Open Guard Edges and Edge Guards in Simple Polygons

Abstract This paper presents an efficient algorithm for determining the intersection of two simple polygons. The proposed algorithm is based on the idea of searching for the vertices of the intersection polygon vertex by vertex along the boundary in a clockwise direction. This method finds the intersection polygon vertices and their order in one pass. The algorithm almost eliminates the need for testing whether candidate vertices are inside both polygons and the sorting stage is no longer needed.

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Morphing Simple Polygons

Discrete & Computational Geometry ◽

10.1007/s004540010017 ◽

2000 ◽

Vol 24 (1) ◽

pp. 1-34 ◽

Cited By ~ 18

Author(s):

L. Guibas ◽

J. Hershberger ◽

S. Suri

Keyword(s):

Simple Polygons

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Partitioning Graph Drawings and Triangulated Simple Polygons into Greedily Routable Regions

International Journal of Computational Geometry & Applications ◽

10.1142/s0218195917600068 ◽

2017 ◽

Vol 27 (01n02) ◽

pp. 121-158 ◽

Cited By ~ 1

Author(s):

Martin Nöllenburg ◽

Roman Prutkin ◽

Ignaz Rutter

Keyword(s):

Routing Protocol ◽

Graph Drawing ◽

Geographic Routing ◽

Np Hard ◽

Line Drawings ◽

Simple Polygons ◽

Straight Line ◽

Starting Point ◽

Minimum Decomposition ◽

Geographic Routing Protocol

A greedily routable region (GRR) is a closed subset of [Formula: see text], in which any destination point can be reached from any starting point by always moving in the direction with maximum reduction of the distance to the destination in each point of the path. Recently, Tan and Kermarrec proposed a geographic routing protocol for dense wireless sensor networks based on decomposing the network area into a small number of interior-disjoint GRRs. They showed that minimum decomposition is NP-hard for polygonal regions with holes. We consider minimum GRR decomposition for plane straight-line drawings of graphs. Here, GRRs coincide with self-approaching drawings of trees, a drawing style which has become a popular research topic in graph drawing. We show that minimum decomposition is still NP-hard for graphs with cycles and even for trees, but can be solved optimally for trees in polynomial time, if we allow only certain types of GRR contacts. Additionally, we give a 2-approximation for simple polygons, if a given triangulation has to be respected.

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