Generating realistic roofs over a rectilinear polygon

Type
Conference Paper

Authors
Ahn, Heekap
Bae, Sangwon
Knauer, Christian
Lee, Mira
Shin, Chansu
Vigneron, Antoine E.

KAUST Department
Visual Computing Center (VCC)
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Computer Science Program
Geometric Algorithms Group

Date
2011

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)/4⌋ (n-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(n 4) preprocessing time. We also present an O(n 5)-time algorithm for computing a realistic roof with minimum height or volume. © 2011 Springer-Verlag.

Citation
Ahn, H.-K., Bae, S. W., Knauer, C., Lee, M., Shin, C.-S., & Vigneron, A. (2011). Generating Realistic Roofs over a Rectilinear Polygon. Lecture Notes in Computer Science, 60–69. doi:10.1007/978-3-642-25591-5_8

Publisher
Springer Nature

Journal
Lecture Notes in Computer Science

Conference/Event Name
22nd International Symposium on Algorithms and Computation, ISAAC 2011

DOI
10.1007/978-3-642-25591-5_8

Permanent link to this record
http://hdl.handle.net/10754/564348
Collections
Conference Papers
Computer Science Program
Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division
Visual Computing Center (VCC)