The numerical problem of using Bézier curves and surfaces in the power basis - Aix-Marseille Université Access content directly
Journal Articles Computer Aided Geometric Design Year : 1989

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

Jean-Claude Daubisse
  • Function : Author

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.

Domains

Other [cs.OH]

Dates and versions

hal-01281358 , version 1 (02-03-2016)

Identifiers

Cite

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

Altmetric

Share

Gmail Facebook X LinkedIn More