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Kinetic Voronoi diagrams and Delaunay triangulations under polygonal distance functions, manuscript
, 2014
"... Let P be a set of n points and Q a convex kgon in R2. We analyze in detail the topological (or discrete) changes in the structure of the Voronoi diagram and the Delaunay triangulation of P, under the convex distance function defined by Q, as the points of P move along prespecified continuous trajec ..."
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Cited by 1 (1 self)
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Let P be a set of n points and Q a convex kgon in R2. We analyze in detail the topological (or discrete) changes in the structure of the Voronoi diagram and the Delaunay triangulation of P, under the convex distance function defined by Q, as the points of P move along prespecified continuous
Primitives for the manipulation of general subdivisions and the computations of Voronoi diagrams
 ACM Tmns. Graph
, 1985
"... The following problem is discussed: Given n points in the plane (the sites) and an arbitrary query point 4, 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. Two algorithms ar ..."
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Cited by 543 (11 self)
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are given, one that constructs the Voronoi diagram in O(n log n) time, and another that inserts a new site in O(n) time. Both are based on the use of the Voronoi dual, or Delaunay triangulation, and are simple enough to be of practical value. The simplicity of both algorithms can be attributed
Surface Reconstruction by Voronoi Filtering
 Discrete and Computational Geometry
, 1998
"... We give a simple combinatorial algorithm that computes a piecewiselinear approximation of a smooth surface from a finite set of sample points. The algorithm uses Voronoi vertices to remove triangles from the Delaunay triangulation. We prove the algorithm correct by showing that for densely sampled ..."
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Cited by 418 (15 self)
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We give a simple combinatorial algorithm that computes a piecewiselinear approximation of a smooth surface from a finite set of sample points. The algorithm uses Voronoi vertices to remove triangles from the Delaunay triangulation. We prove the algorithm correct by showing that for densely sampled
Dirichlet–Voronoi Diagrams and Delaunay Triangulations
"... In this chapter we present very briefly the concepts of a Voronoi diagram and of a Delaunay triangulation. These are important tools in computational geometry, and Delaunay triangulations are important in problems where it is necessary to fit 3D data using surface splines. It is usually useful to co ..."
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and lucid introduction to computational geometry. Some practical applications of Voronoi diagrams and Delaunay triangulations are briefly discussed in Section 8.7. Let E be a Euclidean space of finite dimension, that is, an affine space E whose underlying vector space − → E is equipped with an inner product
A New VoronoiBased Surface Reconstruction Algorithm
, 2002
"... We describe our experience with a new algorithm for the reconstruction of surfaces from unorganized sample points in R³. The algorithm is the first for this problem with provable guarantees. Given a “good sample” from a smooth surface, the output is guaranteed to be topologically correct and converg ..."
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Cited by 422 (9 self)
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, rather than approximates, the input points. Our algorithm is based on the threedimensional Voronoi diagram. Given a good program for this fundamental subroutine, the algorithm is quite easy to implement.
Kinetic Voronoi/Delaunay Drawing Tools
 In Proceedings of the 3rd International Symposium on Voronoi Diagrams in Science and Engineering
, 2006
"... We describe two reversible linedrawing methods for cartographic applications based on the kinetic (movingpoint) Voronoi diagram. Our objectives were to optimize the user’s ability to draw and edit the map, rather than to produce the most efficient batchoriented algorithm for large data sets, and a ..."
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Cited by 2 (2 self)
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) is the locus of a moving point, then segments are drawn by maintaining the topology of a single moving point (MP, or the “pen”) as it moves through the topological network (visualized as either the Voronoi diagram or Delaunay triangulation). The trailing line accumulates the adjacency relationships of MP
Voronoi Diagrams and Delaunay Triangulations: Ubiquitous Siamese Twins
 DOCUMENTA MATH.
, 2012
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Fast Computation of Generalized Voronoi Diagrams Using Graphics Hardware
, 1999
"... We present a new approach for computing generalized 2D and 3D Voronoi diagrams using interpolationbased polygon rasterization hardware. We compute a discrete Voronoi diagram by rendering a three dimensional distance mesh for each Voronoi site. The polygonal mesh is a boundederror approximation of ..."
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Cited by 233 (26 self)
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segments, polygons, polyhedra, curves, and curved surfaces in 2D and 3D. We generalize to weighted and farthestsite Voronoi diagrams, and present efficient techniques for computing the Voronoi boundaries, Voronoi neighbors, and the Delaunay triangulation of points. We also show how to adaptively refine
A Volumetric Method for Building Complex Models from Range Images
, 1996
"... A number of techniques have been developed for reconstructing surfaces by integrating groups of aligned range images. A desirable set of properties for such algorithms includes: incremental updating, representation of directional uncertainty, the ability to fill gaps in the reconstruction, and robus ..."
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Cited by 1018 (18 self)
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, and robustness in the presence of outliers. Prior algorithms possess subsets of these properties. In this paper, we present a volumetric method for integrating range images that possesses all of these properties. Our volumetric representation consists of a cumulative weighted signed distance function. Working
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