On a convex hull algorithm for polygons and its application to triangulation problems

Godfried T. Toussaint; David Avis

doi:10.1016/0031-3203(82)90057-7

On a convex hull algorithm for polygons and its application to triangulation problems

Godfried T. Toussaint, David Avis

Computer Science

Research output: Contribution to journal › Article › peer-review

Abstract

A frequently used algorithm for finding the convex hull of a simple polygon in linear running time has been recently shown to fail in some cases. Due to its simplicity the algorithm is, nevertheless, attractive. In this paper it is shown that the algorithm does in fact work for a family of simple polygons known as weakly externally visible polygons. Some application areas where such polygons occur are briefly discussed. In addition, it is shown that with a trivial modification the algorithm can be used to internally and externally triangulate certain classes of polygons in 0(n) time.

Original language	English (US)
Pages (from-to)	23-29
Number of pages	7
Journal	Pattern Recognition
Volume	15
Issue number	1
DOIs	https://doi.org/10.1016/0031-3203(82)90057-7
State	Published - 1982

Keywords

Algorithm
Computational complexity
Computational geometry
Convex hull
Image processing
Pattern recognition
Simple polygon
Triangulation Polygon decomposition
Weakly externally visible polygon

ASJC Scopus subject areas

Software
Signal Processing
Computer Vision and Pattern Recognition
Artificial Intelligence

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10.1016/0031-3203(82)90057-7

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abstract = "A frequently used algorithm for finding the convex hull of a simple polygon in linear running time has been recently shown to fail in some cases. Due to its simplicity the algorithm is, nevertheless, attractive. In this paper it is shown that the algorithm does in fact work for a family of simple polygons known as weakly externally visible polygons. Some application areas where such polygons occur are briefly discussed. In addition, it is shown that with a trivial modification the algorithm can be used to internally and externally triangulate certain classes of polygons in 0(n) time.",

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AB - A frequently used algorithm for finding the convex hull of a simple polygon in linear running time has been recently shown to fail in some cases. Due to its simplicity the algorithm is, nevertheless, attractive. In this paper it is shown that the algorithm does in fact work for a family of simple polygons known as weakly externally visible polygons. Some application areas where such polygons occur are briefly discussed. In addition, it is shown that with a trivial modification the algorithm can be used to internally and externally triangulate certain classes of polygons in 0(n) time.

KW - Algorithm

KW - Computational complexity

KW - Computational geometry

KW - Convex hull

KW - Image processing

KW - Pattern recognition

KW - Simple polygon

KW - Triangulation Polygon decomposition

KW - Weakly externally visible polygon

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On a convex hull algorithm for polygons and its application to triangulation problems

Abstract

Keywords

ASJC Scopus subject areas

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