Shortest path queries between geometric objects on surfaces

Authors:
Hua Guo;Anil Maheshwari;Doron Nussbaum;Jörg-Rüdiger Sack
Affiliations:
School of Computer Science, Carleton University, Ottawa, Canada;School of Computer Science, Carleton University, Ottawa, Canada;School of Computer Science, Carleton University, Ottawa, Canada;School of Computer Science, Carleton University, Ottawa, Canada
Venue:
ICCSA'07 Proceedings of the 2007 international conference on Computational science and its applications - Volume Part I
Year:
2007

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Abstract

We consider geometric shortest path queries between arbitrary pairs of objects on a connected polyhedral surface P of genus g. The query objects are points, vertices, edges, segments, faces, chains, regions and sets of these. The surface P consists of n positively weighted triangular faces. The cost of a path on P is the weighted sum of Euclidean lengths of the sub-paths within each face of P. We present generic algorithms which provide approximate solutions.