The visibility complex

  • Authors:
  • Michel Pocchiola;Gert Vegter

  • Affiliations:
  • -;-

  • Venue:
  • SCG '93 Proceedings of the ninth annual symposium on Computational geometry
  • Year:
  • 1993

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Abstract

We introduce the visibility complex of a collectionO of n pairwisedisjoint convex objects in the plane. This 2-dimensiotnal cell complexmay be considered as a generalization of the tangent visibility graph ofO. Its space complexityk is proportional to the size of thetangent visibility graph. We give an Onlogn+k algorithm for its construction. Furthermore we showhow the visibility complex can be used to compute the view from a pointor a convex object with respect to O in Omlogn time, wherem is the size of theview. The view from a point is a generalization of the visibilitypolygon of that point with respect to O.