An efficient implementation of Delaunay triangulations in medium dimensions
نویسندگان
چکیده
We propose a new C++ implementation of the well-known incremental algorithm for the construction of Delaunay triangulations in any dimension. Our implementation follows the exact computing paradigm and is fully robust. Extensive comparisons have shown that our implementation outperforms the best currently available codes for convex hulls and Delaunay triangulations, and that it can be used for quite big input sets in spaces of dimensions up to 6. Key-words: geometry, triangulation, Delaunay, implementation, C++ in ria -0 03 43 18 8, v er si on 1 30 N ov 2 00 8 Une implémentation efficace de la triangulation de Delaunay en dimensions moyennes Résumé : Nous prśentons une nouvelle impléntation en C++ de l’algorithme incrémental randomisé de construction de la triangulation de Delaunay dans n’importe quelle dimension. Notre implémentatation utilise des calculs numériques exacts, et est ainsi robuste. Nous effectuons de nombreuses comparaisons qui montrent que notre programme se comporte bien ieux que les programmes existant pour le calcul d’enveloppe convexe ou de triangulation de Delaunay. Nous montrons que notre programme peut-être utilisé pour un grand nombre de points d’entrée dans en dimension jusqu’à 6. Mots-clés : géométrie, triangulation, Delaunay, implémentation, C++ in ria -0 03 43 18 8, v er si on 1 30 N ov 2 00 8 An efficient implementation of Delaunay triangulations in medium dimensions 3
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