Computational geometry: an introduction
Computational geometry: an introduction
Global convergence and empirical consistency of the generalized Lloyd algorithm
IEEE Transactions on Information Theory
Voronoi diagrams—a survey of a fundamental geometric data structure
ACM Computing Surveys (CSUR)
Fitting a set of points by a circle
SCG '97 Proceedings of the thirteenth 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
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
Checking the convexity of polytopes and the planarity of subdivision
WADS '97 Selected papers presented at the international workshop on Algorithms and data structure
Optimal point placement for mesh smoothing
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Triangle: Engineering a 2D Quality Mesh Generator and Delaunay Triangulator
FCRC '96/WACG '96 Selected papers from the Workshop on Applied Computational Geormetry, Towards Geometric Engineering
SMI '03 Proceedings of the Shape Modeling International 2003
An empirical comparison of techniques for updating Delaunay triangulations
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Expected time analysis for Delaunay point location
Computational Geometry: Theory and Applications
Star splaying: an algorithm for repairing delaunay triangulations and convex hulls
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Variational tetrahedral meshing
ACM SIGGRAPH 2005 Papers
Convergence of the Lloyd Algorithm for Computing Centroidal Voronoi Tessellations
SIAM Journal on Numerical Analysis
Geometry and Topology for Mesh Generation (Cambridge Monographs on Applied and Computational Mathematics)
Recent progress in robust and quality Delaunay mesh generation
Journal of Computational and Applied Mathematics - Special issue: The international symposium on computing and information (ISCI2004)
The Effectiveness of Lloyd-Type Methods for the k-Means Problem
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
k-means++: the advantages of careful seeding
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Kinetic data structures in practice
Kinetic data structures in practice
Dynamic Delaunay tetrahedralisation of a deforming surface
The Visual Computer: International Journal of Computer Graphics
Generic Remeshing of 3D Triangular Meshes with Metric-Dependent Discrete Voronoi Diagrams
IEEE Transactions on Visualization and Computer Graphics
SFCS '75 Proceedings of the 16th Annual Symposium on Foundations of Computer Science
Computational Geometry: Theory and Applications
Kinetic convex hulls and delaunay triangulations in the black-box model
Proceedings of the twenty-seventh annual symposium on Computational geometry
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Updating a Delaunay triangulation when its vertices move is a bottleneck in several domains of application. Rebuilding the whole triangulation from scratch is surprisingly a very viable option compared to relocating the vertices. This can be explained by several recent advances in efficient construction of Delaunay triangulations. However, when all points move with a small magnitude, or when only a fraction of the vertices move, rebuilding is no longer the best option. This paper considers the problem of efficiently updating a Delaunay triangulation when its vertices are moving under small perturbations. The main contribution is a set of filters based upon the concept of vertex tolerances. Experiments show that filtering relocations is faster than rebuilding the whole triangulation from scratch under certain conditions.