Generative geometric design and boundary solid grammars

Abstract: "This proposal introduces boundary solid grammars, a formalism for generating complex models of rigid solid objects. Solids are represented by their boundary elements, i.e. vertices, edges and facts, with coordinate geometry associated with the vertices. Labels may be associated with any of these elements. Rules match conditions of a solid or collection of solids and may modify them or create additional solids. A boundary solid grammar uses an initial solid and a set of rules to produce a language of solid models. Unary operations are introduced to ensure the validity of the boundary representations.These operations take models that may have self-intersections, interpret the models considering the given geometry and face orientations, and produce valid models. The unary operations allow the use of boolean operations together with Euler, sweeping, tweaking and gluing operations in a unified, valid scheme. The proposed formalism has been implemented. Grammars have been demonstrated that generate simple geometric forms including snowflakes, recursive octahedrons, 'fractal' mountains, and spirals. Queen Anne houses have been characterized in a more extensive grammar."