Delaunay triangulations and Voronoi diagrams for Riemannian manifolds
Proceedings of the sixteenth annual symposium on Computational geometry
Anisotropic voronoi diagrams and guaranteed-quality anisotropic mesh generation
Proceedings of the nineteenth annual symposium on Computational geometry
Almost-Delaunay simplices: nearest neighbor relations for imprecise points
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Shape Dimension and Intrinsic Metric from Samples of Manifolds
Discrete & Computational Geometry
Manifold reconstruction from point samples
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Controlled perturbation for Delaunay triangulations
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Finding the Homology of Submanifolds with High Confidence from Random Samples
Discrete & Computational Geometry
Kinetic stable Delaunay graphs
Proceedings of the twenty-sixth annual symposium on Computational geometry
Particle-based anisotropic surface meshing
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
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We introduce a parametrized notion of genericity for Delaunay triangulations which, in particular, implies that the Delaunay simplices of δ-generic point sets are thick. Equipped with this notion, we study the stability of Delaunay triangulations under perturbations of the metric and of the vertex positions. We then show that, for any sufficiently regular submanifold of Euclidean space, and appropriate ε and δ, any sample set which meets a localized δ-generic ε-dense sampling criteria yields a manifold intrinsic Delaunay complex which is equal to the restricted Delaunay complex.