On C2 quintic spline functions over triangulations of Powell-Sabin's type

Journal of Computational and Applied Mathematics

Volumn 73, Issue 1-2, 1996, Pages 135-155

  Lai, Ming Jun ^a  

^a UNIVERSITY OF GEORGIA   (United States)

Author keywords

B zier representation; C2 quintic splines; Full approximation order; Powell sabin's triangulation; Spline interpolation

Indexed keywords

APPROXIMATION THEORY; FUNCTIONS; MATHEMATICAL MORPHOLOGY; POLYNOMIALS;

BEZIER REPRESENTATION; FULL APPROXIMATION ORDER; POWELL-SABIN TRIANGULATION; QUINTIC SPLINES; SPLINE INTERPOLATION;

INTERPOLATION;

EID: 0030571104     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/0377-0427(96)00040-4     Document Type: Article

References (16)

1. 2 Clough-Tocher scheme, Comput. Aided Geom. Des. 1 (1984) 257-267.
2. P. Alfeld and L.L. Schumaker, The dimension of spline spaces of smoothness r for d ≥4r + 1, Constr. Approx. 3 (1987) 189-197.
3. C. de Boor, B-form basics, in: G. Farin, Ed., Geometric Modeling (SIAM Publication, Philadelphia, 1987) 131-148.
4. C. de Boor and K. Höllig, Approximation power of smooth bivariate pp functions, Math. Z. 197 (1988) 343-363.
5. J.H. Bramble and S.R. Hubert, Bounds for a class of linear functionals with applications to Hermite interpolation, Numer. Math. 16 (1971) 362-369.
6. C.K. Chui and M.J. Lai, On bivariate super vertex splines, Constr. Approx., Constr. Approx. 6 (1990) 399-419.
7. G. Farin, Triangular Bernstein-Bézier patches, Comput. Aided Geom. Des. 3 (1986) 83-127.
8. 2 interpolation over triangulations, in manuscript, 1993.
9. M.J. Lai, On dual functionals of polynomials in B-form, J. Approx. Theory 67 (1991) 19-37.
10. 2 supersplines of degree six, SIAM J. Numer. Anal., 1997, to appear.
11. M.J.D. Powell and M.A. Sabin, Piecewise quadratic approximation on triangles, ACM Trans. Math. Software 3 (1977) 316-325.
12. K.L. Rescorla, Cardinal interpolation; a bivariate polynomial example, Comput. Aided Geom. Des. 3 (1986) 313-321.
13. 2, in: C.K. Chui, L.L. Schumaker, F.I. Utreras, Eds., Topics in Multivariate Approximation. (Academic Press, New York, 1987) 207-217.
14. L.L. Schumaker, On the dimension of spaces of piecewise polynomials in two variables, in: W. Schempp and K. Zeller, Eds. Multivariate Approximation Theory (Birkhäuser, Basal, 1979) 396-411.
15. E.M. Stein, Singular Integrals and Differentiability Properties of Functions (Princeton University Press, NJ) 1970.
16. 2-quintic spline interpolation scheme on triangulation, Comput. Aided Geom. Des. 9 (1992) 379-386.