A conceptual framework for deriving and analyzing the geometric structures of orthogonal architectural compositions in plan

This paper introduces a conceptual framework for the analysis and generation of the underlying geometry of orthogonal architectural compositions in plan. The proposed framework has three interrelated objectives: (1) to allow the systematic analysis and derivation of the geometric structures of orthogonal architectural compositions in plan, (2) to describe the spatial relations among their constituent elements, and (3) to enumerate the morphological operations involved creating these relations. It comprises of a grammatical formalism and two data structures. The grammatical formalism allows the systematic derivation and analysis of the geometric structures of architectural compositions in plan. The first data structure is a table that enumerates the rules used to derive and/or analyze geometric structures and the sequence of their application. The second data structure is a binary tree that represents the spatial relations between the shapes produced during these processes