Reflections in an octagonal mirror maze.
D. Eppstein.
arXiv:2206.11413.
34th Canadian Conference on Computational Geometry, 2022, pp. 129–134.
For two-dimensional scenes consisting of mirrors and opaque walls that are either axis-parallel or with slope ±1, with integer endpoints, it is possible to determine the eventual destination of rational light rays in time polynomial in the description complexity of the scene, even though the number of reflections before a ray reaches this destination may be exponential. The solution involves transforming the problem into one involving interval exchange transformations and from there into another problem involving normal curves on topological surfaces.
(CCCG'22 reflection slides – Blog post: Reflections in an octagonal mirror maze)