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On the construction of abstract voronoi diagrams [chapter]

K. Mehlhorn, St. Meiser, C. Ó'Dúnlaing
1990 Lecture Notes in Computer Science  
We show that the abstract Voronoi diagram of n sites in the plane can be constructed in time O(n log n) by a randomized algorithm.  ...  Abstract Voronoi diagrams are given by a family of bisecting curves and were recently introduced by Klein [-13].  ...  x i and x~+ 1 to the Voronoi diagram (3) od On the Construction of Abstract Voronoi Diagrams 219 For the time bound we only have to observe that steps 1 and 2 take time O(ILI) and that step 3 takes time  ... 
doi:10.1007/3-540-52282-4_46 fatcat:gytxlxalhbguffqyzo3zd7ey4a

On the construction of abstract voronoi diagrams

K. Mehlhorn, St. Meiser, C. Ó'Dúnlaing
1991 Discrete & Computational Geometry  
We show that the abstract Voronoi diagram of n sites in the plane can be constructed in time O(n log n) by a randomized algorithm.  ...  Abstract Voronoi diagrams are given by a family of bisecting curves and were recently introduced by Klein [-13].  ...  x i and x~+ 1 to the Voronoi diagram (3) od On the Construction of Abstract Voronoi Diagrams 219 For the time bound we only have to observe that steps 1 and 2 take time O(ILI) and that step 3 takes time  ... 
doi:10.1007/bf02574686 fatcat:pzxtfqw5nfealbvkuryjoq6m7e

On the construction of abstract voronoi diagrams, II [chapter]

R. Klein, K. Mehlhorn, S. Meiser
1990 Lecture Notes in Computer Science  
Ou the Construction of Abstract Voronoi Diagrams, Il ' by R. Klein' 1\ . Mehlhorn' S. Meiser' A 03/89 Abstr:· lct.: Abstra<.l Vomnoi Diagrams are defined by a .y.tem of bL:s.:c l ing curve!!  ...  Vorolloi di agrams can be constructed in a purely combinatorial manner. Thi. has the following MI . v.," tllgcs : On the one hand, the construction of a 6v":'site-diagram i. the only operation d.'  ...  into the construction of abstract Voronoi diagrams for five sites.  ... 
doi:10.1007/3-540-52921-7_63 fatcat:7o7t62llb5gixfrc73rpy5e3ii

Characterization of contour elements that generate abstract Voronoi diagrams

Sabine Stifter
1997 Computational geometry  
While the concept of abstract Voronoi diagrams characterizes Voronoi diagrams by the set of bisecting curves, the concept of axiomatic Voronoi diagrams gives a characterization of the contour elements  ...  In this paper we bring two concepts of generalizations of Voronoi diagrams together: the concept of abstract Voronoi diagrams invented by R.  ...  Rolf Klein for extensive discussions on the subject, especially for a personal introduction to abstract Voronoi diagrams. I thank the anonymous referees for useful comments and suggestions.  ... 
doi:10.1016/0925-7721(95)00038-0 fatcat:s7xg3gjuhzcbdmdw3gbcvren4y

Page 10287 of Mathematical Reviews Vol. , Issue 2004m [page]

2004 Mathematical Reviews  
He proposes a class of abstract Voronoi diagrams in 3-space that generalizes the planar abstract Voronoi diagram of Rolf Klein.  ...  Two open problems are stated: 1. to give a tight bound on the complexity of the abstract Voronoi diagram and 2. to find an efficient algorithm to compute the general abstract Voronoi diagram.  ... 

Abstract Voronoi Diagrams [chapter]

Rolf Klein
2014 Encyclopedia of Algorithms  
Voronoi diagrams are a unifying framework that covers many types of concrete Voronoi diagrams. This talk reports on the state of the art, including recent progress.  ...  Abstract Voronoi diagrams [6] are built on what most concrete diagrams have in common: a system of simple bisecting curves J(p, q) = J(q, p), where p, q are just indices from a set S of n elements.  ...  Conclusion Open is the case of closed bisecting curves. abstract Voronoi diagram of S is just the plane minus all Voronoi regions.  ... 
doi:10.1007/978-3-642-27848-8_603-1 fatcat:hcaclpl5rbccvierqzfrtvcebi

Abstract Voronoi Diagrams [chapter]

Rolf Klein
2016 Encyclopedia of Algorithms  
Voronoi diagrams are a unifying framework that covers many types of concrete Voronoi diagrams. This talk reports on the state of the art, including recent progress.  ...  Abstract Voronoi diagrams [6] are built on what most concrete diagrams have in common: a system of simple bisecting curves J(p, q) = J(q, p), where p, q are just indices from a set S of n elements.  ...  Conclusion Open is the case of closed bisecting curves. abstract Voronoi diagram of S is just the plane minus all Voronoi regions.  ... 
doi:10.1007/978-1-4939-2864-4_603 fatcat:n7o77fxrsfdsvfa5ahtmzyc4u4

