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    Realistic roofs over a rectilinear polygon

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    Type
    Article
    Authors
    Ahn, Heekap
    Bae, Sangwon
    Knauer, Christian
    Lee, Mira
    Shin, Chansu
    Vigneron, Antoine E. cc
    KAUST Department
    Visual Computing Center (VCC)
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Computer Science Program
    Geometric Algorithms Group
    Date
    2013-11
    Permanent link to this record
    http://hdl.handle.net/10754/563055
    
    Metadata
    Show full item record
    Abstract
    Given a simple rectilinear polygon P in the xy-plane, a roof over P is a terrain over P whose faces are supported by planes through edges of P that make a dihedral angle π/4 with the xy-plane. According to this definition, some roofs may have faces isolated from the boundary of P or even local minima, which are undesirable for several practical reasons. In this paper, we introduce realistic roofs by imposing a few additional constraints. We investigate the geometric and combinatorial properties of realistic roofs and show that the straight skeleton induces a realistic roof with maximum height and volume. We also show that the maximum possible number of distinct realistic roofs over P is ((n-4)(n-4)/4 /2⌋) when P has n vertices. We present an algorithm that enumerates a combinatorial representation of each such roof in O(1) time per roof without repetition, after O(n4) preprocessing time. We also present an O(n5)-time algorithm for computing a realistic roof with minimum height or volume. © 2013 Elsevier B.V.
    Citation
    Ahn, H.-K., Bae, S. W., Knauer, C., Lee, M., Shin, C.-S., & Vigneron, A. (2013). Realistic roofs over a rectilinear polygon. Computational Geometry, 46(9), 1042–1055. doi:10.1016/j.comgeo.2013.06.002
    Sponsors
    Work by Ahn was supported by the National Research Foundation of Korea grant funded by the Korean Government (MEST) (NRF-2010-0009857). Work by Bae was supported by National Research Foundation of Korea (NRF) grant funded by the Korean Government (MEST) (No. 2011-0005512). Work by Shin was supported by research grant funded by Hankuk University of Foreign Studies.
    Publisher
    Elsevier BV
    Journal
    Computational Geometry
    DOI
    10.1016/j.comgeo.2013.06.002
    ae974a485f413a2113503eed53cd6c53
    10.1016/j.comgeo.2013.06.002
    Scopus Count
    Collections
    Articles; Computer Science Program; Visual Computing Center (VCC); Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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