Numerically robust computation of circular visibility

TL;DR

This paper introduces a simple, efficient, and numerically stable linear-time algorithm to determine if a point inside a domain is circularly visible from a boundary arc, with an easy-to-check non-visibility criterion.

Contribution

It presents a novel linear-time algorithm for circular visibility computation and a practical criterion for non-visibility, improving robustness and simplicity.

Findings

Algorithm runs in linear time

Provides a practical non-visibility criterion

Ensures numerical stability in computations

Abstract

We address the question of whether a point inside a domain bounded by a simple closed arc spline is circularly visible from a specified arc from the boundary. We provide a simple and numerically stable linear time algorithm that solves this problem. In particular, we present an easy-to-check criterion that implies that a point is not visible from a specified boundary arc.