Summary
We present 3 mapping/flattening techniques for triangulations of poor quality triangles. The implementation of those mappings as well as the boundary conditions are presented in a very comprehensive manner such that it becomes accessible to a wider community than the one of computer graphics. The resulting parameterizations are used to generate new triangulations or quadrilateral meshes for the model that are of high quality.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Alliez, P., Meyer, M., Desbrun, M.: Interactive geometry remeshing. In: Computer graphics (Proceedings of the SIGGRAPH 2002), pp. 347–354 (2002)
Batdorf, M., Freitag, L.A., Ollivier-Gooch, C.: A computational study of the effect of unstructured mesh quality on solution efficiency. In: Proc. 13th AIAA Computational Fluid Dynamics Conf. (1997)
Bechet, E., Cuilliere, J.-C., Trochu, F.: Generation of a finite element mesh from stereolithography (stl) files. Computer-Aided Design 34(1), 1–17 (2002)
Ben-Chen, M., Gotsman, C., Bunin, G.: Conformal flattening by curvature prescription and metric scaling. Computer Graphics Forum 27(2) (2008)
Bennis, C., Vézien, J.-M., Iglésias, G.: Piecewise surface flattening for non-distorted texture mapping. In: ACM SIGGRAPH Computer Graphics, pp. 237–246 (1991)
Borouchaki, H., Laug, P., George, P.L.: Parametric surface meshing using a combined advancing-front generalized delaunay approach. International Journal for Numerical Methods in Engineering 49, 223–259 (2000)
Choquet, C.: Sur un type de représentation analytique généralisant la représentation conforme et défininie au moyen de fonctions harmoniques. Bull. Sci. Math. 69(156-165) (1945)
Eck, M., DeRose, T., Duchamp, T., Hoppe, H., Lounsbery, M., Stuetzle, W.: Multiresolution analysis of arbitrary meshes. In: SIGGRAPH 1995: Proceedings of the 22nd Annual Conference on Computer Graphics and Interactive Techniques, pp. 173–182 (1995)
Floater, M.S.: Parametrization and smooth approximation of surface triangulations. Computer Aided Geometric Design 14(231-250) (1997)
Floater, M.S.: Parametric tilings and scattered data approximation. International Journal of Shape Modeling 4, 165–182 (1998)
Floater, M.S.: One-to-one piecewise linear mappings over trinagulations. Math. Comp. 72(685-696) (2003)
Floater, M.S., Hormann, K.: Surface parameterization: a tutorial and survey. In: Advances in Multiresolution for Geometric Modelling (2005)
George, P.-L., Frey, P.: Mesh Generation. Hermes (2000)
Geuzaine, C., Remacle, J.-F.: Gmsh: a three-dimensional finite element mesh generator with built-in pre- and post-processing facilities. International Journal for Numerical Methods in Engineering 79(11), 1309–1331 (2009)
Greiner, G., Hormann, K.: Interpolating and approximating scattered 3d data with hierarchical tensor product splines. In: Surface Fitting and Multiresolution Methods, pp. 163–172 (1996)
Hernandez, V., Roman, J.E., Vidal, V.: Slepc: A scalable and flexible toolkit for the solution of eigenvalue problems. ACM Trans. Math. Soft. 31(3), 351–362 (2005)
Hormann, K., Greiner, G.: Mips: An efficient global. parametrization method. In: Curve and Surface Design, Vanderbilt University Press (2000)
Ito, Y., Nakahashi, K.: Direct surface triangulation using stereolithography data. AIAA Journal 40(3), 490–496 (2002)
Laug, P., Boruchaki, H.: Interpolating and meshing 3d surface grids. International Journal for Numerical Methods in Engineering 58, 209–225 (2003)
Lehoucq, R.B., Sorensen, D.C., Yang, C.: ARPACK Users Guide: Solution of Large Scale Eigenvalue Problems by Implicitly Restarted Arnoldi Methods. Society for Industrial and Applied Mathematics (1997)
Lévy, B., Petitjean, S., Ray, N., Maillot, J.: Least squares conformal maps for automatic texture atlas generation. In: Computer Graphics (Proceedings of SIGGRAPH 2002), pp. 362–371 (2002)
Spagnuolo, M., Attene, M., Falcidieno, B., Wyvill, G.: A mapping-independent primitive for the triangulation of parametric surfaces. Graphical Models 65(260-273) (2003)
