Computational geometry: an introduction
Computational geometry: an introduction
Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
Triangulating a non-convex polytype
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
Separators in two and three dimensions
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
A unified geometric approach to graph separators
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
SODA '91 Proceedings of the second annual ACM-SIAM symposium on Discrete algorithms
Triangulating polygons without large angles
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
Guaranteed-quality mesh generation for curved surfaces
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Computational geometry: a retrospective
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
The cost of balancing generalized quadtrees
SMA '95 Proceedings of the third ACM symposium on Solid modeling and applications
Large mesh generation from boundary models with parametric face representation
SMA '95 Proceedings of the third ACM symposium on Solid modeling and applications
Strategies for polyhedral surface decomposition: an experimental study
Proceedings of the eleventh annual symposium on Computational geometry
A Delaunay based numerical method for three dimensions: generation, formulation, and partition
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
An aspect ratio bound for triangulating a d-grid cut by a hyperplane (extended abstract)
Proceedings of the twelfth annual symposium on Computational geometry
Guaranteed-quality Delaunay meshing in 3D (short version)
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Skeleton-based modeling operations on solids
SMA '97 Proceedings of the fourth ACM symposium on Solid modeling and applications
Tetrahedral mesh generation by Delaunay refinement
Proceedings of the fourteenth annual symposium on Computational geometry
PELLPACK: a problem-solving environment for PDE-based applications on multicomputer platforms
ACM Transactions on Mathematical Software (TOMS)
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
A new and simple algorithm for quality 2-dimensional mesh generation
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
Dihedral bounds for mesh generation in high dimensions
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Optimal good-aspect-ratio coarsening for unstructured meshes
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Approximate minimum weight Steiner triangulation in three dimensions
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Journal of the ACM (JACM)
Generating well-shaped Delaunay meshed in 3D
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Static and kinetic geometric spanners with applications
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Multilevel Mesh Partitioning for Optimizing Domain Shape
International Journal of High Performance Computing Applications
Scalable Parallel Octree Meshing for TeraScale Applications
SC '05 Proceedings of the 2005 ACM/IEEE conference on Supercomputing
Sparse parallel Delaunay mesh refinement
Proceedings of the nineteenth annual ACM symposium on Parallel algorithms and architectures
Atomic volumes for mesh completion
SGP '05 Proceedings of the third Eurographics symposium on Geometry processing
Computer Methods and Programs in Biomedicine
Quadrilateral meshes with bounded minimum angle
Proceedings of the twenty-fifth annual symposium on Computational geometry
Balancing flexibility and performance in three dimensional meshing tools
Advances in Engineering Software
Size competitive meshing without large angles
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
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We show how to triangulate a three dimensional polyhedral region with holes. Our triangulation is optimal in the following two senses. First, our triangulation achieves the best possible aspect ratio up to a constant. Second, for any other triangulation of the same region into m triangles with bounded aspect ratio, our triangulation has size n = O(m). Such a triangulation is desired as an initial mesh for a finite element mesh refinement algorithm. Previous three dimensional triangulation schemes either worked only on a restricted class of input, or did not guarantee well-shaped tetrahedra, or were not able to bound the output size. We build on some of the ideas presented in previous work by Bern, Eppstein, and Gilbert, who have shown how to triangulate a two dimensional polyhedral region with holes, with similar quality and optimality bounds.