当前位置: X-MOL 学术Comput. Geom. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Angle-monotonicity of Delaunay triangulation
Computational Geometry ( IF 0.6 ) Pub Date : 2020-09-29 , DOI: 10.1016/j.comgeo.2020.101711
Davood Bakhshesh , Mohammad Farshi

Given an angle γ>0, a geometric path (v1,,vk) is called angle-monotone with width γ if, for any two integers 1i,j<k, the angle between the two vectors vivi+1 and vjvj+1 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 0<α<140. 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 γ>0,一条几何路径 v1个vķ如果对于任意两个整数,则称为宽度为γ的角单调1个一世Ĵ<ķ,两个向量之间的角度 v一世v一世+1个vĴvĴ+1个最多为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0<α<140。这给Bonichon等人提出的未解决问题给出了否定的答案。(2016)[14]。

更新日期:2020-10-02
down
wechat
bug