# An Algorithm for Computing Constrained Reflection Paths in Simple Polygon

@article{Bishnu2013AnAF, title={An Algorithm for Computing Constrained Reflection Paths in Simple Polygon}, author={Arijit Bishnu and Subir Kumar Ghosh and Partha P. Goswami and Sudebkumar Prasant Pal and Swami Sarvattomananda}, journal={ArXiv}, year={2013}, volume={abs/1304.4320} }

Let $s$ be a source point and $t$ be a destination point inside an $n$-vertex simple polygon $P$. Euclidean shortest paths and minimum-link paths between $s$ and $t$ inside $P$ have been well studied. Both these kinds of paths are simple and piecewise-convex. However, computing optimal paths in the context of diffuse or specular reflections does not seem to be an easy task. A path from a light source $s$ to $t$ inside $P$ is called a diffuse reflection path if the turning points of the path lie…

## 3 Citations

### Diffuse Reflection Radius in a Simple Polygon

- MathematicsAlgorithmica
- 2015

It is shown that every simple polygon in general position with n walls can be illuminated from a single point light source after at most at least four diffuse reflections, and this bound is the best possible.

### On the Complexity of Minimum-Link Path Problems

- Computer Science, MathematicsSoCG
- 2016

It is proved that computing the minimum-link diffuse reflection path, motivated by ray tracing in computer graphics, is NP-hard, even for two-dimensional polygonal domains with holes.

### On the complexity of minimum-link path problems

- Computer Science, MathematicsJ. Comput. Geom.
- 2017

The minimum-link diffuse reflection path is proved to be NP-hard, even for two-dimensional polygonal domains with holes, and the open problem from [Mitchell et al.'1992] mentioned in the handbook and The Open Problems Project is resolved.

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