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Finding All Shortest Path Edge Sequences on a convex polyhedron

  • Yie-Huei Hwang
  • Ruei-Chuan Chang
  • Hung-Yi Tu
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 382)

Abstract

In this paper, the problems of computing the Euclidean shortest path between two points on the surface of a convex polyhedron and finding all shortest path edge sequences are considered. We propose an O(n6logn) algorithm to find All Shortest Path Edge Sequences, construct n Edge Sequence Trees, and draw out n(n−1)/2 Visibility Relation Diagrams for a given convex polyhedron. According to these data structures, not only can we enumerate all shortest path edge sequences and draw out all maximal ones, but we can also find the shortest path between any two points lying on edges in O(k+logn) time where k is the number of edges crossed by the shortest path.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Yie-Huei Hwang
    • 1
    • 2
  • Ruei-Chuan Chang
    • 1
    • 2
  • Hung-Yi Tu
    • 1
    • 2
  1. 1.Department of Computer and Information ScienceNational Chiao Tung UniversityHsinchuTaiwan, Republic of China
  2. 2.Institute of Information ScienceAcademia sinicaNankang, TaipeiRepublic of China

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