### Abstract

We extend the concept of the polygon visible from a source point S in a simple polygon by considering visibility with two types of reflection, specular and diffuse. In specular reflection a light ray reflects from an edge of the polygon according to Snell's law: the angle of incidence equals the angle of reflection. In diffuse reflection a light ray reflects from an edge of the polygon in all inward directions. Several geometric and combinatorial properties of visibility polygons under these two types of reflection are revealed, when at most one reflection is permitted. We show that the visibility polygon Vs(S) under specular reflection may be non-simple, while the visibility polygon Vd(S) under diffuse reflection is always simple. We present a 9(n^{2}) worst case bound on the combinatorial complexity of both Vs(S) and Vd(S) and describe simple 0(n^{2} log^{2} n) time algorithms for constructing the sets.

Original language | English (US) |
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Title of host publication | Proceedings of the 11th Annual Symposium on Computational Geometry, SCG 1995 |

Publisher | Association for Computing Machinery |

Pages | 316-325 |

Number of pages | 10 |

Volume | Part F129372 |

ISBN (Electronic) | 0897917243 |

DOIs | |

State | Published - Sep 1 1995 |

Event | 11th Annual Symposium on Computational Geometry, SCG 1995 - Vancouver, Canada Duration: Jun 5 1995 → Jun 7 1995 |

### Other

Other | 11th Annual Symposium on Computational Geometry, SCG 1995 |
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Country | Canada |

City | Vancouver |

Period | 6/5/95 → 6/7/95 |

### Fingerprint

### ASJC Scopus subject areas

- Theoretical Computer Science
- Geometry and Topology
- Computational Mathematics

### Cite this

*Proceedings of the 11th Annual Symposium on Computational Geometry, SCG 1995*(Vol. Part F129372, pp. 316-325). Association for Computing Machinery. https://doi.org/10.1145/220279.220313

**Visibility with reflection.** / Aronov, Boris; Davis, Alan R.; Dey, Tamal K.; Pal, Sudebkumar P.; Prasad, D. Chithra.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the 11th Annual Symposium on Computational Geometry, SCG 1995.*vol. Part F129372, Association for Computing Machinery, pp. 316-325, 11th Annual Symposium on Computational Geometry, SCG 1995, Vancouver, Canada, 6/5/95. https://doi.org/10.1145/220279.220313

}

TY - GEN

T1 - Visibility with reflection

AU - Aronov, Boris

AU - Davis, Alan R.

AU - Dey, Tamal K.

AU - Pal, Sudebkumar P.

AU - Prasad, D. Chithra

PY - 1995/9/1

Y1 - 1995/9/1

N2 - We extend the concept of the polygon visible from a source point S in a simple polygon by considering visibility with two types of reflection, specular and diffuse. In specular reflection a light ray reflects from an edge of the polygon according to Snell's law: the angle of incidence equals the angle of reflection. In diffuse reflection a light ray reflects from an edge of the polygon in all inward directions. Several geometric and combinatorial properties of visibility polygons under these two types of reflection are revealed, when at most one reflection is permitted. We show that the visibility polygon Vs(S) under specular reflection may be non-simple, while the visibility polygon Vd(S) under diffuse reflection is always simple. We present a 9(n2) worst case bound on the combinatorial complexity of both Vs(S) and Vd(S) and describe simple 0(n2 log2 n) time algorithms for constructing the sets.

AB - We extend the concept of the polygon visible from a source point S in a simple polygon by considering visibility with two types of reflection, specular and diffuse. In specular reflection a light ray reflects from an edge of the polygon according to Snell's law: the angle of incidence equals the angle of reflection. In diffuse reflection a light ray reflects from an edge of the polygon in all inward directions. Several geometric and combinatorial properties of visibility polygons under these two types of reflection are revealed, when at most one reflection is permitted. We show that the visibility polygon Vs(S) under specular reflection may be non-simple, while the visibility polygon Vd(S) under diffuse reflection is always simple. We present a 9(n2) worst case bound on the combinatorial complexity of both Vs(S) and Vd(S) and describe simple 0(n2 log2 n) time algorithms for constructing the sets.

UR - http://www.scopus.com/inward/record.url?scp=0038850747&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0038850747&partnerID=8YFLogxK

U2 - 10.1145/220279.220313

DO - 10.1145/220279.220313

M3 - Conference contribution

AN - SCOPUS:0038850747

VL - Part F129372

SP - 316

EP - 325

BT - Proceedings of the 11th Annual Symposium on Computational Geometry, SCG 1995

PB - Association for Computing Machinery

ER -