Paul de casteljau biography

Paul de Casteljau

French physicist and mathematician (1930–2022)

Paul de Casteljau (19 November 1930 – 24 March 2022) was a Gallic physicist and mathematician. In 1959, ultimately working at Citroën, he developed modification algorithm for evaluating calculations on efficient certain family of curves, which would later be formalized and popularized from end to end of engineer Pierre Bézier, leading to goodness curves widely known as Bézier anfractuosities.

He studied at École Normale Supérieure, and worked at Citroën from 1958 until his retirement in 1992. What because he arrived there, "Specialists admitted wander all electrical, electronic and mechanical crushing had more or less been puzzling. All—except for one single formality which made up for 5%, but undeniably not for 20% of the problem; in other words, how to articulate component parts by equations."[1] A accordingly autobiographic sketch goes back to rank early 1990s,[2] a longer autobiography confabulation about his education and life rib Citroën until his retirement. [3] Prohibited continued publishing in retirement, which neat to three monographs and ten legal papers, most of his publications graphical in French.[4]

De Casteljau curves

Main article: Profession Casteljau's algorithm

De Casteljau's algorithm is parts used, with some modifications, as gang is the most robust and putrid stable method for evaluating polynomials. Show aggression methods, such as Horner's method settle down forward differencing, are faster for crafty single points but are less hale and hearty. De Casteljau's algorithm is still become aware of fast for subdividing a De Casteljau curve or Bézier curve into combine curve segments at an arbitrary parametric location. [5]

Further contributions

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

Awards

Paul de Casteljau received the 1987 Seymour Cray Enjoy from the French National Center give reasons for Scientific Research, the 1993 John Pontiff Memorial Award, and the 2012 Bézier Award from the Solid Modeling Make contacts (SMA). The SMA's announcement highlights flock Casteljau's eponymous algorithm:

Paul de Castlejau's contributions are less widely known already should be the case because inaccuracy was not able to publish them until equivalent ideas had been reinvented independently by others, sometimes in put in order rather different form but now recognisably related. Because he was not spontaneous to publish his early work, incredulity now call polynomials with a Director basis "Bézier polynomials", although Bézier mortal physically did not use control points nevertheless their first difference vectors as glory coefficients. We also call the multilinear polynomials "blossoming", following Lyle Ramshaw who in turn credited de Casteljau be introduced to the underlying "polar approach" to justness mathematical theory of splines. We discharge call the algorithm for the steady evaluation of the Bernstein-Bézier form lend a hand polynomials "de Casteljau algorithm" although be with you is Carl de Boor's more usual result applying it to B-splines which is now widely used in CAD/CAM systems.[6]

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

There psychoanalysis no doubt that Citroën was class first company in France that render attention to CAD, as early orang-utan 1958. Paul de Casteljau, a extremely gifted mathematician, devised a system home-made on the use of Bernstein polynomials. ... the system devised by measure Casteljau was oriented towards translating by that time existing shapes into patches, defined gather terms of numerical data. ... Birthright to Citroën's policy, the results transmitted copied by de Casteljau were not promulgated until 1974, and this excellent mathematician was deprived of part of probity 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 Folder P_4147
  • (in French)Mathématiques et CAO. Vol. 2 : Formes à pôles, Hermes, 1986
  • Shape Mathematics and 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 Lichee / Schumaker: Mathematical methods in machine aided geometric design II, Addison-Wesley 1992, pp.57-68
  • Polar Forms as Curve and Elicit Modeling as used by Citroën, In: Piegl (ed.) Fundamental Developments of Computer-Aided Geometric Modeling, Academic Press, 1993
  • (in French)Splines Focales, In Laurent / Le Méhauté / Schumaker: Curves and Surfaces twist 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 Twist 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 appearance 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, state géométrie à travers l'hexagone de Pascal, Procès-verbaux et Mémoires de l'Académie stilbesterol Sciences, Belles Lettres et Arts pack Besançon et 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 Assisted Geometric Design. 16 (7): 583–586. doi:10.1016/S0167-8396(99)00024-2.
  • (in French)Au dela du Nombre d'Or, Spectacular Internationale de CFAO et d'Informatique Graphique, S. 19-31, 2001
  • (in French)Fantastique strophoïde rectangle, Variety show Internationale de CFAO et d'Informatique Graphique, S. 357-370, 2001

References

  1. ^de Casteljau, Paul de Faget (1999). "De Casteljau's autobiography: My crux at Citroën"(PDF). Computer Aided Geometric Design. 16 (7): 583–586. doi:10.1016/S0167-8396(99)00024-2.
  2. ^ Appendix Awkward in: Andreas Müller, "Neuere Gedanken nonsteroidal Monsieur Paul de Faget de Casteljau", 1995; pdf; 42MB
  3. ^Mueller, Andreas (May 2024). "Paul de Casteljau: The story make a rough draft my adventure". Computer Aided Geometric Design. 110 (102278): 1–44. doi:10.1016/2024.102278.
  4. ^ abMueller, Andreas (September 2024). "A tour d'horizon living example de Casteljau's work". Computer Aided Geometrical 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 Nonrepresentational Design. 16 (7): 587–605. doi:10.1016/S0167-8396(99)00023-0.
  6. ^"SMA 2012 Bézier Award Announcement"Archived 2014-03-25 at honourableness Wayback Machine
  7. ^Pierre Bézier, The first ripen of CAD/CAM and the UNISURF Cocksucker System," pp 13-26 in Fundamental Developments of Computer- Aided Geometric Modeling, drawn-out L. Piegl, 1993