Automatic constraint-based synthesis of non-uniform rational B-spline surfaces

In this dissertation a technique for the synthesis of sculptured surface models subject to several constraints based on design and manufacturability requirements is presented. A design environment is specified as a collection of polyhedral models which represent components in the vicinity of the surface to be designed, or regions which the surface should avoid. Non-uniform rational B-splines (NURBS) are used for surface representation, and the control point locations are the design variables. For some problems the NURBS surface knots and/or weights are included as additional design variables. The primary functional constraint is a proximity metric which induces the surface to avoid a tolerance envelope around each component. Other functional constraints include: an area/arc-length constraint to counteract the expansion effect of the proximity constraint, orthogonality and parametric flow constraints (to maintain consistent surface topology and improve machinability of the surface), and local constraints on surface derivatives to exploit part symmetry. In addition, constraints based on surface curvatures may be incorporated to enhance machinability and induce the synthesis of developable surfaces;The surface synthesis problem is formulated as an optimization problem. Traditional optimization techniques such as quasi-Newton, Nelder-Mead simplex and conjugate gradient, yield only locally good surface models. Consequently, simulated annealing (SA), a global optimization technique is implemented. SA successfully synthesizes several highly multimodal surface models where the traditional optimization methods failed. Results indicate that this technique has potential applications as a conceptual design tool supporting concurrent product and process development methods