Mixed geometric-topological representation for electromechanical design

Abstract

Avoiding unintended representational commitments is a key challenge in generative design. We have developed a mixed geometric-topological representation based on CW-complexes, which represents structure and geometric constraints such that commitments regarding position and layout are latebinding and resolve only during the evaluation of a design instance. Complicated designs can be elaborated into a full representation using a small number of biologically-inspired developmental operators. We illustrate the new representation with a number of examples of electromechanical design. MOTIVATIONA key challenge in generative design is to find representations that allow smooth navigation of the design space. Natural biological organisms, which are remarkably adaptable both as individuals and in evolving populations over time, derive much of their adaptability from the process of morphogenesis [4,8], in which the basic topological structures and relations laid out in these early stages of development then persist throughout development, even as the various body parts and organs assume their full-grown dimensions.Prior development-inspired representations for electromechanical design (e.g., [7, 3, 6, 5, 2]) represent topological relations and constraints implicitly, through the geometric simulation of development. This is often computationally expensive, and in many cases results in unintended dependencies or representational commitments imposed by the progress of a design through intermediate forms on its way to a "mature" state where the design can be evaluated.We propose instead to base a representation on topology and attach geometric parameters and constraints to this model only as they become relevant, creating a "latebinding" geometry that preserves flexibility and symmetry * Sponsored by DARPA under contract W91CRB-11-C-0052; views and conclusions contained in this document are those of the authors and not DARPA or the U.S. Gov't. ACM 978-1-4503-1964-5/13/07. except where explicitly broken and allows constraints and dependent parameters to be specified implicitly. HYBRID REPRESENTATIONWe have developed a hybrid topological-geometric representation in four layers of objects and directed binary relations. The foundation layer is a construct of topological cells, specifying the collection of geometric components making up a design and their attachment and containment relations. We based this on a topological object known as a CW-complex [9], a topological cousin to familiar geometric engineering constructs such as the polygonal mesh and thus a natural fit for representing electromechanical designs.To this topological base, we attach numerical parameters and measurements. In some cases, these parameters represent aspects of geometry, and thereby add constraint to the topology, while in other cases they associate other types of specification information (e.g., material properties). Each parameter's units are specified, though its value is not set at this layer of the representation.The third layer is a collection of ...