The Shortest Path with Increasing Chords in a Simple Polygon

TL;DR

This paper investigates the shortest path with increasing chords within a simple polygon, proving its uniqueness and providing an algorithm for its construction, which advances understanding of geometric path optimization.

Contribution

The paper introduces the first algorithm to construct the shortest path with increasing chords in a simple polygon and proves its uniqueness.

Findings

Shortest path with increasing chords is unique.

An algorithm for constructing the shortest increasing chord path is provided.

Theoretical proof of uniqueness of the path.

Abstract

We study the problem of finding the shortest path with increasing chords in a simple polygon. A path has increasing chords if and only if for any points a, b, c, and d that lie on the path in that order, |ad| >= |bc|. In this paper we show that the shortest path with increasing chords is unique and present an algorithm to construct it.