Maillot, J., Yahia, H., Verroust, A.: Interactive texture mapping. In: Proceedings of ACM SIGGRAPH 1993, pp. 27–34 (1993)
Marchandise, E., Carton de Wiart, C., Vos, W.G., Geuzaine, C., Remacle, J.-F.: High quality surface remeshing using harmonic maps. Part II: Surfaces with high genus and of large aspect ratio. International Journal for Numerical Methods in Engineering 86(11), 1303–1321 (2011)
Marchandise, E., Compère, G., Willemet, M., Bricteux, G., Geuzaine, C., Remacle, J.-F.: Quality meshing based on stl triangulations for biomedical simulations. International Journal for Numerical Methods in Biomedical Engineering 83, 876–889 (2010)
Marcum, D.L.: Efficient generation of high-quality unstructured surface and volume grids. Engrg. Comput. 17, 211–233 (2001)
Marcum, D.L., Gaither, A.: Unstructured surface grid generation using global mapping and physical space approximation. In: Proceedings, 8th International Meshing Roundtable, pp. 397–406 (1999)
Mullen, P., Tong, Y., Alliez, P., Desbrun, M.: Spectral conformal parameterization. In: In ACM/EG Symposium of Geometry Processing (2008)
Rado, T.: Aufgabe 41. Math-Verien, p. 49 (1926)
Rebay, S.: Efficient unstructured mesh generation by means of delaunay triangulation and bowyer-watson algorithm. Journal of Computational Physics 106, 25–138 (1993)
Remacle, J.-F., Henrotte, F., Carrier-Baudouin, T., Bechet, E., Marchandise, E., Geuzaine, C., Mouton, T.: A frontal delaunay quad mesh generator using the l ∞ norm. International Journal for Numerical Methods in Engineering (2011)
Remacle, J.-F., Lambrechts, J., Seny, B., Marchandise, E., Johnen, A., Geuzaine, C.: Blossom-quad: a non-uniform quadrilateral mesh generator using a minimum cost perfect matching algorithm. International Journal for Numerical Methods in Engineering (submitted 2011)
Sheffer, A., Praun, E., Rose, K.: Mesh parameterization methods and their applications. Found. Trends. Comput. Graph. Vis. 2(2), 105–171 (2006)
Sheffer, A., Lévy, B., Lorraine, I., Mogilnitsky, M., Bogomyakov, E.: Abf++: fast and robust angle based flattening. ACM Transactions on Graphics 24(311-330) (2005)
Szczerba, D., McGregor, R.H.P., Székely, G.: High quality surface mesh generation for multi-physics bio-medical simulations. In: Shi, Y., van Albada, G.D., Dongarra, J., Sloot, P.M.A. (eds.) ICCS 2007. LNCS, vol. 4487, pp. 906–913. Springer, Heidelberg (2007)
Tristano, J.R., Owen, S.J., Canann, S.A.: Advancing front surface mesh generation in parametric space using riemannian surface definition. In: Proceedings of 7th International Meshing Roundtable, Sandia National Laboratory, pp. 429–455 (1998)
Tutte, W.T.: How to draw a graph. In: Proceedings of the London Mathematical Society, vol. 13, pp. 743–768 (1963)
Wang, D., Hassan, O., Morgan, K., Weatheril, N.: Enhanced remeshing from stl files with applications to surface grid generation. Commun. Numer. Meth. Engng 23, 227–239 (2007)
Zayer, R., Lévy, B., Seidel, H.-P.: Linear angle based parameterization. In: ACM/EG Symposium on Geometry Processing Conference Proceedings (2007)
Zheng, Y., Weatherill, N.P., Hassan, O.: Topology abstraction of surface models for three-dimensional grid generation. Engrg. Comput. 17(28-38) (2001)
Zigelman, G., Kimmel, R., Kiryati, N.: Texture mapping using surface flattening via multi-dimensional scaling. IEEE Trans. on Visualisation and Computer Graphics 8(198-207) (2002)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Marchandise, E., Remacle, JF., Geuzaine, C. (2011). Quality Surface Meshing Using Discrete Parametrizations. In: Quadros, W.R. (eds) Proceedings of the 20th International Meshing Roundtable. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24734-7_2
Download citation
DOI: https://doi.org/10.1007/978-3-642-24734-7_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-24733-0
Online ISBN: 978-3-642-24734-7
eBook Packages: EngineeringEngineering (R0)