The Farthest Point Delaunay Triangulation Minimizes Angles (1990) [9 citations — 4 self]
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author = {David Eppstein},
title = {The Farthest Point Delaunay Triangulation Minimizes Angles},
year = {1990}
}
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Abstract:
We show that the planar dual to the Euclidean farthest point Voronoi diagram for the set of vertices of a convex polygon has the lexicographic minimum possible sequence of triangle angles, sorted from sharpest to least sharp. As a consequence, the sharpest angle determined by three vertices of a convex polygon can be found in linear time. 1. Introduction A celebrated result in computational geometry is that the Delaunay triangulation of a planar point set maximizes the minimum angle in any triangle [7]. More specifically, if the points are in general position (by which we mean no four points are cocircular), then the sequence of triangle angles, sorted from sharpest to least sharp, is lexicographically maximized over all such sequences constructed from triangulations of the points. In this paper we study a similar result for the farthest point Delaunay triangulation; that is, the planar dual of the farthest point Voronoi diagram of a planar point set. Since the farthest point V...
Citations
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| 41 | A Linear Time Algorithm for Computing the Voronoi Diagram of a Convex Polygon, Discrete and Computational Geometry 4 – Aggarwal, Guibas, et al. - 1989 |
| 16 | Globally-equiangular triangulations of co-circular points in O(n log n) time – Mount, Saalfeld - 1988 |
| 14 | A Polynomial Time Algorithm for the Minmax Angle Triangulation – Edelsbrunner, Tan, et al. - 1990 |
| 9 | Partitioning space for range queries – Dobkin, Yao, et al. - 1989 |
| 1 | book III props. 20–21. Trans. Sir T.L – Euclid - 1956 |
