Euclidean Shortest Paths in Simple Cube Curves at a Glance

Details Euclidean Shortest Paths in Simple Cube Curves at a Glance Euclidean Shortest Paths in Simple Cube Curves at a Glance

2007-04-24

arxiv.org/abs/0704.3197v1

Computer Science

Computational Geometry

8 pages

Scientific paper

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.

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