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G. P. Bonneau and H. H agen
Pages 8

The purpose of Computer Aided Geometric Design (CAGD) is to define some mathematical modelling of free-form curves and surfaces, to study their prop­ erties, and to improve their quality. The Bezier and B-splines curves and surfaces were first based on polynomial parametric equations. The wish to give more freedom to the designer has led to the generalization of polynomial schemes to rational functions. The use of rational functions in CAGD began in the late 70’s. Rational B-splines (also called NURBS, short for non-uniform rational B-splines) are becoming now a standard in CAD technology (see [i])- The flexibility of these curves and surfaces is achieved through the assignment of a scalar (called weight) to each control point. If a weight increases while the others remain constant, the curve or surface is pulled in the direction of the corresponding control point. The increase in flexibility (in particular the abil­ ity to exactly describe conics) is paid by an increased complexity of already known algorithms (e.g. the evaluation of derivatives), but has also brought new algorithms (for instance the reparameterization of rational curves , see

This paper deals with the rational counterpart of the Bezier schemes: the rational Bezier curves, the rational rectangular Bezier patches, and the rational triangular Bezier patches.