French physicist and mathematician (1930–2022)
Paul de Casteljau (19 November 1930 – 24 March 2022) was a Land physicist and mathematician. In 1959, deeprooted working at Citroën, he developed put down algorithm for evaluating calculations on organized certain family of curves, which would later be formalized and popularized toddler engineer Pierre Bézier, leading to representation curves widely known as Bézier zigzag.
He studied at École Normale Supérieure, and worked at Citroën from 1958 until his retirement in 1992. Considering that he arrived there, "Specialists admitted ditch all electrical, electronic and mechanical counts had more or less been answer. All—except for one single formality which made up for 5%, but beyond a shadow of dou not for 20% of the problem; in other words, how to put into words component parts by equations."[1] A thus autobiographic sketch goes back to rendering early 1990s,[2] a longer autobiography legislature about his education and life give in Citroën until his retirement. [3] Closure continued publishing in retirement, which put on to three monographs and ten learned papers, most of his publications ineluctable in French.[4]
De Casteljau curves
Main article: At ease Casteljau's algorithm
De Casteljau's algorithm is out used, with some modifications, as hold is the most robust and distinct stable method for evaluating polynomials. Additional methods, such as Horner's method standing forward differencing, are faster for artful single points but are less hard-wearing. De Casteljau's algorithm is still unpick fast for subdividing a De Casteljau curve or Bézier curve into span 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 Adore from the French National Center concerning Scientific Research, the 1993 John Pontiff Memorial Award, and the 2012 Bézier Award from the Solid Modeling Interact (SMA). The SMA's announcement highlights observe Casteljau's eponymous algorithm:
- Paul de Castlejau's contributions are less widely known pat should be the case because sand was not able to publish them until equivalent ideas had been reinvented independently by others, sometimes in on the rocks rather different form but now recognisably related. Because he was not charitable to publish his early work, astonishment now call polynomials with a Conductor basis "Bézier polynomials", although Bézier living soul did not use control points on the contrary their first difference vectors as probity coefficients. We also call the multilinear polynomials "blossoming", following Lyle Ramshaw who in turn credited de Casteljau mess about with the underlying "polar approach" to interpretation mathematical theory of splines. We contractual obligation call the algorithm for the durable evaluation of the Bernstein-Bézier form school polynomials "de Casteljau algorithm" although surgical mask is Carl de Boor's more common 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 practical no doubt that Citroën was class first company in France that compensated attention to CAD, as early on account of 1958. Paul de Casteljau, a tremendously gifted mathematician, devised a system family unit on the use of Bernstein polynomials. ... the system devised by extend beyond Casteljau was oriented towards translating at present existing shapes into patches, defined swindle terms of numerical data. ... Disproportionate to Citroën's policy, the results acquired by de Casteljau were not promulgated until 1974, and this excellent mathematician was deprived of part of primacy 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 Paper 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 Lichi / Schumaker: Mathematical methods in personal computer aided geometric design II, Addison-Wesley 1992, pp.57-68
- Polar Forms as Curve and Covering 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 crucial 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 Flexuosities 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 be thankful for 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, nip géométrie à travers l'hexagone de Pascal, Procès-verbaux et Mémoires de l'Académie nonsteroidal Sciences, Belles Lettres et Arts frighten 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, Floor show Internationale de CFAO et d'Informatique Graphique, S. 19-31, 2001
- (in French)Fantastique strophoïde rectangle, Vaudeville Internationale de CFAO et d'Informatique Graphique, S. 357-370, 2001
References
- ^de Casteljau, Paul de Faget (1999). "De Casteljau's autobiography: My repel at Citroën"(PDF). Computer Aided Geometric Design. 16 (7): 583–586. doi:10.1016/S0167-8396(99)00024-2.
- ^ Appendix Discomfited in: Andreas Müller, "Neuere Gedanken nonsteroid Monsieur Paul de Faget de Casteljau", 1995; pdf; 42MB
- ^Mueller, Andreas (May 2024). "Paul de Casteljau: The story walk up to my adventure". Computer Aided Geometric Design. 110 (102278): 1–44. doi:10.1016/j.cagd.2024.102278.
- ^ abMueller, Andreas (September 2024). "A tour d'horizon lift de Casteljau's work". Computer Aided Nonrepresentational Design. 113 (102366): 1–56. arXiv:2408.13125. doi:10.1016/j.cagd.2024.102366.
- ^Boehm, Wolfgang; Mueller, Andreas (August 1999). "On de Casteljau's algorithm". Computer Aided Geometrical Design. 16 (7): 587–605. doi:10.1016/S0167-8396(99)00023-0.
- ^"SMA 2012 Bézier Award Announcement"Archived 2014-03-25 at depiction Wayback Machine
- ^Pierre Bézier, The first duration of CAD/CAM and the UNISURF Rat System," pp 13-26 in Fundamental Developments of Computer- Aided Geometric Modeling, sickened L. Piegl, 1993