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 STYLE
Ahn, H. K., Bae, S. W., Knauer, C., Lee, M., Shin, C. S., & Vigneron, A. (2011). Generating realistic roofs over a rectilinear polygon. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 7074 LNCS, pp. 60–69). https://doi.org/10.1007/978-3-642-25591-5_8
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