Quality mesh generation in three dimensions
SCG '92 Proceedings of the eighth 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
Guaranteed-quality Delaunay meshing in 3D (short version)
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Tetrahedral mesh generation by Delaunay refinement
Proceedings of the fourteenth annual symposium on Computational geometry
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
Smoothing and cleaning up slivers
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Sliver-free three dimensional delaunay mesh generation
Sliver-free three dimensional delaunay mesh generation
Dense point sets have sparse Delaunay triangulations: or "…but not too nasty"
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Quality meshing with weighted Delaunay refinement
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Graded conforming Delaunay tetrahedralization with bounded radius-edge ratio
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Generating well-shaped d-dimensional Delaunay meshes
Theoretical Computer Science - Computing and combinatorics
Local polyhedra and geometric graphs
Proceedings of the nineteenth annual symposium on Computational geometry
A fast solver for the Stokes equations with distributed forces in complex geometries
Journal of Computational Physics
Quality meshing for polyhedra with small angles
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Star splaying: an algorithm for repairing delaunay triangulations and convex hulls
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Local polyhedra and geometric graphs
Computational Geometry: Theory and Applications - Special issue on the 19th annual symposium on computational geometry - SoCG 2003
Sliver removal by lattice refinement
Proceedings of the twenty-second annual symposium on Computational geometry
On the sizes of Delaunay meshes
Computational Geometry: Theory and Applications
A generic software design for Delaunay refinement meshing
Computational Geometry: Theory and Applications
Sparse parallel Delaunay mesh refinement
Proceedings of the nineteenth annual ACM symposium on Parallel algorithms and architectures
Isosurface stuffing: fast tetrahedral meshes with good dihedral angles
ACM SIGGRAPH 2007 papers
Sampling and Reconstruction of Surfaces and Higher Dimensional Manifolds
Journal of Mathematical Imaging and Vision
Locally uniform anisotropic meshing
Proceedings of the twenty-fourth annual symposium on Computational geometry
On the sizes of Delaunay meshes
Computational Geometry: Theory and Applications
Local polyhedra and geometric graphs
Computational Geometry: Theory and Applications - Special issue on the 19th annual symposium on computational geometry - SoCG 2003
A template for developing next generation parallel Delaunay refinement methods
Finite Elements in Analysis and Design
Geometric sampling of manifolds for image representation and processing
SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
Dynamic well-spaced point sets
Proceedings of the twenty-sixth annual symposium on Computational geometry
Tetrahedral image-to-mesh conversion for biomedical applications
Proceedings of the 2nd ACM Conference on Bioinformatics, Computational Biology and Biomedicine
Multitissue Tetrahedral Image-to-mesh Conversion with Guaranteed Quality and Fidelity
SIAM Journal on Scientific Computing
Dynamic well-spaced point sets
Computational Geometry: Theory and Applications
Guaranteed quality tetrahedral Delaunay meshing for medical images
Computational Geometry: Theory and Applications
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A triangular mesh in 3D is a decomposition of a given geometric domain into tetrahedra. The mesh is well-shaped if the aspect ratio of every of its tetrahedra is bounded from above by a constant. It is Delaunay if the interior of the circum-sphere of each of its tetrahedra does not contain any other mesh vertices. Generating a well-shaped Delaunay mesh for any 3D domain has been a long term outstanding problem. In this paper, we present an efficient 3D Delaunay meshing algorithm that mathematically guarantees the well-shape quality of the mesh, if the domain does not have acute angles. The main ingredient of our algorithm is a novel refinement technique which systematically forbids the formation of shivers, a family of bad elements that none of the previous known algorithms can cleanly remove, especially near the domain boundary — needless to say, that our algorithm ensure that there is no sliver near the boundary of the domain.