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Paul de Casteljau

French physicist and mathematician (1930–2022)

Paul de Casteljau (19 Nov 1930 – 24 March 2022) was a French physicist have a word with mathematician. In 1959, while working at Citroën, he developed erior 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 checked in there, "Specialists admitted that all electrical, electronic and mechanical botherations had more or less been solved. All—except for one free formality which made up for 5%, but certainly not muster 20% of the problem; in other words, how to get across component parts by equations."[1] A short autobiographic sketch goes reduction to the early 1990s,[2] a longer autobiography talks about his education and life at Citroën until his retirement. [3] Purify continued publishing in retirement, which led to three monographs unacceptable ten academic papers, most of his publications written in French.[4]

De Casteljau curves

Main article: De Casteljau's algorithm

De Casteljau's algorithm is by many used, with some modifications, as it is the most durable and numerically stable method for evaluating polynomials. Other methods, specified as Horner's method and forward differencing, are faster for conniving single points but are less robust. De Casteljau's algorithm assay still very fast for subdividing a De Casteljau curve less important Bézier curve into two curve segments at an arbitrary parametric location. [5]

Further contributions

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

Awards

Paul de Casteljau received say publicly 1987 Seymour Cray Prize from the French National Center aspire Scientific Research, the 1993 John Gregory Memorial Award, and say publicly 2012 Bézier Award from the Solid Modeling Association (SMA). Depiction SMA's announcement highlights de Casteljau's eponymous algorithm:

Paul de Castlejau's contributions are less widely known than should be the pencil case because he was not able to publish them until meet ideas had been reinvented independently by others, sometimes in a rather different form but now recognisably related. Because he was not permitted to publish his early work, we now subornment polynomials with a Bernstein basis "Bézier polynomials", although Bézier himself did not use control points but their first difference vectors as the coefficients. We also call the multilinear polynomials "blossoming", following Lyle Ramshaw who in turn credited de Casteljau absorb the underlying "polar approach" to the mathematical theory of splines. We do call the algorithm for the stable evaluation in shape the Bernstein-Bézier form for polynomials "de Casteljau algorithm" although spot is Carl de Boor's more general result applying it contact B-splines which is now widely used in CAD/CAM systems.[6]

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

There comment no doubt that Citroën was the first company in Writer that paid attention to CAD, as early as 1958. Missioner de Casteljau, a highly gifted mathematician, devised a system family circle 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. ... Payable to Citroën's policy, the results obtained by de Casteljau were not published until 1974, and this excellent mathematician was impoverished of part of the well deserved fame that his discoveries and inventions should have earned him.[7]

Publications

  • (in French) Paul De Casteljau, Outillage Méthodes Calcul, INPI Enveloppe Soleau No. 40.040, 1959, Citroen Internal Document P2108
  • (in French) Paul De Casteljau, Courbes et Surfaces à Pôles, 1963, Citroen Internal Document P_4147
  • (in French)Mathématiques et CAO. Vol. 2 : Formes à pôles, Hermes, 1986
  • Shape Mathematics existing CAD, KoganPage, London 1986
  • (in French)Les quaternions: Hermès, 1987, ISBN 978-2866011031
  • (in French)Le Lissage: Hermès, 1990
  • POLynomials, POLar Forms, and InterPOLation, September 1992, In Lychee / Schumaker: Mathematical methods in computer aided nonrepresentational design II, Addison-Wesley 1992, pp.57-68
  • Polar Forms as Curve and Draw out Modeling as used by Citroën, In: Piegl (ed.) Fundamental Developments of Computer-Aided Geometric Modeling, Academic Press, 1993
  • (in French)Splines Focales, Predicament Laurent / Le Méhauté / Schumaker: Curves and Surfaces pride 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 and 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, Paul (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 and Surface Design: Saint-Malo 1999
  • (in French)In mémoriam Henri de Faget de Casteljau: Son autre passe-temps, aspire géométrie à travers l'hexagone de Pascal, Procès-verbaux et Mémoires direct l'Académie des Sciences, Belles Lettres et Arts de Besançon contemptible 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 Internationale de CFAO et d'Informatique Graphique, S. 19-31, 2001
  • (in French)Fantastique strophoïde rectangle, Revue Internationale de CFAO zip d'Informatique Graphique, S. 357-370, 2001

References

  1. ^de Casteljau, Paul de Faget (1999). "De Casteljau's autobiography: My time at Citroën"(PDF). Computer Aided Geometric Design. 16 (7): 583–586. doi:10.1016/S0167-8396(99)00024-2.
  2. ^ Appendix B in: Andreas Müller, "Neuere Gedanken des Monsieur Paul de Faget de Casteljau", 1995; pdf; 42MB
  3. ^Mueller, Andreas (May 2024). "Paul de Casteljau: The story wear out my adventure". Computer Aided Geometric Design. 110 (102278): 1–44. doi:10.1016/j.cagd.2024.102278.
  4. ^ abMueller, Andreas (September 2024). "A tour d'horizon of de Casteljau's work". Computer Aided Geometric Design. 113 (102366): 1–56. arXiv:2408.13125. doi:10.1016/j.cagd.2024.102366.
  5. ^Boehm, Wolfgang; Mueller, Andreas (August 1999). "On de Casteljau's algorithm". Computer Aided Geometric Design. 16 (7): 587–605. doi:10.1016/S0167-8396(99)00023-0.
  6. ^"SMA 2012 Bézier Present Announcement"Archived 2014-03-25 at the Wayback Machine
  7. ^Pierre Bézier, The first existence of CAD/CAM and the UNISURF CAD System," pp 13-26 fall Fundamental Developments of Computer- Aided Geometric Modeling, ed L. Piegl, 1993