On the stability of normalized Powell-Sabin B-splines

Journal of Computational and Applied Mathematics

Volumn 170, Issue 1, 2004, Pages 181-196

  Maes, Jan ^a   Vanraes, Evelyne ^a   Dierckx, Paul ^a   Bultheel, Adhemar ^a  

^a UNIVERSITY OF LEUVEN   (Belgium)

Author keywords

Approximation; Powell Sabin splines; Stable bases

Indexed keywords

APPROXIMATION THEORY; COMPUTER SIMULATION; MATHEMATICAL MODELS; NUMERICAL METHODS; TRIANGULATION;

APPROXIMATION CONSTANTS; POWELL-SABIN B-SPLINES;

COMPUTATION THEORY;

MATHEMATICAL METHOD;

EID: 3042647618     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2004.01.001     Document Type: Article

References (11)

1. Dierckx P. On calculating normalized Powell-Sabin B-splines Comput. Aided Geom. Design 15 3 1997 61-78
2. Farin G. Triangular Bernstein-Bézier patches Comput. Aided Geom. Design 3 2 1986 83-128
3. Farin G. Curves and Surfaces for Computer Aided Geometric Design: A Practical Guide 4th Edition 1997 Academic Press Boston
4. Jia R.Q. Approximation order from certain spaces of smooth bivariate splines on a three-direction mesh Trans. Amer. Math. Soc. 295 1986 199-212
5. Lai M. Schumaker L. On the approximation power of bivariate splines Adv. Comput. Math. 9 1998 251-279
6. Lai M. Schumaker L. Macro-elements and stable local bases for splines on Powell-Sabin splits Math. Comput. 72 2003 335-354
7. Powell M.J.D. Sabin M.A. Piecewise quadratic approximations on triangles ACM Trans. Math. Software 3 1977 316-325
8. Sablonnière P. Error bounds for Hermite interpolation by quadratic splines on an α-triangulation IMA J. Numer. Anal. 7 1987 495-508
9. E. Vanraes, P. Dierckx, A. Bultheel, On the choice of the PS-triangles, TW Report 353, Department of Computer Science, Katholieke Universiteit Leuven, Belgium, February 2003.
10. E. Vanraes, J. Maes, A. Bultheel, Powell-Sabin spline wavelets, Int. J. Wavelets, Multiresolution and Information processing 1 (2004), to appear.
11. J. Windmolders, Powell-Sabin splines for computer aided geometric design, Ph.D. Thesis, Department of Computer Science, Katholieke Universiteit Leuven, Belgium, 2003.