Qualitative Approach to Designing a Class of Geometries

We consider the problem of creative geometric design: i.e. creating a shape that can represent a class of geometries, either by varying parameters associated with the boundary data, or by changing aspects of the shape itself. The model of shape we use is based on subdividing the dis-cretizations in qualitative spatial reasoning, called Qualitative Subdivision Algebra, resulting in a nal resolution that can be reened over the course of the design process. By changing the model of shape, the design can be made to fullll diierent levels of functional demand. It is said that 80% of the design value is locked up in the initial design shape or template. Qualitative models for design rarely address spatial aspects in suucient detail, and when they do, they rely on quantitative substrate to construct and work with that data. Today's CAD systems suuer from the weakness that a) they cannot model the abstract geometries that convey conceptual designs, and b) they do not have a mechanism for modeling the constraints that lead eventually to the nal design. The former makes it impossible to perform conceptual design, and the latter makes it diicult to edit the design later, when the basic functional constraints typically have to be regenerated. In this work we present a method for 1. modeling the conceptual uncertainties using a Hybrid Qualitative Spatial Model, and providing visual feedback during the stage when the geometry is not well-deened. 2. obtaining a parametrization for the design template 3. instantiating the parameters with a set of values for fulllling speciic level of functionality. Thus, this is a vertically integrated work, starting from the ambiguous geometries that need to be modeled at the design phase, and ending with a fully instantiated design model. The design constraints are stored in a Parameter Constraint Digraph, which provides valuable information for any editing that may take place subsequently. We use the design of a crankshaft to highlight the basic ideas behind the method, and show how 1 diiering initial templates lead to diierent popular crankshafts used in India today.