Computational geometry: an introduction
Computational geometry: an introduction
Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
Construction of three-dimensional Delaunay triangulations using local transformations
Computer Aided Geometric Design
Voronoi diagrams—a survey of a fundamental geometric data structure
ACM Computing Surveys (CSUR)
Randomized multidimensional search trees: lazy balancing and dynamic shuffling (extended abstract)
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Spatial tessellations: concepts and applications of Voronoi diagrams
Spatial tessellations: concepts and applications of Voronoi diagrams
Incremental topological flipping works for regular triangulations
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
On the randomized construction of the Delaunay tree
Theoretical Computer Science
Four results on randomized incremental constructions
Computational Geometry: Theory and Applications
Implementation of a randomized algorithm for Delaunay and regular triangulations in three dimensions
Computer Aided Geometric Design
Enumeration of regular triangulations
Proceedings of the twelfth annual symposium on Computational geometry
Improved incremental randomized Delaunay triangulation
Proceedings of the fourteenth annual symposium on Computational geometry
Primitives for the manipulation of general subdivisions and the computation of Voronoi
ACM Transactions on Graphics (TOG)
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
On deletion in Delaunay triangulations
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
ACMOS'06 Proceedings of the 8th WSEAS international conference on Automatic control, modeling & simulation
Gap processing for adaptive maximal poisson-disk sampling
ACM Transactions on Graphics (TOG)
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The Delaunay triangulations of a set of points are a class of triangulations which play an important role in a variety of different disciplines of science. Regular triangulations are a generalization of Delaunay triangulations that maintain both their relationship with convex hulls and with Voronoi diagrams. In regular triangulations, a real value, its weight, is assigned to each point.In this paper a simple data structure is presented that allows regular triangulations of sets of points to be dynamically updated, that is, new points can be incrementally inserted in the set and old points can be deleted from it. The algorithms we propose for insertion and deletion are based on a geometric interpretation of the history data structure in one more dimension and use lifted flips as the unique topological operation. This results in rather simple and efficient algorithms. The algorithms have been implemented and experimental results are given.