Computational Geometry ( IF 0.6 ) Pub Date : 2020-09-29 , DOI: 10.1016/j.comgeo.2020.101711 Davood Bakhshesh , Mohammad Farshi
Given an angle , a geometric path is called angle-monotone with width γ if, for any two integers , the angle between the two vectors and is at most γ. Let S be a set of n points in the plane. A geometric graph G with vertex set S is called angle-monotone with width γ, if there exists an angle-monotone path with width γ between every pair of vertices of G. In this paper, we show that the Delaunay triangulation of a given point set in the plane is not necessarily angle-monotone with width α, for . This gives a negative answer to an open problem posed by Bonichon et al. (2016) [14].
中文翻译:
Delaunay三角剖分的角度单调性
给定角度 ,一条几何路径 如果对于任意两个整数,则称为宽度为γ的角单调,两个向量之间的角度 和 最多为γ。令S为平面中n个点的集合。几何图ģ与顶点集小号被称为角单调与宽度γ,如果存在与宽度的角度单调路径γ每对顶点之间ģ。在本文中,我们表明,平面中给定点集的Delaunay三角剖分不一定是宽度为α的角单调,对于。这给Bonichon等人提出的未解决问题给出了否定的答案。(2016)[14]。