New Computation Techniques for Shape Modeling and Design

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9400823 Cheng The techniques of shape modeling and design will be broadened and improved. Computation techniques that combine interpolation and approximation into a single process (called interproximation) will be developed. The curve and surface representations that will be considered here include B-splines, NURBS, Beta-splines and rational Beta-splines. Different ways of building polynomial (integral) and rational B-spline curves and surfaces as well as their properties when viewed as digital filters will be studied. A general model for the automatic smoothing of sharp corners and edges formed by intersecting parametric surfaces in the design and modeling process will be built. This work will also include filling an n-sided hole with an n-sided patch with n 3. A general model will be developed for the automatic smooth connection of disjoint parametric surfaces. Computational techniques for shape modeling and design are rapidly becoming important tools for modern industrial design and manufacture. Computer models are replacing physical models. They are cheaper to construct, easier to change, and simpler to analyze. Computer-generated images increase productivity by allowing rapid and accurate visualization during design. Applications include the design and manufacture of car bodies, ship hulls, airplane wings, and mechanical parts as well as a large variety of ducts, blends, and fillets. Many important open theoretical and practical issues need to be explored to provide effective tools for industrial design.