Manifolds, tensor analysis, and applications: 2nd edition
Manifolds, tensor analysis, and applications: 2nd edition
An O(n2logn) time algorithm for the minmax angle triangulation
SIAM Journal on Scientific and Statistical Computing
Direct discretization of planar div-curl problems
SIAM Journal on Numerical Analysis
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
Linear-size nonobtuse triangulation of polygons
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Journal of Computer and System Sciences - Special issue: 31st IEEE conference on foundations of computer science, Oct. 22–24, 1990
A Delaunay refinement algorithm for quality 2-dimensional mesh generation
SODA '93 Selected papers from the fourth annual ACM SIAM symposium on Discrete algorithms
Geometry and topology for mesh generation
Geometry and topology for mesh generation
Acute triangulations of polygons
European Journal of Combinatorics
Triangle: Engineering a 2D Quality Mesh Generator and Delaunay Triangulator
FCRC '96/WACG '96 Selected papers from the Workshop on Applied Computational Geormetry, Towards Geometric Engineering
Constrained Centroidal Voronoi Tessellations for Surfaces
SIAM Journal on Scientific Computing
Computational Geometry: Theory and Applications
Discrete exterior calculus
Tiling space and slabs with acute tetrahedra
Computational Geometry: Theory and Applications
Anisotropic Centroidal Voronoi Tessellations and Their Applications
SIAM Journal on Scientific Computing
Variational tetrahedral meshing
ACM SIGGRAPH 2005 Papers
Acute Triangulations of Polygons
Discrete & Computational Geometry
Convergence of the Lloyd Algorithm for Computing Centroidal Voronoi Tessellations
SIAM Journal on Numerical Analysis
Mesh shape-quality optimization using the inverse mean-ratio metric
Mathematical Programming: Series A and B
Generating the Voronoi-Delaunay Dual Diagram for Co-Volume Integration Schemes
ISVD '07 Proceedings of the 4th International Symposium on Voronoi Diagrams in Science and Engineering
Nondegeneracy and Weak Global Convergence of the Lloyd Algorithm in $\mathbb{R}^d$
SIAM Journal on Numerical Analysis
On Nonobtuse Simplicial Partitions
SIAM Review
A dihedral acute triangulation of the cube
Computational Geometry: Theory and Applications
HOT: Hodge-optimized triangulations
ACM SIGGRAPH 2011 papers
Computational Geometry: Theory and Applications
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Meshes composed of well-centered simplices have nice orthogonal dual meshes (the dual Voronoi diagram). This is useful for certain numerical algorithms that prefer such primal-dual mesh pairs. We prove that well-centered meshes also have optimality properties and relationships to Delaunay and minmax angle triangulations. We present an iterative algorithm that seeks to transform a given triangulation in two or three dimensions into a well-centered one by minimizing a cost function and moving the interior vertices while keeping the mesh connectivity and boundary vertices fixed. The cost function is a direct result of a new characterization of well-centeredness in arbitrary dimensions that we present. Ours is the first optimization-based heuristic for well-centeredness and the first one that applies in both two and three dimensions. We show the results of applying our algorithm to small and large two-dimensional meshes, some with a complex boundary, and obtain a well-centered tetrahedralization of the cube. We also show numerical evidence that our algorithm preserves gradation and that it improves the maximum and minimum angles of acute triangulations created by the best known previous method.