Generating Realistic Roofs over a Rectilinear Polygon

  • Hee-Kap Ahn
  • Sang Won Bae
  • Christian Knauer
  • Mira Lee
  • Chan-Su Shin
  • Antoine Vigneron
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7074)

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. 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 a connection with the straight skeleton of P. We show that the maximum possible number of distinct realistic roofs over P is \((n-4)/2 \choose \lfloor(n-4)/4\rfloor\) 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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Hee-Kap Ahn
    • 1
  • Sang Won Bae
    • 2
  • Christian Knauer
    • 3
  • Mira Lee
    • 4
  • Chan-Su Shin
    • 5
  • Antoine Vigneron
    • 6
  1. 1.Department of Computer Science and EngineeringPOSTECHPohangKorea
  2. 2.Department of Computer ScienceKyonggi UniversitySuwonKorea
  3. 3.Institute of Computer ScienceUniversität BayreuthBayreuthGermany
  4. 4.Department of Computer ScienceKAISTDaejeonKorea
  5. 5.Department of Digital and Information EngineeringHankuk University of Foreign StudiesYonginKorea
  6. 6.Geometric Modeling and Scientific Visualization CenterKAUSTThuwalSaudi Arabia

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