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Abstract: . Recently, we have introduced spaces of splines defined on triangulations lying on the sphere or on sphere-like surfaces. These spaces arose out of a new kind of Bernstein-B'ezier theory on such surfaces. The purpose of this paper is to contribute to the development of a constructive theory for such spline spaces analogous to the well-known theory of polynomial splines on planar triangulations. Rather than working with splines on sphere-like surfaces directly, we instead investigate more... (Update)
Context of citations to this paper: More
...space A = H 2 0 [T ] S 2 , which has dimension 42. This is the lowest degree homogeneous space wich has an Alfeld Neamtu Schumeker basis [1] The gauge space F is the family Y 2 6 of spherical harmonics of maximum order 6, which has dimension 49. The intersection of the two...
...of spherical functions as functions of the spatial cartesian coordinates (x; y; z) restricted to the sphere. Alfeld, Neamtu e Schumaker [1,2,3] investigated the use of homogeneous spherical polynomial splines as an approximation space for functions de ned on S 2 . We showed...
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BibTeX entry: (Update)
Alfeld, P., M. Neamtu, and L. L. Schumaker, Dimension and local bases of homogeneous spline spaces, SIAM J. Math. Anal., to appear. http://citeseer.ist.psu.edu/145692.html More
@article{ alfeld96dimension,
author = "Peter Alfeld and Marian Neamtu and Larry L. Schumaker",
title = "Dimension and Local Bases of Homogeneous Spline Spaces",
journal = "SIAM Journal on Mathematical Analysis",
volume = "27",
number = "5",
pages = "1482--1501",
year = "1996",
url = "citeseer.ist.psu.edu/145692.html" }
Citations (may not include all citations):474 Curves and Surfaces for Computer Aided Geometric Design (context) - Farin - 1990 ACM
23 Superspline spaces of smoothness r and degree d 3r (context) - Ibrahim - 1991
23 The dimension of bivariate spline spaces of smoothness r for.. (context) - Alfeld - 1987
22 form basics (context) - de Boor - 1987
20 quartic bivariate splines (context) - Alfeld, Piper et al. - 1987
12 piecewise polynomials of degree n (context) - Morgan, Scott et al. - 1975
11 Dual bases for spline spaces on cells (context) - Schumaker - 1988 ACM DBLP
11 the dimension of bivariate splines spaces of smoothness r an.. (context) - Alfeld - 1990
6 On dimension and existence of local bases for multivariate s.. (context) - Alfeld, Schumaker et al. - 1992
5 Bernstein-B'ezier polynomials on circles (context) - Alfeld, Neamtu et al.
4 Multivariate piecewise polynomials - de Boor - 1993
3 The exact analysis of sparse rectangular linear systems (context) - Alfeld - 1991 ACM
2 The generic dimension of the space of C 1 splines of degree .. (context) - Alfeld, Schumaker et al. - 1993
2 A software system for the exact analysis of rectangular rank.. (context) - Alfeld - 1991
2 Recent progress on multivariate splines (context) - Schumaker - 1991
2 The dimension of multivariate spline spaces (context) - Sirvent - 1990
1 Fitting scattered data on the sphere (context) - Alfeld, Neamtu et al.
1 Triangulation methods in CAGD (context) - Schumaker - 1993
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