The numerical problem of using Be´zier curves and surfaces in the power basis

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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.

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