Triangulating and guarding realistic polygons

Authors:
Greg Aloupis;Prosenjit Bose;Vida Dujmović;Chris Gray;Stefan Langerman;Bettina Speckmann
Affiliations:
Carleton University, Canada and Université Libre de Bruxelles, Belgium;Carleton University, Canada;Carleton University, Canada;TU Eindhoven, Netherlands;Chercheur Qualifié du FNRS, Université Libre de Bruxelles, Belgium;TU Eindhoven, Netherlands
Venue:
Computational Geometry: Theory and Applications
Year:
2014

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Abstract

We propose a new model of realistic input: k-guardable objects. An object is k-guardable if its boundary can be seen by k guards. We show that k-guardable polygons generalize two previously identified classes of realistic input. Following this, we give two simple algorithms for triangulating k-guardable polygons. One algorithm requires the guards as input while the other does not. Both take linear time assuming that k is constant and both are easily implementable.