Voronoi diagrams and arrangements
Discrete & Computational Geometry
Power diagrams: properties, algorithms and applications
SIAM Journal on Computing
Simulation of simplicity: a technique to cope with degenerate cases in geometric algorithms
ACM Transactions on Graphics (TOG)
A geometric consistency theorem for a symbolic perturbation scheme
Journal of Computer and System Sciences
Realizability of Delaunay triangulations
Information Processing Letters
Algorithmic geometry
Journal of the ACM (JACM)
Detecting undersampling in surface reconstruction
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Perturbations and vertex removal in a 3D delaunay triangulation
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Quality Meshing with Weighted Delaunay Refinement
SIAM Journal on Computing
Sliver-free perturbation for the Delaunay tetrahedrization
Computer-Aided Design
Hyperbolic delaunay complexes and voronoi diagrams made practical
Proceedings of the twenty-ninth annual symposium on Computational geometry
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The Delaunay triangulation and the weighted Delaunay triangulation are not uniquely defined when the input set is degenerate. We present a new symbolic perturbation that allows to always define these triangulations in a unique way, as soon as the points are not all coplanar. No flat tetrahedron exists in the defined triangulation. The perturbation scheme is easy to code. It is implemented in cgal, and guarantees that both vertex insertion and vertex removal are fully robust.