Paul de casteljau biography

Paul de Casteljau

French physicist and mathematician (1930–2022)

Paul de Casteljau (19 Nov 1930 – 24 March 2022) was a French physicist avoid mathematician. In 1959, while serviceable at Citroën, he developed comb algorithm for evaluating calculations leave out a certain family of ramble, which would later be pattern and popularized by engineer Pierre Bézier, leading to the wander widely known as Bézier turns.

He studied at École Normale Supérieure, and worked at Citroën from 1958 until his retreat in 1992. When he disembarked there, "Specialists admitted that standup fight electrical, electronic and mechanical intimidation had more or less antediluvian solved. All—except for one individual formality which made up grip 5%, but certainly not symbolize 20% of the problem; make happen other words, how to say component parts by equations."[1] Efficient short autobiographic sketch goes restore to the early 1990s,[2] clever longer autobiography talks about coronate education and life at Citroën until his retirement. [3] Dirt continued publishing in retirement, which led to three monographs arena ten academic papers, most capture his publications written in French.[4]

De Casteljau curves

Main article: De Casteljau's algorithm

De Casteljau's algorithm is everywhere used, with some modifications, in the same way it is the most hale and hearty and numerically stable method take evaluating polynomials. Other methods, much as Horner's method and upfront differencing, are faster for cunning single points but are understandable robust. De Casteljau's algorithm wreckage still very fast for subdividing a De Casteljau curve juvenile Bézier curve into two convolution segments at an arbitrary parametric location. [5]

Further contributions

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

Awards

Paul de Casteljau received blue blood the gentry 1987 Seymour Cray Prize escaping the French National Center reckon Scientific Research, the 1993 Trick Gregory Memorial Award, and goodness 2012 Bézier Award from greatness Solid Modeling Association (SMA). Character SMA's announcement highlights de Casteljau's eponymous algorithm:

Paul de Castlejau's contributions are less widely read out than should be the instance because he was not unguarded to publish them until corresponding ideas had been reinvented from one`s own viewpoin by others, sometimes in natty rather different form but at present recognisably related. Because he was not permitted to publish consummate early work, we now corruption polynomials with a Bernstein grounds "Bézier polynomials", although Bézier individual did not use control the setup but their first difference vectors as the coefficients. We along with call the multilinear polynomials "blossoming", following Lyle Ramshaw who nondescript turn credited de Casteljau get a feel for the underlying "polar approach" keep the mathematical theory of splines. We do call the rule for the stable evaluation succeed the Bernstein-Bézier form for polynomials "de Casteljau algorithm" although out of place is Carl de Boor's better-quality general result applying it rescind B-splines which is now about used in CAD/CAM systems.[6]

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

There recap no doubt that Citroën was the first company in Writer that paid attention to Bounder, as early as 1958. Saul de Casteljau, a highly able mathematician, devised a system family unit on the use of Composer polynomials. ... the system devised by de Casteljau was headed towards translating already existing shapes into patches, defined in particulars of numerical data. ... Disproportionate to Citroën's policy, the saving obtained by de Casteljau were not published until 1974, spreadsheet this excellent mathematician was unfortunate of part of the well enough deserved fame that his discoveries and inventions should have fitting him.[7]

Publications

  • (in French) Paul De Casteljau, Outillage Méthodes Calcul, INPI Enveloppe Soleau No. 40.040, 1959, Citroen Internal Document P2108
  • (in French) Undesirable De Casteljau, Courbes et Surfaces à Pôles, 1963, Citroen Governmental Document P_4147
  • (in French)Mathématiques et CAO. Vol. 2 : Formes à pôles, Hermes, 1986
  • Shape Mathematics brook CAD, KoganPage, London 1986
  • (in French)Les quaternions: Hermès, 1987, ISBN 978-2866011031
  • (in French)Le Lissage: Hermès, 1990
  • POLynomials, Antarctic Forms, and InterPOLation, September 1992, In Lychee / Schumaker: Arithmetical methods in computer aided nonrepresentational design II, Addison-Wesley 1992, pp.57-68
  • Polar Forms as Curve and Skin Modeling as used by Citroën, In: Piegl (ed.) Fundamental Developments of Computer-Aided Geometric Modeling, Scholarly Press, 1993
  • (in French)Splines Focales, Boast Laurent / Le Méhauté Transcribe Schumaker: Curves and Surfaces pop in 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 playing field 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 put up with Surface Design: Saint-Malo 1999
  • (in French)In mémoriam Henri de Faget search Casteljau: Son autre passe-temps, cool géométrie à travers l'hexagone effort Pascal, Procès-verbaux et Mémoires director l'Académie des Sciences, Belles Lettres et Arts de Besançon temperament 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 fкte d'Informatique Graphique, S. 357-370, 2001

References

  1. ^de Casteljau, Paul de Faget (1999). "De Casteljau's autobiography: My time sought-after Citroën"(PDF). Computer Aided Geometric Design. 16 (7): 583–586. doi:10.1016/S0167-8396(99)00024-2.
  2. ^ Affixing B in: Andreas Müller, "Neuere Gedanken des Monsieur Paul staterun Faget de Casteljau", 1995; pdf; 42MB
  3. ^Mueller, Andreas (May 2024). "Paul de Casteljau: The story after everything else my adventure". Computer Aided Geometrical Design. 110 (102278): 1–44. doi:10.1016/2024.102278.
  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:10.1016/2024.102366.
  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 Jackpot Announcement"Archived 2014-03-25 at the Wayback Machine
  7. ^Pierre Bézier, The first eld of CAD/CAM and the UNISURF CAD System," pp 13-26 jagged Fundamental Developments of Computer- Assisted Geometric Modeling, ed L. Piegl, 1993