Power diagrams: properties, algorithms and applications
SIAM Journal on Computing
Three-dimensional triangulations from local transformations
SIAM Journal on Scientific and Statistical Computing
Incremental topological flipping works for regular triangulations
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
A comparison of sequential Delaunay triangulation algorithms
Proceedings of the eleventh annual symposium on Computational geometry
A practical evaluation of kinetic data structures
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Surface reconstruction by Voronoi filtering
Proceedings of the fourteenth annual symposium on Computational geometry
A condition guaranteeing the existence of higher-dimensional constrained Delaunay triangulations
Proceedings of the fourteenth annual symposium on Computational geometry
Improved incremental randomized Delaunay triangulation
Proceedings of the fourteenth annual symposium on Computational geometry
Kinetic data structures: a state of the art report
WAFR '98 Proceedings of the third workshop on the algorithmic foundations of robotics on Robotics : the algorithmic perspective: the algorithmic perspective
Interval methods for kinetic simulations
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
Data structures for mobile data
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Voronoi diagrams and arrangements
SCG '85 Proceedings of the first annual symposium on Computational geometry
Structural tolerance and delauny triangulation
Information Processing Letters
Collision detection for deforming necklaces
Proceedings of the eighteenth annual symposium on Computational geometry
Dense point sets have sparse Delaunay triangulations: or "…but not too nasty"
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Perturbations and vertex removal in a 3D delaunay triangulation
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Collision Detection Optimization in a Multi-particle System
ICCS '02 Proceedings of the International Conference on Computational Science-Part III
Local polyhedra and geometric graphs
Proceedings of the nineteenth annual symposium on Computational geometry
Complexity of the delaunay triangulation of points on surfaces the smooth case
Proceedings of the nineteenth annual symposium on Computational geometry
Incremental constructions con BRIO
Proceedings of the nineteenth annual symposium on Computational geometry
Nonconvex rigid bodies with stacking
ACM SIGGRAPH 2003 Papers
Almost-Delaunay simplices: nearest neighbor relations for imprecise points
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Star splaying: an algorithm for repairing delaunay triangulations and convex hulls
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Kinetic 3D convex hulls via self-adjusting computation
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
A package for exact kinetic data structures and sweepline algorithms
Computational Geometry: Theory and Applications
Out-of-order event processing in kinetic data structures
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Kinetic algorithms via self-adjusting computation
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Robust Kinetic Convex Hulls in 3D
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
An experimental analysis of self-adjusting computation
ACM Transactions on Programming Languages and Systems (TOPLAS)
Filtering relocations on a Delaunay triangulation
SGP '09 Proceedings of the Symposium on Geometry Processing
Self-adjusting computation with Delta ML
AFP'08 Proceedings of the 6th international conference on Advanced functional programming
ACMOS'06 Proceedings of the 8th WSEAS international conference on Automatic control, modeling & simulation
A GPU accelerated algorithm for 3D Delaunay triangulation
Proceedings of the 18th meeting of the ACM SIGGRAPH Symposium on Interactive 3D Graphics and Games
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The computation of Delaunay triangulations from static point sets has been extensively studied in computational geometry. When the points move with known trajectories, kinetic data structures can be used to maintain the triangulation. However, there has been little work so far on how to maintain the triangulation when the points move without explicit motion plans, as in the case of a physical simulation. In this paper we examine how to update Delaunay triangulations after small displacements of the defining points, as might be provided by a physics-based integrator. We have implemented a variety of update algorithms, many new, toward this purpose. We ran these algorithms on a corpus of data sets to provide running time comparisons and determined that updating Delaunay can be significantly faster than recomputing.