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Show 154 applications. In addition, higher order splines which would have more than the present two kinds of shape parameters could be investigated. Also, the Beta-spline representation could be extended to include the case of non-uniformly spaced or multiple parametriC knot values. Finally, there are additional end and boundary conditions which could be explored for the Beta-spline. Since the Beta-spline is a new representation, it will engender a wide range of future research. From a mathematical pOint of view, the fundamental approximation theoretic implications of the Beta-spline have yet to be explored. For example, it would be of interest to derive the variational principle which corresponds to the Beta-spline. For computer graphiCS, rendering algorithms for the creation and display of Beta-spline objects will be developed. In the computer aided design field, its utility as a three-dimensional object representation should be investigated. In terms of hardware, it would be very desirable to design evaluation and perturbation algorithms using parallel processing techniques and to build a "Beta-spline box" based on this multiprocessor architecture. A particularly likely direction of immediate research would be the development of subdivision techniques for Beta-splines. The technique of subdivision has been employed in computer aided geometric design and modeling to provide good design handles, and in computer graphics to generate smooth models for display in a kind of di vide and conquer approach [21]. The combination of the geometriC nature of this technique with shape control via the shape parameters as well as the presence of |
