The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
Convex hulls of finite sets of points in two and three dimensions
Communications of the ACM
Optimal Search in Planar Subdivisions
Optimal Search in Planar Subdivisions
Computational geometry.
Linear data structures for two types of range search
SCG '86 Proceedings of the second annual symposium on Computational geometry
Establishing order in planar subdivisions
SCG '87 Proceedings of the third annual symposium on Computational geometry
Locating a robot with angle measurements
Journal of Symbolic Computation
Triangulation and shape-complexity
ACM Transactions on Graphics (TOG)
A Pyramidal Data Structure for Triangle-Based Surface Description
IEEE Computer Graphics and Applications
A Parallel Algorithm for Finding the Constrained Voronoi Diagram of Line Segments in the Plane
WADS '99 Proceedings of the 6th International Workshop on Algorithms and Data Structures
Intersecting is easier than sorting
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
Object-based and image-based object representations
ACM Computing Surveys (CSUR)
Artificial Intelligence Review
A realtime GPU subdivision kernel
ACM SIGGRAPH 2005 Papers
Navigation protocols in sensor networks
ACM Transactions on Sensor Networks (TOSN)
A pattern-based data structure for manipulating meshes with regular regions
GI '05 Proceedings of Graphics Interface 2005
A mesh refinement library based on generic design
Proceedings of the 43rd annual Southeast regional conference - Volume 1
The MarineGrid project in Ireland with Webcom
Computers & Geosciences
Designing and proving correct a convex hull algorithm with hypermaps in Coq
Computational Geometry: Theory and Applications
On the existence of weak greedy matching heuristics
Operations Research Letters
Parallel computing 2D Voronoi diagrams using untransformed sweepcircles
Computer-Aided Design
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We discuss the following problem: given n points in the plane (the “sites”), and an arbitrary query point q, find the site that is closest to q. This problem can be solved by constructing the Voronoi diagram of the given sites, and then locating the query point in one of its regions. We give two algorithms, one that constructs the Voronoi diagram in O(n lg n) time, and another that inserts a new site in O(n) time. Both are based on the use of the Voronoi dual, the Delaunay triangulation, and are simple enough to be of practical value. The simplicity of both algorithms can be attributed to the separation of the geometrical and topological aspects of the problem, and to the use of two simple but powerful primitives, a geometric predicate and an operator for manipulating the topology of the diagram. The topology is represented by a new data structure for generalized diagrams, that is embeddings of graphs in two-dimensional manifolds. This structure represents simultaneously an embedding, its dual, and its mirror-image. Furthermore, just two operators are sufficient for building and modifying arbitrary diagrams.