Abstract
A sweeping algorithm can generate hexahedral meshes by sweeping an all-quad mesh on the source surface to the target surface. For one-to-one sweeping, the most difficult thing is to generate an all-quad mesh on the target surface which has the same mesh connectivity as that of the source surface. The traditional method is to use the affine transformation, like translation, rotation, scaling or combinations of them. This method works very well on the convex cases, while it fails for concave and multiply-connected surfaces. In this paper, harmonic function is used to map meshes from a source surface to its target surface. The result shows that it can generate an all-quad mesh on the target surface with good quality without any inverted elements and thus avoid expensive smoothing algorithm (untangling). In order to generate interior nodes between the source and target surface, cage-based deformation method is applied with good mesh quality as well.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
References
Biswas, R., Strawn, R.C.: Tetrahedral and hexahedral mesh adaptation for CFD problems. Applied Numerical Mathematics 26(1-2), 135–151 (1988)
Samareh, J.A.: Geometry and grid/mesh generation issues for CFD and CSM shape optimization. Optimization and Engineering 6(1), 21–32 (2005)
Owen, S.J.: A Survey of Unstructured Mesh Generation Technology. In: 7th IMR, pp. 239–267 (1998)
Taniguchi, T., Goda, T., Kasper, H., et al.: Hexahedral Mesh Generation of Complex Composite Domain. In: 5th International Conference on Grid Generation in Computational Field Simmulations, pp. 699–707 (1996)
Schneiders, R.: A Grid-based Algorithm for the Generation of Hexahedral Element Meshes. Engineering with Computers 12(3-4), 168–177 (1996)
Price, M.A., Armstrong, C.G.: Hexahedral Mesh Generation by Medial Surface Subdivision: Part I. IJNME 38(19), 3335–3359 (1995)
Price, M.A., Armstrong, C.G.: Hexahedral Mesh Generation by Medial Surface Subdivision: Part II. IJNME 40, 111–136 (1997)
Blacker, T.D., Myers, R.J.: Seams and Wedgers in Plastering: A 3D Hexahedral Mesh Generation Algorithm. Engineering With Computers 2, 83–93 (1993)
Tautges, T.J., Blacker, T.D., Mitchell, S.A.: The Whisker-Weaving Algorithm: A Connectivity Based Method for Constructing All-Hexahedral Finite Element Meshes. IJNME 39, 3327–3349 (1996)
Patric, M.K.: Next-Generation Sweep Tool: A Method for Generating All-Hex Meshes on Two-And-One-Half Dimensional Geometries. In: 7th IMR, pp. 505–513 (1998)
Staten, M.L., Canann, S.A., Owen, S.J.: BMSweep: Locating Interior Nodes During Sweeping. In: 7th IMR, pp. 7–18 (1998)
Roca, X., Sarrate, J., Huerta, A.: Surface Mesh Projection for Hexahedral Mesh Generation by Sweeping. In: 13th IMR, pp. 169–180 (2004)
Roca, X., Sarrate, J., Huerta, A.: A new least-squares approximation of affine mappings for sweep algorithms. In: 14th IMR, pp. 433–448 (2005)
White, D.R., Lai, M.W., et al.: Automated Hexahedral Mesh Generation by Virtual Decomposition. In: 4th IMR, pp. 165–176 (1995)
Scott, M.A., Earp, M.N., Benzley, S.E., et al.: Adaptive Sweeping Techniques. In: 14th IMR, pp. 417–432 (2005)
Staten, M.L., Owen, S.J., Shontz, S.M., Salinger, A.G., Coffey, T.S.: A comparison of mesh morphing methods for 3D shape optimization. In: Quadros, W.R. (ed.) Proceedings of the 20th International Meshing Roundtable, vol. 90, pp. 293–311. Springer, Heidelberg (2011)
Shontz, S.M., Vavasis, S.A.: A mesh warping algorithm based on weighted Laplacian smoothing. In: 12th IMR, pp. 147–158 (2003)
Vurputoor, R.M., et al.: A Mesh Morphing Technique for Geometrically Dissimilar Tessellated Surfaces. In: 16th IMR, pp. 315–334 (2008)
Sigal, I.A., Hardisty, M.R., Whyne, C.M.: Mesh-morphing algorithms for specimen-specific finite element modeling. Journal of Biomechanics 41(7), 1381–1389 (2008)
Lee, A., Dobkin, D., Sweldens, W., Schroder, P.: Multiresolution Mesh Morphing. In: Proceedings of SIGGRAPH 1999, pp. 343–350 (1999)
Kanai, T., Suzuki, H., Kimura, F.: Three-dimensional geometric metamorphosis based on Harmonic Maps. The Visual Computer 14(4), 166–176 (1998)
Lee, A.W.F., Sweldens, W., Schroder, P., et al.: MAPS: Multiresolution Adaptive Parameterization of Surfaces. In: SIGGRAPH 1998 Proceedings, pp. 95–104 (1998)
Fan, Z.W., Jin, X.G., Feng, J.Q.: Mesh Morphing using polycube-based cross-parameterization. Computer Animation and Virtual Worlds 16, 499–508 (2005)
Kanai, T., Fujita, M., Chiyokura, H.: Multiresolution interpolation meshes. In: 9th Pacific Graphics International Conference, vol. 10, pp. 60–69 (2001)
Marc, A.: Recent Advances in Mesh Morphing. CG Forum, 1–23 (2002)
Wang, Y., Gupa, M., Gu, X.F., et al.: High Resolution Tracking of non-Rigid 3D Motion of Densely Sampled Data Using Harmonic Maps. In: IEEE International Conference on Computer Vision (2005)
Joshi, P., Meyer, M., et al.: Harmonic Coordinates for Character Articulation. ACM Transactions on Graphics 26(3(7)) (2007)
Zhang, D., Hebert, M.: Harmonic maps and their applications in surface matching. In: IEEE Conference on Computer Vision and Pattern Recognition (1999)
Remacle, J.F., Geuzaine, C., Compere, G., et al.: High Quality Surface Remeshing Using Harmonic Maps. IJNME 83(4), 403–425 (2009)
Zeng, W., Yin, X.T., Zhang, M., Luo, F., Gu, X.F.: Generalized Koebe’s method for conformal mapping multiply connected domains. In: SIAM/ACM Joint Conference on Geometric and Physical Modeling, pp. 89–100. ACM (2009)
Joshi, P., Meyer, M., DeRose, T., et al.: Harmonic coordinates for character articulation. ACM Transactions on Graphics (TOG) 26(3) (2007)
MeshKit, https://trac.mcs.anl.gov/projects/fathom/wiki/MeshKit
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Cai, S., Tautges, T.J. (2014). Robust One-to-One Sweeping with Harmonic S-T Mappings and Cages. In: Sarrate, J., Staten, M. (eds) Proceedings of the 22nd International Meshing Roundtable. Springer, Cham. https://doi.org/10.1007/978-3-319-02335-9_1
Download citation
DOI: https://doi.org/10.1007/978-3-319-02335-9_1
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-02334-2
Online ISBN: 978-3-319-02335-9
eBook Packages: EngineeringEngineering (R0)