Paul de Casteljau

Paul de Casteljau (born 1930 in Besançon, France), a physicist and mathematician at Citroën, developed an algorithm for computation of a Bézier curve, in 1959. Author of the book Mathématiques et CAO. Vol. 2: Formes à pôles from Hermes. De Casteljau's algorithm is widely used although it might have gone through some modifications. De Casteljau's algorithm is the most robust and numerically stable method for evaluating polynomials, though it is slower for computing a single point than other methods, such as Horner's method (faster, less robust) and forward differencing (fastest, least robust). However, De Casteljau's algorithm is still very fast for subdiving a Bézier curve into two curve segments at an arbitrary parametric location.

[edit] References

• (French) Paul de Casteljau, Courbes à pôles, INPI, 1959^{[clarify (if this is a patent, the number would be welcome)]}
• (French) Paul de Casteljau, Surfaces à pôles, INPI, 1963^{[clarify (if this is a patent, the number would be welcome)]}
• (French) Mathématiques et CAO. Vol. 2 : Formes à pôles, Hermes, 1986
• (French) Les quaternions: Hermes, 1987
• (French) Le Lissage: Hermes, 1990
• POLoynomials, POLar Forms, and InterPOLation, September 1992, Mathematical methods in computer aided geometric design II, Academic Press Professional, Inc.
• Andreas Müller, "Neuere Gedanken des Monsieur Paul de Faget de Casteljau", 1995
• de Casteljau's autobiography: My time at Citroën (August 1999) Computer Aided Geometric Design 16(7):583–586

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