A common task in automatically reconstructing a three dimensional city model from its two dimensional map is to compute all the possible roofs over the ground plans. A roof over a simple polygon in the xy-plane is a terrain over the polygon such that each face f of the terrain is supported by a plane passing through at least one polygon edge and making a dihedral angle with the xy-plane [3]. This definition, however, allows roofs with faces isolated from the boundary of the polygon and local minimum edges inducing pools of rainwater. Recently, Ahn et al. [1,2] introduced realistic roofs over a simple rectilinear polygon P with n vertices by imposing two additional constraints under which no isolated faces and no local minimum vertices are allowed. Their definition is, however, too restrictive that it excludes a large number of roofs with no local minimum edges. In this paper, we propose a new definition of realistic roofs corresponding to the class of roofs without isolated faces and local minimum edges. We investigate the geometric and combinatorial properties of realistic roofs and show that the maximum possible number of distinct realistic roofs over P is at most, where. We also present an algorithm that generates all combinatorial representations of realistic roofs. © 2013 Springer-Verlag Berlin Heidelberg.
CITATION STYLE
Sherette, J., & Yoon, S. D. (2013). Realistic roofs over a rectilinear polygon revisited. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 7936 LNCS, pp. 233–244). https://doi.org/10.1007/978-3-642-38768-5_22
Mendeley helps you to discover research relevant for your work.