Finding Shortest Paths in a Sequence of Triangles in 3D by the Planar Unfolding |
| |
Authors: | P. T. An |
| |
Affiliation: | 1. Institute of Mathematics, Vietnam Academy of Science and Technology, Hanoi, Vietnam;2. Institute of Mathematics and Computer Sciences, University of S?o Paulo, S?o Carlos, Brasil |
| |
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. |
| |
Keywords: | Funnel algorithm geometric shortest path method of orienting curves polyhedral surface straightest geodesic |
|
|