This dissertation is concerned with curve and surface modelling. In the past, curves and surfaces were modeled by first making wooden models, from which the final results were obtained by means of'copy-milling'. Since the early 1960s, people have started to use computers to support the design of curves and surfaces. The increasing computing power and the increasing potential of graphical hardware in the last decade has opened many new possibilities for Computer Aided Geometric Design (CAGD). Especially the field of curve and surface modelling is rapidly evolving. This is reflected in the recently started series called'Geometric Design Publications'that contains several books on curve and surface modelling. The most important applications of curve and surface modelling are found in industrial design, for instance in the automobile, aerospace and shipbuilding industries. An often encountered application is the interpolation and approximation of data with B-splines and Bézier curves and surfaces or other representation schemes. Another related application is variational curve and surface modelling, where one is looking for smooth curves and surfaces that satisfy a number of geometric constraints
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