scholarly journals Clipping simple polygons with degenerate intersections

2019 ◽  
Vol 2 ◽  
pp. 100007
Author(s):  
Erich L Foster ◽  
Kai Hormann ◽  
Romeo Traian Popa
Keyword(s):  
Author(s):  
S. Miao ◽  
D. Howard

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.


2000 ◽  
Vol 24 (1) ◽  
pp. 1-34 ◽  
Author(s):  
L. Guibas ◽  
J. Hershberger ◽  
S. Suri
Keyword(s):  

2017 ◽  
Vol 27 (01n02) ◽  
pp. 121-158 ◽  
Author(s):  
Martin Nöllenburg ◽  
Roman Prutkin ◽  
Ignaz Rutter

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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