### Abstract

It is known that a scene consisting of A- convex polyhedra of total complexity n has at most 0(n^{4} k^{2}) distinct orthographic views, and that the number of such views is Ω((nk^{2} + n^{2})^{2}) in the worst case. The corresponding bounds for perspective views are 0(n^{6} k^{3}) and Ω((nk^{2}+n^{2})^{3}), respectively. In this paper, we close these gaps by improving the lower bounds. We construct an example of a scene with Ө(n^{4} k^{2}) orthographic views, and another with Ө(n^{6} k^{3}) perspective views. Our construction can also be used to improve the known lower bounds for the number of silhouette views and for the number of distinct views from a viewpoint moving along a straight line.

Original language | English (US) |
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Title of host publication | Discrete and Computational Geometry - Japanese Conference, JCDCG 2000, Revised Papers |

Publisher | Springer Verlag |

Pages | 81-90 |

Number of pages | 10 |

Volume | 2098 |

ISBN (Print) | 9783540477389 |

State | Published - 2001 |

Event | Japanese Conference on Discrete and Computational Geometry, JCDCG 2000 - Tokyo, Japan Duration: Nov 22 2000 → Nov 25 2000 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 2098 |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | Japanese Conference on Discrete and Computational Geometry, JCDCG 2000 |
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Country | Japan |

City | Tokyo |

Period | 11/22/00 → 11/25/00 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science(all)
- Theoretical Computer Science

### Cite this

*Discrete and Computational Geometry - Japanese Conference, JCDCG 2000, Revised Papers*(Vol. 2098, pp. 81-90). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2098). Springer Verlag.

**On the number of views of polyhedral scenes.** / Aronov, Boris; Brönnimann, Hervé; Halperin, Dan; Schiffenbauer, Robert.

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

*Discrete and Computational Geometry - Japanese Conference, JCDCG 2000, Revised Papers.*vol. 2098, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 2098, Springer Verlag, pp. 81-90, Japanese Conference on Discrete and Computational Geometry, JCDCG 2000, Tokyo, Japan, 11/22/00.

}

TY - GEN

T1 - On the number of views of polyhedral scenes

AU - Aronov, Boris

AU - Brönnimann, Hervé

AU - Halperin, Dan

AU - Schiffenbauer, Robert

PY - 2001

Y1 - 2001

N2 - It is known that a scene consisting of A- convex polyhedra of total complexity n has at most 0(n4 k2) distinct orthographic views, and that the number of such views is Ω((nk2 + n2)2) in the worst case. The corresponding bounds for perspective views are 0(n6 k3) and Ω((nk2+n2)3), respectively. In this paper, we close these gaps by improving the lower bounds. We construct an example of a scene with Ө(n4 k2) orthographic views, and another with Ө(n6 k3) perspective views. Our construction can also be used to improve the known lower bounds for the number of silhouette views and for the number of distinct views from a viewpoint moving along a straight line.

AB - It is known that a scene consisting of A- convex polyhedra of total complexity n has at most 0(n4 k2) distinct orthographic views, and that the number of such views is Ω((nk2 + n2)2) in the worst case. The corresponding bounds for perspective views are 0(n6 k3) and Ω((nk2+n2)3), respectively. In this paper, we close these gaps by improving the lower bounds. We construct an example of a scene with Ө(n4 k2) orthographic views, and another with Ө(n6 k3) perspective views. Our construction can also be used to improve the known lower bounds for the number of silhouette views and for the number of distinct views from a viewpoint moving along a straight line.

UR - http://www.scopus.com/inward/record.url?scp=84974717485&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84974717485&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84974717485

SN - 9783540477389

VL - 2098

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 81

EP - 90

BT - Discrete and Computational Geometry - Japanese Conference, JCDCG 2000, Revised Papers

PB - Springer Verlag

ER -