Homogeneous simplex splines

Journal of Computational and Applied Mathematics

Volumn 73, Issue 1-2, 1996, Pages 173-189

  Neamtu, Marian ^a  

^a VANDERBILT UNIVERSITY   (United States)

Author keywords

Cone splines; Divided differences; Homogeneous simplex splines; Knot insertion; Multivariate truncated powers; Polar forms; Spherical splines

Indexed keywords

COMPUTATIONAL METHODS; FUNCTIONS; MATHEMATICAL MORPHOLOGY; PIECEWISE LINEAR TECHNIQUES; POLES AND ZEROS;

CONE SPLINES; HOMOGENEOUS DIVIDED DIFFERENCES; HOMOGENEOUS SIMPLEX SPLINES; KNOT INSERTION; MULTIVARIATE TRUNCATED POWER; POLAR FORMS;

POLYNOMIALS;

EID: 0030571087     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/0377-0427(96)00042-8     Document Type: Article

References (24)

1. P. Alfeld, M. Neamtu and L.L. Schumaker, Circular Bernstein-Bézier polynomials, in: M. Dæhlen, T. Lyche and L.L. Schumaker, Eds., Mathematical Methods for Curves and Surfaces (Vanderbilt Univ. Press, Nashville, 1995) 11-20.
2. P. Alfeld, M. Neamtu and L.L. Schumaker, Bernstein-Bézier polynomials on spheres and sphere-like surfaces, Comput. Aided Geom. Design. to appear.
3. P. Alfeld, M. Neamtu and L.L. Schumaker, Dimension and local bases of homogeneous spline spaces, SIAM J. Math. Anal., to appear.
4. P. Alfeld, M. Neamtu and L.L. Schumaker, Fitting scattered data on sphere-like surfaces using spherical splines, J. Comput. Appl. Math., this volume.
5. E.T. Cohen, T. Lyche and R. Riesenfeld, Cones and recurrence relations for simplex splines, Constr. Approx. 3 (1987) 131-141.
6. W. Dahmen, Multivariate B-splines - recurrence relations and linear combinations of truncated powers, in: W. Schempp and K. Zeller, Eds., Multivariate Approximation Theory (Birkhäuser. Basel, 1979) 64-82.
7. W. Dahmen, On multivariate B-splines, SIAM J. Numer. Anal. 17 (1980) 179-191.
8. W. Dahmen and C.A. Micchelli, On the linear independence of multivariate B-splines. II: complete configurations, Math. Comp. 41 (1983) 143-163.
9. W. Dahmen, C.A. Micchelli and H.-P. Seidel. Blossoming begets B-splines built better by B-patches, Math. Comp. 59 (1992) 97-115.
10. D.E. Gonsor and M. Neamtu, Null spaces of differential operators, polar forms and splines, J. Approx. Theory, to appear.
11. T.N.T. Goodman and S.L. Lee, Homogeneous polynomial splines, Proc. Roy. Soc. Edinburgh Sect. A 117 (1991) 89-102.
12. P.E. Koch. Multivariate trigonometric B-splines. J. Approx. Theory 54 (1988) 162-168.
13. S.L. Lee, The use of homogeneous coordinates in spline functions and polynomial interpolation, in: W. Haussman and K. Jetter. Eds., Multivariate Approximation and Interpolation. ISNM 94 (Birkhäuser, Basel, 1990) 167-178.
14. C.A. Micchelli, On a numerically efficient method for computing multivariate B-splines, in: W. Schempp and K. Zeller, Eds., Multivariate Approximation Theory (Birkhäuser, Basel, 1979) 211-248.
15. k: multivariate B-splines and Lagrange interpolation, Rocky Mountain J. Math. 10 (1980) 485-497.
16. M. Neamtu, Multivariate divided differences I: basic properties, SIAM J. Numer. Anal. 29 (1992) 1435-1445.
17. R.N Pfeifle and H.-P. Seidel, Spherical triangular B-splines with application to data fitting, Proc. EURO-GRAPHICS '95. Blackwell (1995) 89-96.
18. L. Ramshaw, Blossoming: a connect-the-dots approach to splines. Digital Systems Research Center, Technical report #19. Palo Alto, 1987.
19. L. Ramshaw, Blossoms are polar forms, Comput. Aided Geom. Design 6 (1989) 323-358.
20. L. Ramshaw, Suitening our nomenclature, SIGACT News 70 (1989) 60-61.
21. H.-P. Seidel, Symmetric recursive algorithms for surfaces: B-patches and the de Boor algorithm for polynomials over triangles, Constr. Approx. 7 (1991) 257-279.
22. H.-P. Seidel, Representing piecewise polynomials as linear combinations of multivariate B-splines, in: T. Lyche and L. Schumaker. Eds., Mathematical Methods in Computer Aided Geometric Design II (Academic Press, New York, 1992) 559-566.
23. H.-P. Seidel and A.H. Vermeulen, Simplex splines support surprisingly strong symmetric structures and subdivision, in: P.-J. Laurent, A. Le Méhauté and L.L. Schumaker, Eds., Curves and Surfaces in Geometric Design (A.K. Peters, Wellesley, MA, 1994) 443-455.
24. K. Strøm, B-splines with homogenized knots. Adv. Comp. Math. 3 (1995) 291-308.