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https://hdl.handle.net/10119/9518
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| 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: | https://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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