On de Casteljau's algorithm

Computer Aided Geometric Design

Volumn 16, Issue 7, 1999, Pages 587-605

  Boehm, Wolfgang ^a   Müller, Andreas ^a  

^a TECHNICAL UNIVERSITY OF BRAUNSCHWEIG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

AIRCRAFT MANUFACTURE; ALGORITHMS; COMPUTATIONAL GEOMETRY; COMPUTER PROGRAMMING; CURVE FITTING; MEDICAL APPLICATIONS; RAILROAD CARS; SHIPS;

BEZIER CURVES; COMPUTER AIDED GEOMETRIC DESIGN; DE CASTELJAU ALGORITHM; FOCAL CURVES; POLAR FORMS;

COMPUTER AIDED DESIGN;

EID: 0033172460     PISSN: 01678396     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-8396(99)00023-0     Document Type: Article

References (45)

1. Barnhill, R.E. and Riesenfeld, R.F. (eds.) (1974), Computer Aided Geometric Design, Academic Press, New York.
2. Bézier, P. (ed.) (1971), La Commande Numérique, Ingénieurs de l'automobile XLIV, Journal de la SIA, Numéro spécial publié à l'occasion du salon de l'automobile Octobre 1971, Paris, 493-622.
3. Bézier, P. (1972), Numerical Control, Mathematics and Applications, Wiley, London; See also Barnhill, R.E. and Riesenfeld, R.F. (eds.) (1974), Computer Aided Geometric Design, Academic Press, New York, 127-152.
4. Bézier, P. (1972), Numerical Control, Mathematics and Applications, Wiley, London; See also Barnhill, R.E. and Riesenfeld, R.F. (eds.) (1974), Computer Aided Geometric Design, Academic Press, New York, 127-152.
5. Bézier, P. (1988), How a simple system was born, in: Farin, G.E., ed., Curves and Surfaces for CAGD, Academic Press, Boston, 1-12.
6. Boehm, W. (1976), Parameterdarstellung kubischer und bikubischer Splines, Computing 17, 87-92.
7. Boehm, W. (1977), Über die Konstruktion von B-Spline-Kurven, Computing 18, 161-166.
8. Boehm, W. (1980), Inserting new knots into B-spline curves, Computer-Aided Design 12, 199-291.
9. Boehm, W. and Prautzsch, H. (1994), Geometric Concepts for Geometric Design, AK Peters, Wellesley, 257, 359 and 361.
10. Browne, L.J.I, (ed.) (1972), Curved Surfaces in Engineering, Computer Methods for Design and Manufacture, Computer-Aided Design, IPC Science and Technology Press, Guildford.
11. Chasles, M. (1830), Mémoire de géométrie pure sur les propriétés générales des cônes du second degré, Nouv. Mem. Bruxelles 6, 1-59.
12. Cohen, E., Lyche, T. and Riesenfeld, R. (1980), Discrete B-splines and subdivision techniques in computer aided geometric design and computer graphics, Comp. Graphics and Image Processing 14, 87-111.
13. Coons, S.A. (1964) and (1967), Surfaces for Computer Aided Design, Technical Reports, MIT, 1964 and MIT 1967, see Faux, I.D. and Pratt, M.J. (1979), Computational Geometry for Design and Manufacture, Ellis Horwood, Chichester, 198-203 and also Barnhill, R.E. and Riesenfeld, R.F. (eds.) (1974), Computer Aided Geometric Design, Academic Press, New York, 1-16.
14. Coons, S.A. (1964) and (1967), Surfaces for Computer Aided Design, Technical Reports, MIT, 1964 and MIT 1967, see Faux, I.D. and Pratt, M.J. (1979), Computational Geometry for Design and Manufacture, Ellis Horwood, Chichester, 198-203 and also Barnhill, R.E. and Riesenfeld, R.F. (eds.) (1974), Computer Aided Geometric Design, Academic Press, New York, 1-16.
15. Coons, S.A. (1964) and (1967), Surfaces for Computer Aided Design, Technical Reports, MIT, 1964 and MIT 1967, see Faux, I.D. and Pratt, M.J. (1979), Computational Geometry for Design and Manufacture, Ellis Horwood, Chichester, 198-203 and also Barnhill, R.E. and Riesenfeld, R.F. (eds.) (1974), Computer Aided Geometric Design, Academic Press, New York, 1-16.
16. de Boor, C. (1972), On calculating with B-splines, J. Approx. Theory 6, 50-62.
17. de Casteljau, P. (1959), Outillage methodes calcul, Enveloppe Soleau 40.040, Institute National de la Propriété Industrielle, Paris.
18. de Casteljau, P. (1963), Courbes et surfaces à pôles, Microfiche P 4147-1, André Citroën Automobile SA, Paris, 1-58.
19. de Casteljau, P. (1985), Formes à Pôles, Mathematiques et CAO 2, Hermes Publishing, Paris.
20. de Casteljau, P. (1987), Les Quaternions, Editions Hermès, Paris.
21. de Faget de Casteljau, P. (1990), Le Lissage, Editions Hermès, Paris.
22. de Faget de Casteljau, P. (1992), POLynomials, POLar forms, and InterPOLation, in: Lyche, T. and Schumaker, L.L., eds., Mathematical Methods in Computer Aided Geometric Design, Addison-Wesley, 57-68.
