A weak definition of Delaunay triangulation
<|reference_start|>A weak definition of Delaunay triangulation: 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 approximating a point-cloud data set with a simplical complex.<|reference_end|>
@article{de silva2003a,
    title={A weak definition of Delaunay triangulation},
    author={Vin de Silva},
    journal={arXiv preprint arXiv:cs/0310031},
    year={2003},
    archivePrefix={arXiv},
    eprint={cs/0310031},
    primaryClass={cs.CG}
}