A Short Note on Modeling 2D Taut Ropes with Visibility Decompositions

TL;DR

This paper presents a novel, efficient algorithm for modeling 2D ropes around polygonal obstacles using visibility decompositions, with applications in haptic feedback for surgical robotics.

Contribution

It introduces a new algorithm that simplifies and speeds up 2D rope modeling around obstacles, improving computational efficiency.

Findings

Algorithm runs in linear time O(n)

Visibility decompositions simplify the modeling process

Applicable to real-time haptic feedback systems

Abstract

The problem of modeling ropes arises in many applications, including providing haptic feedback to surgeons who are using surgical robots to realign the distal and proximal ends of split bones. Here, we consider a simplified, 2D variant of the haptic feedback estimation problem and discuss how visibility decompositions greatly simplify the problem. Then, we introduce an efficient, concise algorithm for modeling the dynamics of 2D ropes around polygonal obstacles in O($n$) time, where $n$ is the number of line segment obstacles.