Reflections in an octagonal mirror maze
David Eppstein

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.
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Taxonomy
TopicsDigital Image Processing Techniques · Computational Geometry and Mesh Generation · Computer Graphics and Visualization Techniques
