Generalized Higher-Order Voronoi Diagrams on Polyhedral Surfaces

  • Authors:

  • Marta Fort;J. Antoni Sellares

  • Affiliations:

  • Universitat de Girona, Spain;Universitat de Girona, Spain

  • Venue:
  • ISVD '07 Proceedings of the 4th International Symposium on Voronoi Diagrams in Science and Engineering
  • Year:
  • 2007

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Abstract

We present an algorithm for computing exact shortest paths, and consequently distances, from a generalized source (point, segment, polygonal chain or polygonal region) on a possibly non-convex polyhedral surface in which polygonal chain or polygon obstacles are allowed. We also present algorithms for computing discrete Voronoi diagrams of a set of generalized sites (points, segments, polygonal chains or polygons) on a polyhedral surface with obstacles. To obtain the discrete Voronoi diagrams our algorithms, exploiting hardware graphics capabilities, compute shortest path distances defined by the sites.