Reflections in an octagonal mirror maze

TL;DR

This paper presents a polynomial-time algorithm to determine the eventual path of a light ray in a complex environment with reflective and non-reflective segments, modeled as an octagonal mirror maze.

Contribution

It introduces an efficient method for analyzing light ray trajectories in environments with mixed reflective properties and complex geometries.

Findings

Algorithm runs in polynomial time

Can handle environments with both reflective and non-reflective segments

Applicable to environments with integer-coordinate segments

Abstract

Suppose we are given an environment consisting of axis-parallel and diagonal line segments with integer endpoints, each of which may be reflective or non-reflective, with integer endpoints, and an initial position for a light ray passing through points of the integer grid. Then in time polynomial in the number of segments and in the number of bits needed to specify the coordinates of the input, we can determine the eventual fate of the reflected ray.