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Issue No.05 - September/October (1992 vol.12)
pp: 87-95
ABSTRACT
<p>The interval Bezier curve, which, unlike other curve and surface approximation schemes, can transfer a complete description of approximation errors between diverse CAD/CAM systems that impose fundamentally incompatible constraints on their canonical representation schemes, is described. Interval arithmetic, which offers an essentially infallible way to monitor error propagation in numerical algorithms that use floating-point arithmetic is reviewed. Affine maps, the computations of which are key operations in the de Casteljau subdivision and degree-elevation algorithms for Bezier curves, the floating-point error propagation in such computations, approximation by interval polynomials, and approximation by interval Bezier curves are discussed.</p>
CITATION
Thomas W. Sederberg, Rida T. Farouki, "Approximation by Interval Bezier Curves", IEEE Computer Graphics and Applications, vol.12, no. 5, pp. 87-95, September/October 1992, doi:10.1109/38.156018
REFERENCES
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3. S.P. Mudur and P.A. Koparkar, "Interval Methods for Processing Geometric Objects,"IEEE CG&A, Vol. 4, No. 2, Feb. 1984, pp. 7-17.
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5. R.T. Farouki and V.T. Rajan, "Algorithms for Polynomials in Bernstein Form,"Computer-Aided Geometric Design, Vol. 5, No. 1, June 1988, pp. 1-26.
6. R.T. Farouki and V.T. Rajan, "On the Numerical Condition of Poly-1 nomials in Bernstein Form,"Computer-Aided Geometric Design, Vol. 4, No. 3, Nov. 1987, pp. 191-216.
7. P.J. Davis,Interpolation and Approximation, Dover, New York, 1963.
8. T.W. Sederberg and M. Kakimoto, "Approximating Rational Curves Using Polynomial Curves," inNURBS for Curve and Surface Design, G. Farin, ed., SIAM, Philadelphia, 1991, pp. 149-158.
9. T.W. Sederberg and D.B. Buehler, "Offsets of Bezier Curves: Hermite Approximation with Error Bound," to appear inMathematical Methods, in CAGD II, T. Lyche and L. Schumaker, eds., Academic Press, New York, 1992.
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