The quickhull algorithm for convex hulls
ACM Transactions on Mathematical Software (TOMS)
Robust adaptive floating-point geometric predicates
Proceedings of the twelfth annual symposium on Computational geometry
Interval arithmetic yields efficient dynamic filters for computational geometry
Proceedings of the fourteenth annual symposium on Computational geometry
Generic programming and the STL: using and extending the C++ Standard Template Library
Generic programming and the STL: using and extending the C++ Standard Template Library
The C++ standard library: a tutorial and reference
The C++ standard library: a tutorial and reference
Modern C++ design: generic programming and design patterns applied
Modern C++ design: generic programming and design patterns applied
Effective STL: 50 specific ways to improve your use of the standard template library
Effective STL: 50 specific ways to improve your use of the standard template library
C++ Templates
The CGAL Kernel: A Basis for Geometric Computation
FCRC '96/WACG '96 Selected papers from the Workshop on Applied Computational Geormetry, Towards Geometric Engineering
Geometric transforms for fast geometric algorithms
Geometric transforms for fast geometric algorithms
Mining protein family specific residue packing patterns from protein structure graphs
RECOMB '04 Proceedings of the eighth annual international conference on Resaerch in computational molecular biology
Almost-Delaunay simplices: nearest neighbor relations for imprecise points
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
A geometric framework for robust nearest neighbor analysis of protein structure and function
A geometric framework for robust nearest neighbor analysis of protein structure and function
Computational Geometry: Theory and Applications
Delaunay triangulations of imprecise pointsin linear time after preprocessing
Proceedings of the twenty-fourth annual symposium on Computational geometry
Triangulating input-constrained planar point sets
Information Processing Letters
Delaunay triangulation of imprecise points in linear time after preprocessing
Computational Geometry: Theory and Applications
An algorithm for triangulating multiple 3D polygons
SGP '13 Proceedings of the Eleventh Eurographics/ACMSIGGRAPH Symposium on Geometry Processing
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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.