DOI QR코드

DOI QR Code

CONSTRAINED JACOBI POLYNOMIAL AND CONSTRAINED CHEBYSHEV POLYNOMIAL

  • 발행 : 2008.04.30

초록

In this paper, we present the constrained Jacobi polynomial which is equal to the constrained Chebyshev polynomial up to constant multiplication. For degree n=4, 5, we find the constrained Jacobi polynomial, and for $n{\geq}6$, we present the normalized constrained Jacobi polynomial which is similar to the constrained Chebyshev polynomial.

키워드

참고문헌

  1. Y. J. Ahn, Degree reduction of Bezier curves with $C^{\kappa}$-continuity using Jacobi polynomials, Comp. Aided Geom. Desi. 20 (2003), 423-434 https://doi.org/10.1016/S0167-8396(03)00082-7
  2. Y. J. Ahn, Degree reduction of Bezier curves using constrained Chebyshev polynomials of second kind, ANZIAM J. 45 (2003), 195-205 https://doi.org/10.1017/S1446181100013262
  3. Y. J. Ahn, B. G. Lee, Y. B. Park, and J. C. Yoo, Constrained polynomial degree reduction in the $L_{2}$-norm equals best weighted Euclidean approximation of Bezier coefficients, Comp. Aided Geom. Desi. 21 (2004), 181-191 https://doi.org/10.1016/j.cagd.2003.10.001
  4. T. S. Chihara, An introduction to orthogonal polynomials, Gordon and Breach, New York, 1978
  5. P. J. Davis, Interpolation and approximation, Dover publications, New York, 1975
  6. M. Eck, Degree reduction of Bezier curves, Comp. Aided Geom. Desi. 10 (1993), 237-251 https://doi.org/10.1016/0167-8396(93)90039-6
  7. M. Eck, Least squares degree reduction of Bezier curves, Computer-Aided Design 27 (1995), 845-851 https://doi.org/10.1016/0010-4485(95)00008-9
  8. H. J. Kim and Y. J. Ahn, Good degree reduction of Bezier curves using Jacobi polynomials, Comp. Math. Appl. 40 (2000), 1205-1215 https://doi.org/10.1016/S0898-1221(00)00232-7
  9. H. O. Kim, J. H. Kim, and S. Y. Moon, Degree reduction of Bezier curves and filter banks, Comp. Math. Appl. 31 (1996), 23-30 https://doi.org/10.1016/0898-1221(96)00049-1
  10. H. S. Kim and Y. J. Ahn, Constrained degree reduction of polynomials in Bernstein Bezier form over simplex domain, Journal of Computational and Applied Mathematics, In Press, 2007 https://doi.org/10.1016/j.cam.2007.04.001
  11. M. A. Lachance, Chebyshev economization for parametric surfaces, Comp. Aided Geom. Desi. 5 (1988), 195-208 https://doi.org/10.1016/0167-8396(88)90003-9
  12. M. A. Lachance, Approximation by constrained parametric polynomials, Rocky Mountain J. Math. 21 (1991), 473-488 https://doi.org/10.1216/rmjm/1181073018
  13. B. G. Lee and Y. Park, Distance for Bezier curves and degree reduction, Bull. Australian Math. Soc. 56 (1997), 507-515 https://doi.org/10.1017/S0004972700031312
  14. B. G. Lee, Y. Park, and J. Yoo, Application of Legendre-Bernstein basis transformations to degree elevation and degree reduction, Comp. Aided Geom. Desi. 19 (2002), 709-718 https://doi.org/10.1016/S0167-8396(02)00164-4
  15. D. Lutterkort, J. Peters, and U. Reif, Polynomial degree reduction in the L$_{2}$-norm equals best Euclidean approximation of Bezier coefficients, Comp. Aided Geom. Desi 16 (1999), 607-612 https://doi.org/10.1016/S0167-8396(99)00025-4
  16. J. Peters and U. Reif, Least squares approximation of Bezier coefficients provides best degree reduction in the $L_{2}$-norm, J. Approximation Theory 104 (2000), 90-97 https://doi.org/10.1006/jath.1999.3440
  17. H. Sunwoo and N. Lee, A unified matrix representation for degree reduction of Bezier curves, Comp. Aided Geom. Desi. 21 (2004), 151-164 https://doi.org/10.1016/j.cagd.2003.07.007
  18. H. Sunwoo, Matrix representation for multi-degree reduction of Bezier curves, Comp. Aided Geom. Desi. 22 (2005), 261-273 https://doi.org/10.1016/j.cagd.2004.12.002
  19. G. Szego, Orthogonal polynomials, AMS Coll. Publ., 23, Providence
  20. M. Watkins and A. Worsey, Degree reduction for Bezier curves, Computer-Aided Design 20 (1988), 398-405 https://doi.org/10.1016/0010-4485(88)90216-3