Approximation Theory in CADCAM

Books:

• Acton, F. S., Numerical Methods That (Usually) Work, Harper and Row Publishers, New York, New York, 1970.
• Acton, F. S., Numerical Methods That (Usually) Work, Mathematical Assosiation of America, Washington, DC, 1990.
• Cheney, E. W., Introduction to Approximation Theory, McGraw Hill Publishers, New York, New York, 1966.

• Cheng, F., Estimating Subdivision Depths for Rational Curves and Surfaces, ACM Transactions on Graphics, Vol. 11, No. 2, 1992, pp. 140-151.
• Dobkin, D. P., Levy, S. V. F., Thurston, W. P., and Wilks, A. R., Contour Tracing by Piecewise Linear Approximations, ACM Transactions on Graphics, Vol. 9, No. 4, 1990, pp. 389-423.
• Emery, J. D., The Definition and Computation of a Metric on Plane Curves, Computer Aided Design, Vol. 18, No. 1, 1986, pp. 25-28.
• Ferguson, D. R., Construction of Curves and Surfaces Using Numerical Techniques, Computer AIded Design, Vol. 18, No. 1, 1986, pp. 15-21.
• Filip, D., Magedson, R. M., and Markot, R., Surface Algorithms Using Bounds on Derivatives, Computer Aided Geometric Design, Vol. 3, 1986, pp. 295-311.
• Fritsch, F. N., and Nielson, G., M., On the Problem of Determining the Distance Between Parametric Curves, Curve and Surface Design, Tempe, Arizona, 1989, pp. 123-141.
• Gopalsamy, S., Khandekar, D., and Mudur, S. P., A New Method of Evaluating Compact Geometric Bounds for Use in Subdivision Algorithms, Computer Aided Geometric Design, Vol. 8, 1991, pp. 337-356.
• Juttler, B. J., Shape Preserving Least-Squares Approximation by Polynomial Parametric Spline Curves, Computer Aided Geometric Design, Vol. 14, 1997, pp. 731-747.
• Hermann, T., On a Tolerance Problem of Parametric Curves and Surfaces, Computer Aided Geometric Design, Vol. 9, 1992, pp. 109-117.
• Hoschek, J., Intrinsic Parametrization for Approximation, Computer Aided Geometric Design, Vol. 5, 1988, pp. 27-31.
• Koparkar, P. A., and Mudur, S., Computational Techniques for Processing Parametric Surfaces, Computer Vision, Graphics, and Image Processing, Vol. 28, 1984, pp. 303-322.
• Kosters, M., Curvature Dependent Parametrization of Curves and Surfaces, Computer Aided Design, Vol. 23, No. 8, 1991, pp. 569-578.
• Lachance, M. A., Chebyshev Economization for Parametric Surfaces, Computer Aided Geometric Design, Vol. 5, 1988, pp. 195-208.
• Lane, J. M., and Riesenfeld, R. F., Bounds on a Polynomial, BIT, Vol. 21, 1981, pp. 112-117.
• Lyche, T., and Morken, K., A Metric for Parametric Approximation, Curves and Surfaces in Geometric Design, A. LeMehaute and L. L. Schumaker ed., 1994, pp. 311-318.
• Manocha, D., and Canny, J. F., Rational Curves with Polynomial Parametrization, Computer Aided Design, Vol. 23, No. 9, 1991, pp. 645-652.
• Meier, H., Nowacki, H., Interpolating Curves with Gradual Changes in Curvature, Computer Aided Geometric Design, Vol. 4, 1987, pp. 297-305.
• Montaudouin, Y., Tiller, W., and Vold, H., Applications of Power Series in Computational Geometry, Computer Aided Design, Vol. 18, No. 10, 1986, pp. 514-524.
• Pratt, M. J., Smooth Parametric Surface Approximations to Discrete Data, Computer Aided Geometric Design, Vol. 2, 1985, pp. 165-171.
• Renka, R. J., Interpolatory Tension Splines With Automatic Selection of Tension Factors, SIAM Journal on Scientific and Statistical Computing, Vol. 8, No. 3, 1987, pp. 393-415.
• Renka, R. J., Algorithm 716 TSPACK: Tension Spline Curve-Fitting Package, ACM Transactions on Mathematical Software, Vol. 19, No. 1, 1993, pp. 81-94.
• Sarkar, B., and Menq, C-H., Parameter Optimization in Approximating Curves and Surfaces to Measurement Data, Computer Aided Geometric Design, Vol. 8, 1991, pp. 267-290.
• Sederberg, T. W., and Farouki, R. T., Approximation by Interval Bezier Curves, IEEE Computer Graphics and Applications, Vol. 12, 1992, pp. 87-94.
• Sederberg, T. W., and Chnag, G-Z., Best Linear Common Divisors for Approximate Degree Reduction, Computer Aided Design, Vol. 25, No. 3, 1993, pp. 163-167.
• Sederberg, T. W., and Nishita, T., Geometric Hermite Approximation of Surface Patch Intersection Curves, Computer Aided Geometric Design, Vol. 8, 1991, pp. 97-114.
• Sederberg, T. W., Zhao, J., and Zundel, A. K., Approximate Parametrization of Algebraic Curves, Theory and Practice of Geometric Modeling, W. Strasser and H. P. Seidel Eds., 1989, pp. 33-54.
• Sederberg, T. W., and Snively, J. P., Parametrization of Cubic Algebraic Curves, The Mathematics of Surfaces II, 1987, pp. 299-341.
• Sharpe, R. J., and Thorne, R. W., Numerical Method for Extracting and Arc Length Parametrization from Parametric Curves, Computer Aided Design, Vol. 14, No. 2, 1982, pp. 79-82.
• Shimada, T., and Tada, Y., Approximate Transformation of an Arbitrary Curved Surface into a Plane Using Dynamic Programming, Computer Aided Design, Vol. 23, No. 2, 1991, pp. 153-159.
• Wolter, F-E., Tuhoy, S. T., Approximation of High Degree Procedural Curves, Engineering With Computers, Vol. 8, 1992, pp. 61-80.