Variational tetrahedral meshing
- 1 July 2005
- journal article
- conference paper
- Published by Association for Computing Machinery (ACM) in ACM Transactions on Graphics
- Vol. 24 (3), 617-625
- https://doi.org/10.1145/1073204.1073238
Abstract
In this paper, a novel Delaunay-based variational approach to isotropic tetrahedral meshing is presented. To achieve both robustness and efficiency, we minimize a simple mesh-dependent energy through global updates of both vertex positions distance between an isotropic quadratic function and its linear interpolation on the mesh, our minimization procedure generates well-shaped tetrahedra. Mesh design is controlled through a gradation smoothness parameter and selection of the desired number of vertices. We provide the foundations of our approach by explaining both the underlying variational principle and its geometric interpretation. We demonstrate the quality of the resulting meshes through a series of examples.Keywords
This publication has 22 references indexed in Scilit:
- Provably good sampling and meshing of surfacesGraphical Models, 2005
- Variational shape approximationACM Transactions on Graphics, 2004
- Tetrahedral mesh generation and optimization based on centroidal Voronoi tessellationsInternational Journal for Numerical Methods in Engineering, 2003
- Constrained Centroidal Voronoi Tessellations for SurfacesSIAM Journal on Scientific Computing, 2003
- Delaunay refinement algorithms for triangular mesh generationComputational Geometry, 2002
- Variational Delaunay approach to the generation of tetrahedral finite element meshesInternational Journal for Numerical Methods in Engineering, 2001
- UNSTRUCTURED MESH GENERATION: THEORY, PRACTICE, AND PERSPECTIVESInternational Journal of Computational Geometry & Applications, 2000
- Quality Mesh Generation in Higher DimensionsSIAM Journal on Computing, 2000
- Delaunay mesh generation governed by metric specifications. Part I. AlgorithmsFinite Elements in Analysis and Design, 1997
- Delaunay mesh generation governed by metric specifications Part II. ApplicationsFinite Elements in Analysis and Design, 1997