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.
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Submitted on : Wednesday, March 2, 2016 - 8:44:43 AM
Last modification on : Thursday, March 15, 2018 - 4:56:06 PM

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Marc Daniel, Jean-Claude Daubisse. The numerical problem of using Bézier curves and surfaces in the power basis. Computer Aided Geometric Design, Elsevier, 1989, 6 (2), pp.121-128. ⟨10.1016/0167-8396(89)90015-0⟩. ⟨hal-01281358⟩

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