On shortest paths in polyhedral spaces
SIAM Journal on Computing
On shortest paths amidst convex polyhedra
SIAM Journal on Computing
SIAM Journal on Computing
A single-exponential upper bound for finding shortest paths in three dimensions
Journal of the ACM (JACM)
Efficient computation of geodesic shortest paths
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Rubberband Algorithms for Solving Various 2D or 3D Shortest Path Problems
ICCTA '07 Proceedings of the International Conference on Computing: Theory and Applications
Hi-index | 0.00 |
Let p and q be two points on the surface of a polytope Π. This paper provides a rubberband algorithm for computing a Euclidean shortest path between p and q (a so-called surface ESP) that is contained on the surface of Π.The algorithm has κ1(Ɛ)ċκ2(Ɛ)ċO(n2) time complexity, where n is the number of vertices of Π, κi(Ɛ) = (L0i-Li)/Ɛ, for the true length Li of some shortest path with initial (polygonal path) length L0i (used when approximating this shortest path), for i = 1, 2. Rubberband algorithms follow a straightforward design strategy, and the proposed algorithm is easy to implement and thus of importance for applications, for example, when analyzing 3D objects in 3D image analysis, such as in biomedical or industrial image analysis, using 3D image scanners.