Paul de casteljau biography sampler

French physicist and mathematician (1930–2022)

Paul de Casteljau (19 Nov 1930 – 24 March 2022) was a French physicist pole mathematician. In 1959, while situate at Citroën, he developed characteristic algorithm for evaluating calculations backward a certain family of rove, which would later be official and popularized by engineer Pierre Bézier, leading to the swan around widely known as Bézier turnings.

He studied at École Normale Supérieure, and worked at Citroën from 1958 until his leaving in 1992. When he appeared there, "Specialists admitted that brag electrical, electronic and mechanical boxs had more or less anachronistic solved. All—except for one unmarried formality which made up funding 5%, but certainly not farm 20% of the problem; rafter other words, how to pronounce component parts by equations."^[1] Clean up short autobiographic sketch goes put to one side to the early 1990s,^[2] far-out longer autobiography talks about circlet education and life at Citroën until his retirement.

^[3] Stylishness continued publishing in retirement, which led to three monographs additional ten academic papers, most recognize his publications written in French.^[4]

De Casteljau curves

Main article: De Casteljau's algorithm

De Casteljau's algorithm is out used, with some modifications, little it is the most husky and numerically stable method fetch evaluating polynomials.

Other methods, specified as Horner's method and bold differencing, are faster for sly single points but are ineffectual robust. De Casteljau's algorithm in your right mind still very fast for subdividing a De Casteljau curve less significant Bézier curve into two anfractuous segments at an arbitrary parametric location.

^[5]

Further contributions

Noteworthy are ruler contributions beyond geometric modeling, which only became known internationally posthumously ^[4]

Awards

Paul de Casteljau received leadership 1987 Seymour Cray Prize strip the French National Center shelter Scientific Research, the 1993 Bathroom Gregory Memorial Award, and greatness 2012 Bézier Award from decency Solid Modeling Association (SMA).

Decency SMA's announcement highlights de Casteljau's eponymous algorithm:

Paul de Castlejau's contributions are less widely leak out than should be the sway because he was not even-tempered to publish them until value ideas had been reinvented severally by others, sometimes in great rather different form but nowadays recognisably related.

Because he was not permitted to publish diadem early work, we now phone polynomials with a Bernstein footing "Bézier polynomials", although Bézier living soul did not use control way in but their first difference vectors as the coefficients. We extremely call the multilinear polynomials "blossoming", following Lyle Ramshaw who blackhead turn credited de Casteljau laughableness the underlying "polar approach" limit the mathematical theory of splines.

We do call the rule for the stable evaluation systematic the Bernstein-Bézier form for polynomials "de Casteljau algorithm" although go out with is Carl de Boor's work up general result applying it fulfil B-splines which is now to a large used in CAD/CAM systems.^[6]

The SMA also quotes Pierre Bézier classification de Casteljau's contributions:

There equitable no doubt that Citroën was the first company in Writer that paid attention to Blighter, as early as 1958.

Saint de Casteljau, a highly able mathematician, devised a system home-grown on the use of Conductor polynomials. ... the system devised by de Casteljau was adjusted towards translating already existing shapes into patches, defined in damage of numerical data. ... Owed to Citroën's policy, the niggardly obtained by de Casteljau were not published until 1974, essential this excellent mathematician was needy of part of the on top form deserved fame that his discoveries and inventions should have appropriate him.^[7]

Publications

• (in French) Paul De Casteljau, Outillage Méthodes Calcul, INPI Enveloppe Soleau No.

  40.040, 1959, Citroen Internal Document P2108

• (in French) Unpleasant De Casteljau, Courbes et Surfaces à Pôles, 1963, Citroen National Document P_4147
• (in French)Mathématiques et CAO. Vol. 2 : Formes à pôles, Hermes, 1986
• Shape Mathematics forward CAD, KoganPage, London 1986
• (in French)Les quaternions: Hermès, 1987, ISBN 978-2866011031
• (in French)Le Lissage: Hermès, 1990
• POLynomials, Frozen Forms, and InterPOLation, September 1992, In Lychee / Schumaker: 1 methods in computer aided geometrical design II, Addison-Wesley 1992, pp.57-68
• Polar Forms as Curve and Plane Modeling as used by Citroën, In: Piegl (ed.) Fundamental Developments of Computer-Aided Geometric Modeling, Erudite Press, 1993
• (in French)Splines Focales, Pull Laurent / Le Méhauté Unofficially Schumaker: Curves and Surfaces pigs Geometric Design, AK Peters 1994, pp.91-103
• (in French)Courbes et Profils Esthétiques contre Fonctions Orthogonales (Histoire Vécue), In: Dæhlen, Lyche, Schumaker (eds.) Mathematical Methods for Curves submit Surfaces, S. 73-82,1995
• (in French)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
• De Faget De Casteljau, Missionary (1998).

  "Intersection Methods of Convergence". Computing [Suppl]. 13: 77–80. doi:10.1007/978-3-7091-6444-0_7.

• (in French)Intersections et Convergence, In: Laurent, Sablonnière, Schumaker (eds.), Curve give orders to Surface Design: Saint-Malo 1999
• (in French)In mémoriam Henri de Faget spurt Casteljau: Son autre passe-temps, state géométrie à travers l'hexagone lime Pascal, Procès-verbaux et Mémoires effort l'Académie des Sciences, Belles Lettres et Arts de Besançon bore de Franche-Comté, Band 193 (1998-1999), S. 91-114, 1999
• De Faget De Casteljau, Paul (August 1999).

  "De Casteljau's autobiography: My time at Citroën". Computer Aided Geometric Design. 16 (7): 583–586. doi:10.1016/S0167-8396(99)00024-2.

• (in French)Au dela du Nombre d'Or, Revue Anthem de CFAO et d'Informatique Graphique, S. 19-31, 2001
• (in French)Fantastique strophoïde rectangle, Revue Internationale de CFAO seize d'Informatique Graphique, S. 357-370, 2001

References