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5-14

5-1 Bohm, W., Farin, G., and Kahmann, J. Survey of Curve and Surface Methods in CAGD, mp. Aid. Geom. Des., Vol. 1, pp. 1-60, 1984.

5-2 Higdon, A., Olisen, E., Stiles, W., and Weese, J. Mechanics of Materials, 2d ed., John Wiley & Sons, New York, 1967.

5-3 South, N.E., and Kelly, J.P., Analytic Surface Methods, Ford Motor Company N/C Development Unit, Product Engineering Office, December 1965.

5-4 Nutbourne, A.W., Cubic Spline Package Part 2 - The Mathematics, mp. Aid. Des., Vol. 5, No. 1, January 1973.

5-5 Adams, J. ., Comparison of Methods for Cubic Spline Curve Fitting, mp. Aid. Des., Vol. 6, pp. 1-9, 1974.

5-6 Schweikert, D. C., An Interpolation Curve Using a Spline in Tension, J. Math. Phys., Vol. 45, pp. 312-317, 1966.

5-7 Cline, A. K., Curve Fitting Using Splines Under Tension, Atmos. Tech., No. 3, pp. 60- 65, 1973.

5-8 Nielson, G., Some Piecewise Polynomial Alternatives to Splines Under Tension, Computer Aided Geometric Design, Barnhill, R. E., and Riesenfeld, R. F. (eds.), pp. 209-235, Academis Press, New York, 1974.

5-9 Overhauser, A. W., Analytic Definition of Curves and Surfaces by Parabolic Blending, Tech. Rep. No. SL68-40, Ford Motor Company Scientific Laboratory, May 8, 1968.

5-10 Brewer, J. A., and Anderson, D. C., Visual Interaction with Overhauser Curves and Surfaces, mp. Graph., Vol. 11, pp. 132-137, 1977 (SIGGRAPH 77).

5-11 Bezier, P. E., How Renault Uses Numerical Control for Car Body Design and Tooling, SAE paper 680010, Society of Automotive Engineers' Congress, Detroit, MI, 1968.

5-12 Bezier P. E., Example of an Existing System in the Motor Industry: The Unisurf System, Proc. Roy. Soc. (London), Vol. A321, pp. 207-218, 1971.

5-13 Bezier, P. E., Emploi des Machines a Commande Numerique, Masson et Cie, Paris, 1970. Translated by Forrest, A. R., and Pankhurst, A. F., as Bezier, P. E., Numerical Control Mathematics and Applications, John Wiley & Sons, London, 1972.

5-14 Forrest, A. R., Interactive Interpolation and Approximation by Bezier Polynomials, mp. J., Vol. 15, pp. 71-79, 1972.

5-15 Gordon, W. J., and Riesenfeld, R. F., Bernstein-Bezier Methods for the Computer Aided Design of Free-from Curves and Surfaces, J. ACM, Vol. 21, pp. 293-310, 1974.

5-16 Bartels, R. H., Beatty, J. C., and Barsky, B. A., Splines for Use in Computer Graphics & Geometric Modeling, Morgan Kaufman, Los Altos, CA, 1987.

5-17 Barsky, B. A., Arbitrary Subdivision of Bezier Curves, TR UCB/CSD 85/265, mp. Asi. Div., Univ. of Cal., Berkeley, November 1985.

5-18 Clark, J. H., Fast Scanline Algorithm for Rendering Parametric Surfaces, mp. Graph., Vol. 14, pp. 7-12, 1979 [addendum to SIGGRAPH 79 Conf. Proc. - papers to be published in the ACM].

5-19 Cohen, E., and Riesenfeld, R. F., General Matrix Representations for Bezier and B- Spline Curves, mp. in Indus., Vol. 3, pp. 9-15, 1982.

5-20 Schoenberg, I. J., Contributions to the Problem of Approximation of Equidistant Data by Analytic Functions, Q. Appl. Math., Vol. 4, pp. 45-99; pp. 112-141, 1946.

5-21 Cox, M. G., The Numerical Evaluation of -Splines, National Physical Laboratory DNAC 4, August 1971.

