Computation of shortest paths on free-form parametric surfaces

Research output: Contribution to journalArticlepeer-review

51 Citations (Scopus)


Computation of shortest paths on free-form surfaces is an important problem in ship design, robot motion planning, computation of medial axis transforms of trimmed surface patches, terrain navigation and NC machining. The objective of this paper is to provide an efficient and reliable method for computing the shortest path between two points on a free-form parametric surface and the shortest path between a point and a curve on a free-form parametric surface. These problems can be reduced to solving a two point boundary value problem. Our approach for solving the two point boundary value problem is based on a relaxation method relying on finite difference discretization. Examples illustrate our method.

Original languageEnglish
Pages (from-to)499-508
Number of pages10
JournalJournal of Mechanical Design, Transactions of the ASME
Issue number4
Publication statusPublished - 1996 Dec
Externally publishedYes

ASJC Scopus subject areas

  • Mechanics of Materials
  • Mechanical Engineering
  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design


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