Euclidean Shortest Paths in Simple Cube Curves at a Glance

Abstract

This paper reports about the development of two provably correct approximate algorithms which calculate the Euclidean shortest path (ESP) within a given cube-curve with arbitrary accuracy, defined by $\epsilon >0$, and in time complexity $\kappa(\epsilon) \cdot {\cal O}(n)$, where $\kappa(\epsilon)$ is the length difference between the path used for initialization and the minimum-length path, divided by $\epsilon$. A run-time diagram also illustrates this linear-time behavior of the implemented ESP algorithm.