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# Minimum Rectilinear Polygons for Given Angle Sequences

• William S. Evans
• Krzysztof Fleszar
• Philipp Kindermann
• Noushin Saeedi
• Chan-Su Shin
• Alexander Wolff
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9943)

## Abstract

A rectilinear polygon is a polygon whose edges are axis-aligned. Walking counterclockwise on the boundary of such a polygon yields a sequence of left turns and right turns. The number of left turns always equals the number of right turns plus 4. It is known that any such sequence can be realized by a rectilinear polygon. In this paper, we consider the problem of finding realizations that minimize the perimeter or the area of the polygon or the area of the bounding box of the polygon. We show that all three problems are NP-hard in general. Then we consider the special cases of x-monotone and xy-monotone rectilinear polygons. For these, we can optimize the three objectives efficiently.

## Keywords

Vertical Edge Full Version Simple Polygon Horizontal Edge Minimum Height
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Copyright information

© Springer International Publishing AG 2016

## Authors and Affiliations

• William S. Evans
• 1
• Krzysztof Fleszar
• 2
• Philipp Kindermann
• 2
• 3
• Noushin Saeedi
• 1
• Chan-Su Shin
• 4
• Alexander Wolff
• 2
1. 1.Department of Computer ScienceUniversity of British ColumbiaVancouverCanada
2. 2.Lehrstuhl für Informatik IUniversität WürzburgWürzburgGermany
3. 3.LG Theoretische InformatikFernUniversität in HagenHagenGermany
4. 4.Division of Computer and Electronic SystemsHankuk University of Foreign StudiesYonginSouth Korea