A uniform characterization of augmented shapes. (May 2019) - Stouffs, Rudi; Krishnamurti, Ramesh
Abstract: Shapes are considered as finite arrangements of spatial elements from among points, line and plane segments, circles and ellipses, (circular) arcs, quadratic Bezier curves, of limited but non-zero measure, in 2D and 3D. Augmented shapes are defined as shapes augmented with attributes, e.g., labels, weights, colors, enumerative values, and (parametric) descriptions. Different attribute types specify different behaviors under operations of sum, product and difference and a part relationship. We review different shape–attribute propositions from the shape grammar literature and characterize them uniformly. This uniform characterization of augmented shapes is intended to assist in formalizing new shape–attribute propositions that may have been visually conceived. Highlights: A uniform characterization of different shape-attribute propositions is presented. A uniform description of the behavior of shapes with attributes is proposed. Characterizations of attribute types and spatial element types are almost uniform.