Almost-Delaunay simplices: Robust neighbor relations for imprecise 3D points using CGAL

Abstract

This paper describes a new computational geometry technique, almost-Delaunay simplices, that was implemented for 3D points using CGAL. Almost-Delaunay simplices capture possible sets of Delaunay neighbors in the presence of a bounded perturbation, and give a framework for nearest neighbor analysis in imprecise point sets such as protein structures. The use of CGAL helps us tune our implementation so that it is reasonably fast and also performs robust computation for all inputs, and also lets us distribute our technique to potential users in a portable, reusable and extensible form. The implementation, available on http://www.cs.unc.edu/~debug/software is faster and more memory efficient than our prototype MATLAB implementation, and enables us to scale our neighbor analysis to large sets of protein structures, each with 100–3000 residues.