5-22 de Boor, C., On Calculation with -splines, J. Approx. Theory, Vol. 6, pp. 50-62, 1972.

5-23 Riesenfeld, R. F., Application of B-Spline Approximation to Geometric Problems of Computer Aided Design, PhD dissertation, Syracuse Univ., Syracuse, NY, 1972. Also available as U. of Utah, UTEC-CSc-73-126, March 1973.

5-24 Barsky, B. A., End Conditions and Boundary Conditions for Uniform B-Spline Curve and Surface Representations, mp. in Indus., Vol. 3, pp. 17-29, 1982.

5-25 Hartley, P. J., and Judd, C. J., Parameterization of Bezier Type B-spline Curves and Surfaces, mp. Aid. Des., Vol. 10, pp. 130-134, 1978.

5-26 Rogers, D. F., and Fog, N. G., Constrained B-spline Curve and Surface Fitting, CADJ, Vol. 21, pp. 641-648, 1989.

5-27 Cohen, E., Lyche, ., and Schumacher, L. L., Algorithms for Degree-Raising of Splines, ACM Trans, on Graph., Vol. 4, pp. 171-181, 1985.

5-28 Cohen, E., Lyche, ., and Riesenfeld, R. F., Discrete B-Splines and Subdivision Techniques in Computer Aided Geometric Design and Computer Graphics, omp. Graph. Imag. Proc., Vol. 14, pp. 87-111, 1980.

5-29 Prautzsch, H., Short Proof of the Oslo Algorithm, mp. Aid. Geom. Des., Vol. 1, pp. 95-96, 1984.

5-30 Bohm, W., Inserting New Knots into B-spline Curves, mp. Aid. Des., Vol. 12, pp. 199-201, 1980.

5-31 Bohm, W., and Prautzsch, H., The Insertion Algorithm, mp. Aid. Des., Vol. 17, pp. 58-59, 1985.

5-32 Coons, S. A., Surfaces for Computer Aided Design of Space Forms, MIT Project MAC- TR-41, 1967.

5-33 Farouki, R., and Hinds, J., Hierarchy of Geometric Forms, IEEE mp. Graph. & Appl., Vol. 5, No. 5, pp. 51-78, 1985.

5-34 Piegl, L., Geometric Investigation of the Rational Bezier Scheme of Computer Aided Design, mp. in Indust., Vol. 7, pp. 401-410, 1986.

5-35 Forrest, A. R., The Twisted Cubic Curve: A Computer Aided Geometric Design Approach, mp. Aid. Des., Vol. 12, pp. 165-172, 1980.

5-36 Bohm, W., On Cubics: A Survey, mp. Graph. Imag. Proc., Vol. 19, pp. 201-226, 1982.

5-37 Forrest, A. R., Curves and Surfaces for Computer-Aided Design, PhD Dissertation, Cambridge Univ., 1968.

5-38 Ball, A. A., Consurf I-III, mp. Aid. Des., Vol. 6, pp. 243-249, 1974; Vol. 7, pp. 237- 242, 1975; Vol. 9, pp. 9-12, 1977.

5-39 Versprille, K. J., Computer-Aided Design Applications of the Rational B-spline Approximation Form, PhD dissertation, Syracuse Univ., Syracuse, NY, February 1975.

5-40 Tiller, W., Rational B-splines for Curve and Surface Representation, IEEE mp. Graph. & Apply Vol. 3, No. 6, pp. 61-69, September 1983.

5-41 Piegl, L., and Tiller, W., Curve and Surface Constructions Using Rational B-splines, mp. Aid. Des., Vol. 19, pp. 485-498, 1987.

5-42 IGES 'Initial Graphics Exchange Specifications, Version 3.0', Doc. No. NB-SIR 86-3359 Nat. Bur. of Stds., Gaithersburg, MD, USA, 1986.

5-43 Lee, E., Rational Bezier Representation for Conics, in Geometric Modeling, Farin, G. (ed.), SIAM, pp. 3-27, 1986.

 



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