# Reflections in an octagonal mirror maze

@article{Eppstein2022ReflectionsIA, title={Reflections in an octagonal mirror maze}, author={David Eppstein}, journal={ArXiv}, year={2022}, volume={abs/2206.11413} }

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.

## One Citation

### The Complexity of Iterated Reversible Computation

- Computer Science, MathematicsArXiv
- 2021

The deﬁnition is robust against variations in the type of reduction used in it, and in whether it requires f to have a polynomial-time inverse or to be computible by a reversible logic circuit.

## References

SHOWING 1-10 OF 10 REFERENCES

### Directly Visible Pairs and Illumination by Reflections in Orthogonal Polygons

- Mathematics, Computer Science
- 2008

Lower bounds are derived on the combinatorial complexity of the visibility polygon of a point source S after k ≥ 1 specular reflections within special classes of polygons.

### Visibility extension via mirror-edges to cover invisible segments

- Mathematics, Computer ScienceTheor. Comput. Sci.
- 2019

### Visibility with Multiple Reflections

- MathematicsSWAT
- 1996

Abstract. We show that the region lit by a point light source inside a simple n -gon after at most k reflections off the boundary has combinatorial complexity O(n2k) , for any k≥ 1 . A lower bound of…

### Visibility with One Reflection

- MathematicsDiscret. Comput. Geom.
- 1998

A Θ(n2) worst-case bound on the combinatorial complexity of both Vs(S) and Vd( S) is presented and simple O( n2 log2 n) time algorithms for constructing the sets are described.

### Computing k-Link Visibility Polygons in Environments with a Reflective Edge

- Computer ScienceCCCG
- 2011

This paper proposes an optimal linear time algorithm for computing the k-link visibility polygon of an object inside a polygonal environment with a reflective edge called a mirror.

### Algorithms for computing diffuse reflection paths in polygons

- Computer ScienceThe Visual Computer
- 2011

Three different algorithms for constructing a diffuse reflection path from s to t inside a polygon P of n vertices are presented which produce suboptimal paths and the combinatorial approach used in the third algorithm gives a better bound on the number of reflections.

### Narrowing light rays with mirrors

- PhysicsCCCG
- 2001

This work explores whether the rays from a point source can be narrowed by a collection of mirrors, leaving all rays that escape to in-nity with nearly the same direction, in the sense that the angle between any pair is less than > 0.

### Tracing Compressed Curves in Triangulated Surfaces

- Computer ScienceSoCG '12
- 2012

The abstract tracing strategy is applied to two different classes of normal curves: abstract curves represented by normal coordinates, which record the number of intersections with each edge of the surface triangulation, and simple geodesics, represented by a starting point and direction in the local coordinate system of some triangle.

### The Complexity of Iterated Reversible Computation

- Computer Science, MathematicsArXiv
- 2021

The deﬁnition is robust against variations in the type of reduction used in it, and in whether it requires f to have a polynomial-time inverse or to be computible by a reversible logic circuit.