Describing the geometric difference of architectural forms in three primary shapes of circle, triangle and square

Abstract

ABSTRACT Defining architectural shapes and then clarifying their geometric differences has always been a demanding task.. There appears to be relatively few research papers on the description of the definite geometric properties in architectural shapes. This research proposes methods for quantitatively describing an architectural shape as the degree to which they represent the three primary shapes of circles, triangles and squares. History has ensured that the shapes are regarded as primary ones, but any shape can also be viewed as one of them. A series of automated models that gradually deform the basic shapes into other forms have been developed to identify and verify the best methods for describing the architectural forms. The three architectural shape descriptors, referred to as “circularity”, “triangularity” and “squareness”, produce the second index of “shape deformity”, measuring the degree of how a shape is deformed from the primary shapes. This measurement makes it possible to investigate the degree to which a particular type of primary shape is dominant among those three primary shape descriptions. These shape description techniques were tested on 60 shapes consisting of the facades and floor plans of 30 well-known buildings.