Finding Shortest Paths in a Sequence of Triangles in 3D by the Planar Unfolding. (11th June 2019)

• Record Type: Journal Article
• Authors: An, P. T.
• Is Part Of: Numerical functional analysis and optimization. Volume 40:Number 8(2019)
• Page Start: 944
• Page End: 952
• Publication Date: 2019-06-11
• Subjects: Funnel algorithm -- geometric shortest path -- method of orienting curves -- polyhedral surface -- straightest geodesic; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2019.1566927
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: We present an efficient algorithm for finding the shortest path joining two points in a sequence of triangles in three-dimensional space using the concept of funnels associated with common edges along the sequence of triangles and the planar unfolding for each funnel. We show that the unfolded image of a funnel is a simple polygon, it thus is non-overlapping. Therefore, such funnels are determined iteratively to their associated common edges by the planar unfolding and the shortest path joining two points is determined by cusps of these funnels.