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Please use this identifier to cite or link to this item: http://hdl.handle.net/10119/9518

Title: Optimal Triangulations of points and segments with steiner points
Authors: Aronov, Boris
Asano, Tetsuo
Funke, Stefan
Keywords: Computational geometry
constrained Delaunay triangulation
polynomial-time algorithm
Steiner point
Voronoi diagram
Issue Date: 2010-02
Publisher: World Scientific Publishing
Magazine name: International Journal of Computational Geometry and Applications
Volume: 20
Number: 1
Start page: 89
End page: 104
DOI: 10.1142/S0218195910003219
Abstract: Consider a set X of points in the plane and a set E of non-crossing segments with endpoints in X. One can efficiently compute the triangulation of the convex hull of the points, which uses X as the vertex set, respects E, and maximizes the minimum internal angle of a triangle. In this paper we consider a natural extension of this problem: Given in addition a Steiner point p, determine the optimal location of p and a triangulation of X ∪ {p} respecting E, which is best among all triangulations and placements of p in terms of maximizing the minimum internal angle of a triangle. We present a polynomial-time algorithm for this problem and then extend our solution to handle any constant number of Steiner points.
Rights: Electronic version of an article published as International Journal of Computational Geometry and Applications, 20(1), 2010, 89-104. DOI:10.1142/S0218195910003219. Copyright World Scientific Publishing Company, http://dx.doi.org/10.1142/S0218195910003219
URI: http://hdl.handle.net/10119/9518
Material Type: author
Appears in Collections:b10-1. 雑誌掲載論文 (Journal Articles)

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