The numerical problem of using Bézier curves and surfaces in the power basis

Abstract The computations of curves and surfaces points for CAD modeling are numerous and important. In the case of modeling using the Be´zier method, these may be achieved either with the De Casteljau algorithm in the Bernstein basis, or with the Horner algorithm in the power basis. The De Casteljau algorithm requires a greater number of operations than Horner's. However, we show that the equations of curves and surfaces in the power basis may be affected by a very important loss of significant digits on the polynomials coefficient; this is due to the required conversion matrices which are ill-conditioned. Examples are given. We conclude that the use of the Horner algorithm should be avoided for the computations of curves and surfaces points with the Be´zier method.