23. de Casteljau, P. (1994), Splines focales, in: Laurent et al., eds., Curves and Surfaces in Geometric Design, AK Peters, Wellesley, 91-103.
24. de Faget de Casteljau, P. (1995), Courbes et profils estétiques contre fonctions orthogonales (histoire vécue), in: Dæhlen et al., eds., Mathematical Methods for Curves and Surfaces, Vanderbilt University Press, 73-82.
25. DeRose, T.D., Goldman, R.N., Hagen, H. and Mann, S. (1993), Functional composition algorithms via blossoming, ACM Trans, on Graphics 12 (2), 113-135.
26. Farin, G.E. (1979), Subsplines über Dreiecken, Ph.D. Thesis, Technische Universität Braunschweig.
27. Farin, G.E. (1983), Algorithms for rational Bézier curves, Computer-Aided Design 15, 73-77.
28. Farin, G.E. (1993), Curves and Surfaces for CAGD, Academic Press, Boston.
29. Faux, I.D. and Pratt, M.J. (1979), Computational Geometry for Design and Manufacture, Ellis Horwood, Chichester.
30. Forrest, A.R. (1972), Interactive interpolation and approximation by Bézier polynomials, Computer J. 15, 71-70; reprinted (1990) in Computer-Aided Design 22, 527-537.
31. Forrest, A.R. (1972), Interactive interpolation and approximation by Bézier polynomials, Computer J. 15, 71-70; reprinted (1990) in Computer-Aided Design 22, 527-537.
32. Haase, J.C.F. (1870), Zur Theorie der ebenen Curven n-ter Ordnung mit (n - 1)(n - 2)/2 Doppelund Rückkehrpunkten, Math. Ann. 2, 515-548.
33. Krautter, J. and Parizot, S. (1971), Systeme d'aide à la définition et à l'usinage des surfaces de carosserie, in: Bézier, P., ed. (1971), La Commande Numérique, Ingénieurs de l'Automobile XLIV, Journal de la SIA, Numéro spécial publié à l'occasion du salon de l'automobile Octobre 1971, Paris, 581-586.
34. Liming, R.A. (1944), Practical Analytic Geometry with Applications to Aircraft, MacMillan, New York.
35. Neamtu, M., Pottmann, H. and Schumaker, L.L. (1996), Homogeneous splines and rational curves with rational offsets, Technische Universität Wien, Institut für Geometrie, Technical Report Nr. 29.
36. Prautzsch, H., Boehm, W. and Paluszny, M. (1999), Bernstein-Bézier and Spline Techniques, Springer, Berlin, to appear.
37. Ramshaw, L. (1987), Blossoming: A connect-the-dot approach to splines, Technical Report, Digital Systems Research Center, Palo Alto, CA.
38. Riesenfeld, R.F. (1973), Applications of B-spline approximation to geometric problems of computer aided design, Ph.D. Thesis, Syracuse University, See also Barnhill, R.E. and Riesenfeld, R.F. (eds.) (1974), Computer Aided Geometric Design, Academic Press, New York, 95-126.
39. Riesenfeld, R.F. (1973), Applications of B-spline approximation to geometric problems of computer aided design, Ph.D. Thesis, Syracuse University, See also Barnhill, R.E. and Riesenfeld, R.F. (eds.) (1974), Computer Aided Geometric Design, Academic Press, New York, 95-126.
40. Sablonnière, P. (1978), Spline and Bézier polygons associated with a polynomial spline curve, Computer-Aided Design 10, 257-261.
41. Sánchez-Reyes, J. (1992), Single-valued spline curves in polar coordinates, Computer-Aided Design 6 (24), 307-315.
42. Seidel, H.-P. (1989), Polynome, Splines und symmetrische rekursive Algorithmen im Computer Aided Geometrie Design, Habilitationsschrift, Universität Tubingen.
43. Stärk, E. (1976), Mehrfach differenzierbare Bézierkurven und Bézierflächen, Ph.D. Thesis, Technische Universität Braunschweig.
44. Vernet, M.D. (1971), Expression mathématique des formes - System UNISURF, in: Bézier, P., ed. (1971), La Commande Numérique, Ingénieurs de l'Automobile XLIV, Journal de la SIA, Numéro spécial publié à l'occasion du salon de l'automobile Octobre 1971, Paris, 509-520;
45. Vernet, M.D. (1971), Expression mathématique des formes - System UNISURF, in: Bézier, P., ed. (1971), La Commande Numérique, Ingénieurs de l'Automobile XLIV, Journal de la SIA, Numéro spécial publié à l'occasion du salon de l'automobile Octobre 1971, Paris, 509-520; see also Barnhill, R.E. and Riesenfeld, R.F. (eds.) (1974), Computer Aided Geometric Design, Academic Press, New York, 127-152. see also Barnhill, R.E. and Riesenfeld, R.F. (eds.) (1974), Computer Aided Geometric Design, Academic Press, New York, 127-152.