Fast triangulation of the plane with respect to simple polygons

Q4 Mathematics
Stefan Hertel, Kurt Mehlhorn
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引用次数: 16

Abstract

Let P1,…, Pk be pairwise non-intersecting simple polygons with a total of n vertices and s start vertices. A start vertex, in general, is a vertex both of which neighbors have larger x coordinate. We present an algorithm for triangulating P1,…, Pk in time O(n + s log s). s may be viewed as a measure of non-convexity. In particular, s is always bounded by the number of concave angles + 1, and is usually much smaller. We also describe two new applications of triangulation. Given a triangulation of the plane with respect to a set of k pairwise non-intersecting simple polygons, then the intersection of this set with a convex polygon Q can be computed in time linear with respect to the combined number of vertices of the k + 1 polygons. Such a result had only be known for two convex polygons. The other application improves the bound on the number of convex parts into which a polygon can be decomposed.

关于简单多边形的平面快速三角剖分
设P1,…,Pk为一对不相交的简单多边形,共n个顶点,s个起始点。一般来说,起始顶点是两个相邻顶点的x坐标都较大的顶点。我们提出了一种在时间O(n + s log s)内三角化P1,…,Pk的算法。s可以被视为非凸性的度量。特别地,s总是以凹角的数量+ 1为界,并且通常要小得多。我们还描述了三角测量的两种新应用。给定一个平面的关于k对不相交简单多边形的三角剖分,那么这个集合与一个凸多边形Q的交点可以根据k + 1个多边形的顶点总数在时间线性上计算出来。这样的结果只对两个凸多边形是已知的。另一个应用改进了一个多边形可以分解成凸部分的数目的界限。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
信息与控制
信息与控制 Mathematics-Control and Optimization
CiteScore
1.50
自引率
0.00%
发文量
4623
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