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dc.contributor.authorAhn, Heekap
dc.contributor.authorBae, Sangwon
dc.contributor.authorKnauer, Christian
dc.contributor.authorLee, Mira
dc.contributor.authorShin, Chansu
dc.contributor.authorVigneron, Antoine E.
dc.date.accessioned2015-08-03T11:34:45Z
dc.date.available2015-08-03T11:34:45Z
dc.date.issued2013-11
dc.identifier.citationAhn, 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
dc.identifier.issn09257721
dc.identifier.doi10.1016/j.comgeo.2013.06.002
dc.identifier.urihttp://hdl.handle.net/10754/563055
dc.description.abstractGiven 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.
dc.description.sponsorshipWork 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.
dc.publisherElsevier BV
dc.subjectEnumeration algorithm
dc.subjectRealistic roof
dc.subjectRectilinear polygon
dc.subjectStraight skeleton
dc.titleRealistic roofs over a rectilinear polygon
dc.typeArticle
dc.contributor.departmentVisual Computing Center (VCC)
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentComputer Science Program
dc.contributor.departmentGeometric Algorithms Group
dc.identifier.journalComputational Geometry
dc.contributor.institutionDepartment of Computer Science and Engineering, POSTECH, Pohang, South Korea
dc.contributor.institutionDepartment of Computer Science, Kyonggi University, Suwon, South Korea
dc.contributor.institutionInstitute of Computer Science, Universität Bayreuth, 95440 Bayreuth, Germany
dc.contributor.institutionDepartment of Computer Science, KAIST, Daejeon, South Korea
dc.contributor.institutionDepartment of Digital and Information Engineering, Hankuk University of Foreign Studies, Yongin, South Korea
kaust.personVigneron, Antoine E.


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