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Relative Convex Hull Determination from Convex Hulls in the Plane

  • Petra WiederholdEmail author
  • Hugo Reyes
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9448)

Abstract

A new algorithm for the determination of the relative convex hull in the plane of a simple polygon A with respect to another simple polygon B which contains A, is proposed. The relative convex hull is also known as geodesic convex hull, and the problem of its determination in the plane is equivalent to find the shortest curve among all Jordan curves lying in the difference set of B and A and encircling A. Algorithms solving this problem known from Computational Geometry are based on the triangulation or similar decomposition of that difference set. The algorithm presented here does not use such decomposition, but it supposes that A and B are given as ordered sequences of vertices. The algorithm is based on convex hull calculations of A and B and of smaller polygons and polylines, it produces the output list of vertices of the relative convex hull from the sequence of vertices of the convex hull of A.

Keywords

Relative convex hull Geodesic convex hull Shortest Jordan curve Shortest path Minimal length polygon Minimal perimeter polygon 

Notes

Acknowledgement

The first author gratefully acknowledges support for this research from SEP and CONACYT Mexico, grant No. CB-2011-01-166223. The authors would like to thank very much to the reviewers for their careful study of the work, and for their constructive criticism and helpful comments which were important to improve the presentation of the paper.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of Automatic ControlCentro de Investigación y de Estudios Avanzados (CINVESTAV-IPN)MexicoMexico

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