Paul de Casteljau

Paul de Casteljau (19 November 1930 – 24 March 2022) was a French physicist and mathematician. In 1959, while working at Citroën, he developed an algorithm for evaluating calculations on a certain family of curves, which would later be formalized and popularized by engineer Pierre Bézier, leading to the curves widely known as Bézier curves.

He studied at École Normale Supérieure, and worked at Citroën from 1958 until his retirement in 1992. When he arrived there, "Specialists admitted that all electrical, electronic and mechanical problems had more or less been solved. All—except for one single formality which made up for 5%, but certainly not for 20% of the problem; in other words, how to express component parts by equations." A short autobiographic sketch goes back to the early 1990s, a longer autobiography talks about his education and life at Citroën until his retirement.

He continued publishing in retirement, which led to three monographs and ten academic papers, most of his publications written in French.

De Casteljau curves De Casteljau's algorithm is widely used, with some modifications, as it is the most robust and numerically stable method for evaluating polynomials. Other methods, such as Horner's method and forward differencing, are faster for calculating single points but are less robust. De Casteljau's algorithm is still very fast for subdividing a De Casteljau curve or Bézier curve into two curve segments at an arbitrary parametric location.

Further contributions Noteworthy are his contributions beyond geometric modeling, which only became known internationally posthumously

The SMA also quotes Pierre Bézier on de Casteljau's contributions:There is no doubt that Citroën was the first company in France that paid attention to CAD, as early as 1958. Paul de Casteljau, a highly gifted mathematician, devised a system based on the use of Bernstein polynomials. ... the system devised by de Casteljau was oriented towards translating already existing shapes into patches, defined in terms of numerical data. ... Due to Citroën's policy, the results obtained by de Casteljau were not published until 1974, and this excellent mathematician was deprived of part of the well deserved fame that his discoveries and inventions should have earned him. Publications

Paul De Casteljau, Outillage Méthodes Calcul, INPI Enveloppe Soleau No. 40.040, 1959, Citroen Internal Document P2108 Paul De Casteljau, Courbes et Surfaces à Pôles, 1963, Citroen Internal Document P_4147 Mathématiques et CAO. Vol. 2 : Formes à pôles, Hermes, 1986 Shape Mathematics and CAD, KoganPage, London 1986 Les quaternions: Hermès, 1987, ISBN 978-2866011031 Le Lissage: Hermès, 1990 POLynomials, POLar Forms, and InterPOLation, September 1992, In Lychee / Schumaker: Mathematical methods in computer aided geometric design II, Addison-Wesley 1992, pp. 57–68 Polar Forms as Curve and Surface Modeling as used by Citroën, In: Piegl (ed.) Fundamental Developments of Computer-Aided Geometric Modeling, Academic Press, 1993 Splines Focales, In Laurent / Le Méhauté / Schumaker: Curves and Surfaces in Geometric Design, AK Peters 1994, pp. 91–103 Courbes et Profils Esthétiques contre Fonctions Orthogonales (Histoire Vécue), In: Dæhlen, Lyche, Schumaker (eds.) Mathematical Methods for Curves and Surfaces, S. 73-82,1995 La Tolérance d'Usinage chez Citroën dans les Années (19)60, In: Le Méhauté, Rabut, Schumaker (eds.), Curves and Surfaces with Applications in CAGD, S. 69-76, 1997

Intersections et Convergence, In: Laurent, Sablonnière, Schumaker (eds.), Curve and Surface Design: Saint-Malo 1999 In mémoriam Henri de Faget de Casteljau: Son autre passe-temps, la géométrie à travers l'hexagone de Pascal, Procès-verbaux et Mémoires de l'Académie des Sciences, Belles Lettres et Arts de Besançon et de Franche-Comté, Band 193 (1998-1999), S. 91-114, 1999

Au dela du Nombre d'Or, Revue Internationale de CFAO et d'Informatique Graphique, S. 19-31, 2001 Fantastique strophoïde rectangle'', Revue Internationale de CFAO et d'Informatique Graphique, S. 357-370, 2001