Almost-Delaunay simplices: nearest neighbor relations for imprecise points

Delaunay tessellations and Voronoi diagrams capture proximity relationships among sets of points in any dimension. When point coordinates are not known exactly, as in the case of 3D points representing protein atom coordinates, the Delaunay tessellation may not be robust; small perturbations in the coordinates may cause the Delaunay simplices to change. In this paper, we define the almost-Delaunay simplices, derive some of their properties, and give algorithms for computing them, especially for neighbor analysis in three dimensions. We sketch applications in proteins that will be described more fully in a companion paper in biology. http://www.cs.unc.edu/debug/papers/AlmDel.

• Type: Conference
• Year: 2004
• Where: SODA
• Authors: Deepak Bandyopadhyay, Jack Snoeyink
• Keywords: Algorithms, Delaunay Tessellation, Points Representing Protein, SODA 2004, Voronoi Diagrams Capture