) On advancing front mesh generation in three dimensions. Int J Numer Methods Fluids 38:3551–3569
Peraire J, Peiro J, Formaggia L, Morgan K, Zienkiewicz OC (1988) Finite Euler computation in three-dimensions. Int J Numer Methods Fluids 26:2135–2159
Rassineux A (1998) Generation and optimization of tetrahedral meshes by advancing front technique. Int J Numer Methods Fluids 41:651–674
Guttman A (1984) Rtrees: a dynamic index structure for spatial searching. In: Proceedings of ACM SIGMOD International Conference on Management of Data, pp 47–57
Rudolf B (1971) Binary B-Trees for virtual memory. ACM-SIGFIDET Workshop, San Diego, California, Session 5B, pp 219–235
Foley TA, Nielson GM (1989) Knot selection for parametric spline interpolation. In: Schumaker L (ed) Mathematical methods in CAGD. Academic Press, New York, pp 445–467
Borouchaki H, Hecht F, Frey PJ (1997) Mesh gradation control. In: Proceedings of 6th International Meshing Roundtable, Sandia National Laboratories, pp 131–141
Owen SJ, Saigal S (1997) Neighborhood-based element sizing control for finite element surface meshing. In: Proceedings of 6th International Meshing Roundtable, Sandia National Laboratories, pp 143–154
George PL, Seveno E (1994) The advancing-front mesh generation method revisited. Int J Numer Methods Fluids 37:3605–3619
Borouchaki H, Hecht F, Frey PJ (1997) H-Correction. INRIA Report No. 3199, INRIA, pp 29
Lohner R, Parikh P, Gumbert C (1988) Interactive generation of unstructured grid for three dimensional problems. Numerical grid generation in computational fluid mechanics ‘88. Pineridge Press, Swansea, pp 687–697
Owen SJ, Saigal S (2000) Surface mesh sizing control. Int J Numer Methods Fluids 47(1):289–312
Mello UT, Cavalcanti PR (2000) A point creation strategy for mesh generation using crystal lattices as templates. In: Proceedings of 9th International Meshing Roundtable, Sandia National Laboratories, pp 253–261
Zhu J (2003) A new type of size function respecting premeshed entities. In: Proceedings of 12th International Meshing Roundtable, Sandia National Laboratories, pp 403–413
Persson P (2004) PDE-based gradient limiting for mesh size functions. In: Proceedings of 13th International Meshing Roundtable, Sandia National Laboratories, pp 377–388
Moller T, Trumbore B (1997) Fast, minimum storage ray-triangle intersection. J Graphics Tools 2(1):21–28
Krysl P (2005) Computational complexity of the advancing front triangulation. Eng Comput 12:16–22
Acknowledgments
The first author acknowledges a post-doctoral fellowship provided by the Brazilian agency CAPES, process 2183-06, and the Cornell Fracture Group. The second author has a PQ grant from CNPq. This work has been developed in the Cornell Fracture Group and in Tecgraf/PUC-Rio, Computer Graphics Technology Group. Tecgraf/PUC-Rio is partially supported by PETROBRAS.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Miranda, A.C.O., Martha, L.F., Wawrzynek, P.A. et al. Surface mesh regeneration considering curvatures. Engineering with Computers 25, 207–219 (2009). https://doi.org/10.1007/s00366-008-0119-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00366-008-0119-9