Journal articles
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.
https://hal-amu.archives-ouvertes.fr/hal-01281358
Contributor : Marc Daniel <>
Submitted on : Wednesday, March 2, 2016 - 8:44:43 AM
Last modification on : Monday, March 30, 2020 - 8:44:11 AM
Contributor : Marc Daniel <>
Submitted on : Wednesday, March 2, 2016 - 8:44:43 AM
Last modification on : Monday, March 30, 2020 - 8:44:11 AM
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