Semi Voronoi Diagrams

We consider a problem that is a variant of the Voronoi diagram problem on the Euclidean plane, with the association of a given direction $\vec{d_i}$ to each point pi in P. For each pi, the direction $\vec{d_i}$ defines a visible half plane of pi. A point p in the plane is said to be controlled by pi...

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Bibliographic Details
Published inComputational Geometry, Graphs and Applications Vol. 7033; pp. 19 - 26
Main Authors Cheng, Yongxi, Li, Bo, Xu, Yinfeng
Format Book Chapter
LanguageEnglish
Published Germany Springer Berlin / Heidelberg 2011
Springer Berlin Heidelberg
SeriesLecture Notes in Computer Science
Subjects
Algorithms & data structures
Discrete mathematics
Euclidean Plane
Graphics programming
Half Plane
Visible Angle
Visible Area
Voronoi Diagram
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ISBN9783642249822
3642249825
ISSN0302-9743
1611-3349
DOI10.1007/978-3-642-24983-9_3

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Summary:We consider a problem that is a variant of the Voronoi diagram problem on the Euclidean plane, with the association of a given direction $\vec{d_i}$ to each point pi in P. For each pi, the direction $\vec{d_i}$ defines a visible half plane of pi. A point p in the plane is said to be controlled by pi if: (1) p is visible to pi; (2) among all the points in P that p is visible to, pi is the closest one to p. The members in P partition the plane into different connected regions, each region is controlled by a member in P or is not controlled by any member in P. We give some preliminary results on this partition and propose some problems for future studies.
Bibliography:Original Abstract: We consider a problem that is a variant of the Voronoi diagram problem on the Euclidean plane, with the association of a given direction \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\vec{d_i}$\end{document} to each point pi in P. For each pi, the direction \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\vec{d_i}$\end{document} defines a visible half plane of pi. A point p in the plane is said to be controlled by pi if: (1) p is visible to pi; (2) among all the points in P that p is visible to, pi is the closest one to p. The members in P partition the plane into different connected regions, each region is controlled by a member in P or is not controlled by any member in P. We give some preliminary results on this partition and propose some problems for future studies.
ISBN:9783642249822
3642249825
ISSN:0302-9743
1611-3349
DOI:10.1007/978-3-642-24983-9_3