Rectangular Shapes

Abstract

Architectural plans whose walls lie along two perpendicular directions are represented by rectangular shapes. The rectangular shapes are classified according to the types of endpoints and the intersection of their component maximal lines. Shape grammars are used to construct members of the classes. The latter part of the paper (sections 5–10) examines the incidence structures among the maximal lines and regions in trivalent rectangular shapes. These are represented by planar maps. First, the maximal line adjacency is considered, followed by two successive ornamentations: the region-maximal line incidence and the oriented region-maximal incidence. Finally, the region adjacency is considered, and its relation to the other incidence structures examined. In each case the incidence structures are characterized.