Summary
This work presents an adaptive mesh generation strategy for parametric surfaces. The proposed strategy is controlled by curvatures and the error measured between the analytical and discrete curvatures guides the adaptive process. The analytical curvature is a mathematical representation that models the domain, whereas the discrete curvature is an approximation of that curvature and depends directly on the used mesh. The proposed strategy presents the following aspects: it is able to refine and coarsen regions of the mesh; it considers the local error measures to ensure good global quality; it ensures good transition of the mesh and it deals with any type of parametric surfaces since it works in the parametric space.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Cheng, S.-W., Dey, T.K., Ramos, E.A., Ray, T.: Sampling and Meshing a Surface with Guaranteed Topology and Geometry. In: Proceedings of the Twentieth Annual Symposium on Computational Geometry, pp. 280–289 (2004)
Boissonnat, J.-D., Oudot, S.: Provably good sampling and meshing of surfaces. Graph. Models 67(5), 405–451 (2005)
Kim, S.J., Jeong, W.K., Kim, C.H.: LOD Generation with Discrete Curvature Error Metric. In: Proceedings of Korea Israel Bi-National Conference, pp. 97–104 (1999)
Meek, D., Walton, D.: On surface normal and Gaussian curvature approximations given data sampled from a smooth surface. Computer Aided Geometric Design 17, 521–543 (2000)
Meyer, M., Desbrun, M., Schröder, P., Barr, A.H.: Discrete Differential-Geometry Operators for Triangulated 2-Manifolds. Visual and Mathematics III, 35–57 (2002)
Xu, G.: Convergence Analysis of a Discretization Scheme for Gaussian Curvature over Triangular Surfaces. Computer Aided Geometric Design 23(2), 193–207 (2006)
Magid, E., Soldea, O., Rivlin, E.: A Comparison of Gaussian and Mean Curvature Estimation Methods on Triangular Meshes of Range Image Data. Computer Vision and Image Understanding 107(3), 139–159 (2007)
Lo, S.H., Lau, T.S.: Finite Element Mesh Generation over Analytical Curved Surfaces. Computers and Structures 59(2), 301–309 (1996)
Lo, S.H., Lau, T.S.: Mesh Generation over Curved Surfaces with Explicit Control on Discretization Error. Engineering Computations 15(3), 357–373 (1998)
Seibold, W., Wyvill, G.: Towards an Understanding of Surfaces through Polygonization. In: Computer Graphics International Conference, p. 416 (1998)
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(1-2), 233–259 (2000)
Tristano, J.R., Owen, S.J., Canann, S.A.: Advancing front surface mesh generation in parametric space using a Riemannian surface definition. In: Proceedings of 7th International Meshing Roundtable, Sandia National Laboratories, pp. 429–445 (1998)
Dyn, N., Hormann, K., Kim, S.J., Levin, D.: Optimizing 3D triangulations using discrete curvature analysis. Mathematical Methods for Curves and Surfaces, pp. 135–146 (2000)
Miranda, A.C.O., Martha, L.F.: Mesh Generation on High-Curvature Surfaces Based on a Background Quadtree Structure. In: Proceedings of 11th International Meshing Roundtable, Sandia National Laboratories, pp. 333–342 (2002)
Miranda, A.C.O., Martha, L.F., Wawrzynek, P.A., Ingraffea, A.R.: Surface mesh regeneration considering curvatures. Engineering with Computers 25(2), 207–219 (2009)
Wang, D., Clark, B., Jiao, X.: An analysis and comparison of parameterization-based computation of differential quantities for discrete surfaces. Computer Aided Geometric Design 26(5), 510–527 (2009)
Borrelli, V., Orgereta, F.: Error Term in Pointwise Approximation of the Curvature Term of a Curve. Computer Aided Geometric Design 27(7), 538–550 (2010)
Rogers, D.F., Adams, J.A.: Mathematical elements for computer graphics, 2nd edn., pp. 420–421. McGraw-Hill Science/Engineering/Math (1990)
Wittchen, S., Baehmann, P., Shephard, M.: Robust geometrically based, automatic two-dimensional mesh generation. International Journal for Numerical Methods in Engineering 24, 1043–1078 (1987)
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
de Siqueira, D.M.B., Freitas, M.O., Cavalcante-Neto, J.B., Vidal, C.A., da Silva, R.J. (2014). An Adaptive Parametric Surface Mesh Generation Method Guided by Curvatures. 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_24
Download citation
DOI: https://doi.org/10.1007/978-3-319-02335-9_24
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-02334-2
Online ISBN: 978-3-319-02335-9
eBook Packages: EngineeringEngineering (R0)