Convergent inversion approximations for polynomials in Bernstein form

Computer Aided Geometric Design

Volumn 17, Issue 2, 2000, Pages 179-196

  Farouki, Rida T ^a  

^a University of California   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER AIDED DESIGN; CONVERGENCE OF NUMERICAL METHODS; INVERSE PROBLEMS; LEAST SQUARES APPROXIMATIONS; POLYNOMIALS;

BERNSTEIN FORM; LEGENDRE POLYNOMIALS;

COMPUTATIONAL GEOMETRY;

EID: 0034139986     PISSN: 01678396     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-8396(99)00046-1     Document Type: Article

References (21)

1. Davis, P.J. (1975), Interpolation and Approximation, Dover, New York (reprint).
2. DeRose, A.D. (1988), Composing sezier simplexes, ACM Trans. Graphics 7, 198-221.
3. Farin, G. (1993), Curves and Surfaces for Computer Aided Geometric Design, 3rd Edn., Academic Press, Boston.
4. Farouki, R.T. (1992), Pythagorean-hodograph curves in practical use, in: R.E. Barnhill, ed., Geometry Processing for Design and Manufacturing SIAM, Philadelphia, 3-33.
5. Farouki, R.T. (1997), Optimal parameterizations, Computer Aided Geometric Design 14, 153-168.
6. Farouki, R.T. and Rajan, V.T. (1987), On the numerical condition of polynomials in Bernstein form, Computer Aided Geometric Design 4, 191-216.
7. Farouki, R.T. and Rajan, V.T. (1988), Algorithms for polynomials in Bernstein form, Computer Aided Geometric Design 5, 1-26.
8. Farouki, R.T. and Sakkalis, T. (1990), Pythagorean hodographs, IBM J. Res. Develop. 34, 736-752.
9. Farouki, R.T. and Sakkalis, T. (1991), Real rational curves are not "unit speed", Computer Aided Geometric Design 8, 151-157.
10. Goetgheluck, P. (1987), Computing binomial coefficients, Amer. Math. Monthly 94, 360-365.
11. Henrici, P. (1974), Applied and Computational Complex Analysis, Vol. 1, Wiley, New York.
12. Isaacson, E. and Keller, H.B. (1994), Analysis of Numerical Methods, Dover, New York (reprint).
13. Jüttler, B. (1997), A vegetarian approach to optimal parameterizations, Computer Aided Geometric Design 14, 887-890.
14. Jüttler, B. (1998), The dual basis functions for the Bernstein polynomials, Adv. Comp. Math. 8, 345-352.
15. Lachance, M.A. (1988), Chebyshev economization for parametric surfaces, Computer Aided Geometric Design 5, 195-208.
16. Lane, J.M. and Riesenfeld, R.F. (1981), Bounds on a polynomial, BIT 21, 112-117.
17. Ong, B.H. (1996), An extraction of almost arc length parameterization from parametric curves, Ann. Numer. Math. 3, 305-316.
18. Sederberg, T.W., Anderson, D.C. and Goldman, R.N. (1984), Implicit representation of parametric curves and surfaces, Comput. Vision Graphics Image Process. 28, 72-84.
19. Sederberg, T.W. and Parry, S.R. (1986), Comparison of three curve intersection algorithms, Computer-Aided Design 18, 58-63.
20. Szegö, G. (1975), Orthogonal polynomials, 4th edn., Amer. Math. Soc., Providence, RI.
21. Watkins, M.A. and Worsey, A.J. (1988), Degree reduction of Bézier curves, Computer-Aided Design 20, 398-405.