On the number of views of polyhedral scenes

Boris Aronov, Hervé Brönnimann, Dan Halperin, Robert Schiffenbauer

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Abstract

    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.

    Original languageEnglish (US)
    Title of host publicationDiscrete and Computational Geometry - Japanese Conference, JCDCG 2000, Revised Papers
    PublisherSpringer Verlag
    Pages81-90
    Number of pages10
    Volume2098
    ISBN (Print)9783540477389
    StatePublished - 2001
    EventJapanese Conference on Discrete and Computational Geometry, JCDCG 2000 - Tokyo, Japan
    Duration: Nov 22 2000Nov 25 2000

    Publication series

    NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    Volume2098
    ISSN (Print)03029743
    ISSN (Electronic)16113349

    Other

    OtherJapanese Conference on Discrete and Computational Geometry, JCDCG 2000
    CountryJapan
    CityTokyo
    Period11/22/0011/25/00

    Fingerprint

    Lower bound
    Distinct
    Convex polyhedron
    Silhouette
    Straight Line

    ASJC Scopus subject areas

    • Computer Science(all)
    • Theoretical Computer Science

    Cite this

    Aronov, B., Brönnimann, H., Halperin, D., & Schiffenbauer, R. (2001). On the number of views of polyhedral scenes. In 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.

    Discrete and Computational Geometry - Japanese Conference, JCDCG 2000, Revised Papers. Vol. 2098 Springer Verlag, 2001. p. 81-90 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2098).

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Aronov, B, Brönnimann, H, Halperin, D & Schiffenbauer, R 2001, On the number of views of polyhedral scenes. in 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.
    Aronov B, Brönnimann H, Halperin D, Schiffenbauer R. On the number of views of polyhedral scenes. In Discrete and Computational Geometry - Japanese Conference, JCDCG 2000, Revised Papers. Vol. 2098. Springer Verlag. 2001. p. 81-90. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
    Aronov, Boris ; Brönnimann, Hervé ; Halperin, Dan ; Schiffenbauer, Robert. / On the number of views of polyhedral scenes. Discrete and Computational Geometry - Japanese Conference, JCDCG 2000, Revised Papers. Vol. 2098 Springer Verlag, 2001. pp. 81-90 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
    @inproceedings{e9df914e351d43e0b1e6e6abd684e670,
    title = "On the number of views of polyhedral scenes",
    abstract = "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.",
    author = "Boris Aronov and Herv{\'e} Br{\"o}nnimann and Dan Halperin and Robert Schiffenbauer",
    year = "2001",
    language = "English (US)",
    isbn = "9783540477389",
    volume = "2098",
    series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
    publisher = "Springer Verlag",
    pages = "81--90",
    booktitle = "Discrete and Computational Geometry - Japanese Conference, JCDCG 2000, Revised Papers",
    address = "Germany",

    }

    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 -