Preparation of Control Space for Remeshing of Polygonal Surfaces
DOI:
https://doi.org/10.7494/csci.2013.14.4.547Keywords:
remeshing, anisotropic metric, control space, mesh adaptation, polygonal meshAbstract
The subject of the article concerns the issues of remeshing, transforminga polygonal mesh into a triangular mesh adapted to surface. From the initial
polygonal mesh the curvature of surface and boundary is retrieved and used to calculate
a metric tensor varying in three-dimensional space.
In the proposed approach the curvature is computed using local approximation of
surfaces and curves on the basis of vertices of the polygonal mesh.
An essential part of the presented remeshing procedure is creation of a control
space structure based on the retrieved discrete data.
The subsequent process of remeshing is then supervised by the contents of this
auxiliary structure.
The article presents various aspects related to the procedure of initialization, creation and adjusting the control space structure.
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References
Alauzet F. and Frey P.: Estimateur d'erreur geometrique et metriques anisotropes pour l'adaptation de maillage. Partie I: aspects theoriques. Tech. Rep. RR-4759, INRIA Rocquencour, 2003.
Alliez P., Ucelli G., Gotsman C., and Attene M.: Recent advances in remeshing of surfaces. In: L. Floriani and M. Spagnuolo, eds., Shape Analysis and Structuring, Mathematics and Visualization. Springer, 2008.
Amenta N.: Surface Reconstruction. In: M. Gross and H. Pfister, eds., Point-Based Graphics. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA, 2007. ISBN 0123706041, 9780080548821.
Amenta N., Choi S., and Kolluri R.K.: The Power Crust, Unions of Balls, and the Medial Axis Transform. Computational Geometry: Theory and Applications, vol. 19, pp. 127--153, 2000.
Botsch M., Kobbelt L., Pauly M., Alliez P., and Levy B.: Polygon Mesh Processing. AK Peters / CRC Press, 2010. ISBN 9781568814261.
Bottasso C.: Anisotropic Mesh Adaptation by Metric-Driven Optimization. Int. J. Numer. Meth. Engng., vol. 60, pp. 597--639, 2004.
Dey T.K.: Curve and Surface Reconstruction: Algorithms with Mathematical Analysis (Cambridge Monographs on Applied and Computational Mathematics). Cambridge University Press, New York, NY, USA, 2006. ISBN 0521863708.
Frey P.: About surface remeshing. In: Proc. 9th Int. Meshing Roundtable, pp. 123--136. Sandia National Laboratories, New Orleans, CA, 2000.
Frey P.: Anisotropic Metrics for Mesh Adaptation. In: Proc. ECCOMAS 2004. Jyvaskyla, Finland, 24-28 July 2004.
Głut B. and Jurczyk T.: Denition and Interpolation of Discrete Metric for Mesh Generation on 3D Surfaces. Computer Science, Annual of University of Science and Technology, vol. 7, pp. 89--103, 2005.
Głut B. and Jurczyk T.: Preparation of the Sizing Field for Volume Mesh Generation. In: Proc. 13th Int. Conf. on Civil, Structural and Environmental Engineering Computing. Chania, Crete, Greece, 2011. Paper 115.
Głut B., Jurczyk T., and Kitowski J.: Anisotropic Volume Mesh Generation Controlled by Adaptive Metric Space. In: Proc. of Int. Conf. NUMIFORM'07, pp. 233--238. Porto, Portugal, 2007.
Hormann K., Polthier K., and Sheer A.: Mesh Parameterization: Theory and Practice. In: SIGGRAPH Asia 2008 Course Notes, 11, pp. v+81. ACM Press, Singapore, 2008.
Jurczyk T. and G lut B.: Metric 3D Surface Mesh Generation Using Coordinate Transformation Method. In: Proc. of Int. Conf. on Computer Methods and Systems CMS'05, vol. 1, pp. 395--405. Krakow, Poland, 2005.
Jurczyk T. and G lut B.: Adaptive Control Space Structure for Anisotropic Mesh Generation. In: Proc. of ECCOMAS CFD 2006 European Conference on Computational Fluid Dynamics. Egmond aan Zee, The Netherlands, 2006.
Jurczyk T. and G lut B.: The Insertion of Metric Sources for Three-dimensional Mesh Generation. In: Proc. 13th Int. Conf. on Civil, Structural and Environmental Engineering Computing. Chania, Crete, Greece, 2011. Paper 116.
Labbe P., Dompierre J., Vallet M.G., Guibault F., and Trepanier J.Y.: A universal measure of the conformity of a mesh with respect to an anisotropic metric field. Int. J. Numer. Meth. Engng, vol. 61, pp. 2675--2695, 2004.
Miranda A.C.O., Martha L.F., Wawrzynek P.A., and Ingraea A.R.: Surface mesh regeneration considering curvatures. Eng. Comput. (Lond.), vol. 25(2), pp. 207--219, 2009.
Morigi S.: Feature-sensitive parameterization of polygonal meshes. Applied Mathematics and Computation, pp. 1561--1572, 2009.
Rassineux A., Villon P., Savignat J.M., and Stab O.: Surface remeshing by local hermite diffuse interpolation. Int. J. Numer. Meth. Engng, vol. 49(1-2), pp. 31--49, 2000. ISSN 1097-0207.
Surazhsky V., Alliez P., and Gotsman C.: Isotropic Remeshing of Surfaces: A Local Parameterization Approach. In: Proc. 12th Int. Meshing Roundtable, pp. 215--224. Sandia National Laboratories, Santa Fe, New Mexico, USA, 2003.
Zhu J., Blacker T., and Smith R.: Background Overlay Grid Size Functions. In: Proc. 11th Int. Meshing Roundtable, pp. 65--74. Sandia National Laboratories, Ithaca, NY, 2002.