An improved algorithm for constructing kth-order voronoi diagrams
IEEE Transactions on Computers
Epsilon geometry: building robust algorithms from imprecise computations
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
Simulation of simplicity: a technique to cope with degenerate cases in geometric algorithms
ACM Transactions on Graphics (TOG)
Higher-dimensional Voronoi diagrams in linear expected time
Discrete & Computational Geometry
Voronoi diagrams—a survey of a fundamental geometric data structure
ACM Computing Surveys (CSUR)
Spatial tessellations: concepts and applications of Voronoi diagrams
Spatial tessellations: concepts and applications of Voronoi diagrams
The quickhull algorithm for convex hulls
ACM Transactions on Mathematical Software (TOMS)
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
A complete roundness classification procedure
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Algorithmic geometry
Computing roundness is easy if the set is almost round
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
Approximation and exact algorithms for minimum-width annuli and shells
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
Efficient approximation and optimization algorithms for computational metrology
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Structural tolerance and delauny triangulation
Information Processing Letters
Digital Principles and Applications
Digital Principles and Applications
Higher order Delaunay triangulations
Computational Geometry: Theory and Applications
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
An empirical comparison of techniques for updating Delaunay triangulations
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Almost-Delaunay simplices: Robust neighbor relations for imprecise 3D points using CGAL
Computational Geometry: Theory and Applications
Delaunay triangulations of imprecise pointsin linear time after preprocessing
Proceedings of the twenty-fourth annual symposium on Computational geometry
Approximating largest convex hulls for imprecise points
Journal of Discrete Algorithms
Delaunay Triangulation of Imprecise Points Simplified and Extended
WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
Delaunay triangulation of imprecise points in linear time after preprocessing
Computational Geometry: Theory and Applications
Graph classification based on pattern co-occurrence
Proceedings of the 18th ACM conference on Information and knowledge management
Computational Biology and Chemistry
Approximating largest convex hulls for imprecise points
WAOA'07 Proceedings of the 5th international conference on Approximation and online algorithms
IEEE Transactions on Information Technology in Biomedicine
Preprocessing Imprecise Points and Splitting Triangulations
SIAM Journal on Computing
The Geometric Stability of Voronoi Diagrams with Respect to Small Changes of the Sites
Proceedings of the twenty-seventh annual symposium on Computational geometry
Geometric computations on indecisive points
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Largest and smallest tours and convex hulls for imprecise points
SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
BALLAST: a ball-based algorithm for structural motifs
RECOMB'12 Proceedings of the 16th Annual international conference on Research in Computational Molecular Biology
Stability of Delaunay-type structures for manifolds: [extended abstract]
Proceedings of the twenty-eighth annual symposium on Computational geometry
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
Range counting coresets for uncertain data
Proceedings of the twenty-ninth annual symposium on Computational geometry
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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.