Procedural modeling of water caustics and foamy water for cartoon animation

Jing Liao, Jin-hui Yu, Long Jia
2011 Journal of Zhejiang University SCIENCE C  
In our method we emulate the visual abstraction of these cartoon effects by the use of Voronoi diagrams and the motion abstraction by designing relevant controlling mechanisms corresponding to each effect  ...  Our system enables the creation of cartoon effects with minimal intervention from the animator.  ...  We adopt the simple algorithm by Lischinski [9] for the incremental construction of the Delaunay triangulation and the Voronoi diagram.  ... 
doi:10.1631/jzus.c1000228 fatcat:runqoaddizhuxghe5vtezjokxm

Procedural Modeling of Water Caustics and Foamy Water for Cartoon Animation

Jing Liao, Jinhui Yu, Long Jia
2010 2010 18th Pacific Conference on Computer Graphics and Applications  
In our method we emulate the visual abstraction of these cartoon effects by the use of Voronoi diagrams and the motion abstraction by designing relevant controlling mechanisms corresponding to each effect  ...  Our system enables the creation of cartoon effects with minimal intervention from the animator.  ...  We adopt the simple algorithm by Lischinski [9] for the incremental construction of the Delaunay triangulation and the Voronoi diagram.  ... 
doi:10.1109/pacificgraphics.2010.8 dblp:conf/pg/LiaoYJ10 fatcat:vbwv6i7aafdi3faj2o2etz4ncq

Randomized Incremental Construction of Abstract Voronoi Diagrams [chapter]

Rolf Klein, Kurt Mehlhorn, Stefan Meiser
1992 TEUBNER-TEXTE zur Informatik  
Klein (1988) as an axiomatic Randomized incremental construction 159 namely the construction of a Voronoi diagram for 5 sites, depends on the specific type of Voronoi diagram and has to be programmed in  ...  We have used it to construct Powerdiagrams, Voronoi diagrams of line segments under the Euclidean metric, and Voronoi diagrams of points under both the Euclidean and the L,-metric.  ...  At present there are two algorithms for the construction of abstract Voronoi diagrams.  ... 
doi:10.1007/978-3-322-95233-2_17 fatcat:ztegg4gxbzgmnieurk37sddo6q

Page 6196 of Mathematical Reviews Vol. , Issue 91K [page]

1991 Mathematical Reviews  
(D-SAAR-I) On the construction of abstract Voronoi diagrams. II. Algorithms (Tokyo, 1990), 138-154, Lecture Notes in Comput. Sci., 450, Springer, Berlin, 1990.  ...  Using this operation, abstract Voronoi diagrams can be constructed in a purely combinatorial manner.  ... 

Randomized incremental construction of abstract Voronoi diagrams

Rolf Klein, Kurt Mehlhorn, Stefan Meiser
1993 Computational geometry  
Klein (1988) as an axiomatic Randomized incremental construction 159 namely the construction of a Voronoi diagram for 5 sites, depends on the specific type of Voronoi diagram and has to be programmed in  ...  We have used it to construct Powerdiagrams, Voronoi diagrams of line segments under the Euclidean metric, and Voronoi diagrams of points under both the Euclidean and the L,-metric.  ...  At present there are two algorithms for the construction of abstract Voronoi diagrams.  ... 
doi:10.1016/0925-7721(93)90033-3 fatcat:bnqk7cxeurdendljn3pmfdj45i

Randomized incremental construction of simple abstract Voronoi diagrams in 3-space

Ngȯc-Minh Lê
1997 Computational geometry  
We introduce the simple abstract Voronoi diagram in 3-space as an abstraction of the usual Voronoi diagram.  ...  The algorithm is based on the randomized incremental construction technique of Clarkson and Shor (1989) .  ...  I especially thank an anonymous referee whose comments have helped to improve the presentation of this paper.  ... 
doi:10.1016/s0925-7721(96)00020-x fatcat:7qzckyxm3nb57e6dqjidb6kz24

Page 3309 of Mathematical Reviews Vol. , Issue 93f [page]

1993 Mathematical Reviews  
We show how to construct abstract Voronoi diagrams in time O(nlogn) by a randomized algorithm; the algorithm is based on K. L. Clarkson and P. W.  ...  It can be adapted to a concrete kind of Voronoi diagram by providing a single basic operation, namely the construction of a Voronoi diagram of five sites.  ... 

Cut Locus Construction Using Deformable Simplicial Complexes

Marek Krzysztof Misztal, Jakob Andreas Bærentzen, Francois Anton, Steen Markvorsen
2011 2011 Eighth International Symposium on Voronoi Diagrams in Science and Engineering  
Other theoretical aspects and applications of geometric computing and design. Abstract Submission Deadline: April 8th, 2011  ...  Spatial and dynamic data modeling and simulation  Image processing  Bioinformatics  Voronoi arts  Other Applications 2.  ...  and Engineering is devoted to the research on the Voronoi diagram and its application to all fields.  ... 
doi:10.1109/isvd.2011.26 dblp:conf/isvd/MisztalBAM11 fatcat:yiw34c6ylzcafojf4b5334drty
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