Quadrangulations of a Polygon with Spirality
Quadrangulations of a Polygon with Spirality
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螺旋多边形的四边形
DOI：
10.1007/s00373-021-02346-1
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发表时间：
2021
影响因子：
0.7
通讯作者：
Nakamoto Atsuhiro
中科院分区：
文献类型：
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作者：
Hidaka Fumiya;Matsumoto Naoki;Nakamoto Atsuhiro
给定平面上的n边四边形P，P的四边形是一个几何平面图，使得外表面的边界为P，且每个有限面都是四边形。显然，P1是可四边形化的（即，承认四边形）只有如果是偶数，但有一个非四边形的偶数边多边形。Ramaswami等[Comp Geom 9：257-276，（1998）]证明了任意n边形Pwitheven允许一个至多有个Steiner点的四边形，其中P的Steiner点是P的一个辅助点，它可以放在P内部的任何位置。本文引入P的螺旋度的概念来控制P的一个结构（与n无关），估计了四角化P的Steiner点的个数。
Given ann-sided polygonPon the plane with, a quadrangulation ofPis a geometric plane graph such that the boundary of the outer face isPand that each finite face is quadrilateral. Clearly,Pis quadrangulatable (i.e., admits a quadrangulation) only ifnis even, but there is a non-quadrangulatable even-sided polygon. Ramaswami et al. [Comp Geom 9:257–276, (1998)] proved that everyn-sided polygonPwitheven admits a quadrangulation with at mostSteiner points, where a Steiner point forPis an auxiliary point which can be put in any position in the interior ofP. In this paper, introducing the notion of the spirality ofPto control a structure ofP(independent ofn), we estimate the number of Steiner points to quadrangulateP.