### 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 |

Editors | Jin Akiyama, Mikio Kano, Masatsugu Urabe |

Publisher | Springer Verlag |

Pages | 81-90 |

Number of pages | 10 |

ISBN (Print) | 9783540477389 |

DOIs | |

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) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### 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 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Discrete and Computational Geometry - Japanese Conference, JCDCG 2000, Revised Papers*(pp. 81-90). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2098). Springer Verlag. https://doi.org/10.1007/3-540-47738-1_6