A weak definition of Delaunay triangulation

@article{Silva2003AWD,
  title={A weak definition of Delaunay triangulation},
  author={Vin de Silva},
  journal={CoRR},
  year={2003},
  volume={cs.CG/0310031}
}
We show that the traditional criterion for a simplex to belong to the Delaunay triangulation of a point set is equivalent to a criterion which is a priori weaker. The argument is quite general; as well as the classical Euclidean case, it applies to hyperbolic and hemispherical geometries and to Edelsbrunner's weighted Delaunay triangulation. In spherical geometry, we establish a similar theorem under a genericity condition. The weak definition finds natural application in the problem of… CONTINUE READING

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E-mail: silva@math.stanford

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