Approximate ESPs on Surfaces of Polytopes Using a Rubberband Algorithm.

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 $\kappa_1(\varepsilon) \cdot \kappa_2(\varepsilon) \cdot {\cal O}(n^2)$ time complexity, where n is the number of vertices of Π, κi(ε) = (L0i − Li)/ε, 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. [ABSTRACT FROM AUTHOR]