Sperical splines
Researchers:
Project description
A spherical spline is a piecewisepolynomial function f
defined on the sphere S^{d}, in terms of
a fixed triangulation T of the latter. Such splines
have a number of applications, e.g. in geophisics and global
weather modeling.
In this project we study the space P_{r}^{g}
of all spherical splines with a given triangulation T and a
given maximum degree g within each triangle, which are also
continuous and differentiable up to a given order r. We have
determined the dimension of this space, and implemented procedured
that construct a locallysupported basis for it.
We are currently improving the basis construction algorithms, and
testing the suitability of spline spaces for leastsquares
approximation and integration of partial differential equations on the
sphere, especially for nonuniform triangulations. For this purpose,
we have developed the concept of approximation error map [??],
a function that shows how the approximation error is distributed
over the sphere  not for a specific target function, but for
a whole linear space of them at once.
Main publications:
 Approximation error maps
A. Gomide and J. Stolfi.
Proceedings of A4A4  IV International Symposium on Algorithms for Approximation,
446453. July 2001. (Published in 2002 by the Univ. of Huddersfield, UK).
[No PS]
[bib]
 Bases for nonhomogeneous polynomial C_{k} splines on the sphere.
Anamaria Gomide and Jorge Stolfi.
Lecture Notes in Computer Science 1380: Proceedings of the 3rd Latin American Theoretical Informatics Conference (LATIN'98), 133140. Campinas, SP (Brazil); April 1998.
[PS,8p,58kB]
[bib]
 Approximation error maps.
A. Gomide and J. Stolfi.
Technical report IC0101, Institute of Computing, Univ. of Campinas;
February 2001.
[PS,23p,2.8MB]
[bib]
 NonHomogeneous Spline Bases for Approximation on the Sphere,
A. Gomide and J. Stolfi.
Technical report IC0019, Institute of Computing, Univ. of Campinas;
December 2000.
[No PS]
[bib]
 Nonhomogeneous polynomial C_{k} splines on the sphere S^{n}.
A. Gomide and J. Stolfi.
Technical report IC0010, Institute of Computing, Univ. of Campinas;
July 2000.
[PS,13p,360kB]
[bib]
 Splines Polinomiais Não Homogêneos na Esfera.
Anamaria Gomide. Doctoral thesis, School of Electrical Engineering
and Computer Science, Univ. of Campinas; May 1999.
[PS,101p,8.2MB]
[bib]
Additional publications (superseded by the above):
 Ordem de aproximação de splines polinomiais esféricos não homogêneos.
A. Gomide and J. Stolfi.
Anais do XXIII Congresso Nacional de Matemática Aplicada e Computacional,
vol. 1, 246246 (in Portuguese). September 2000.
[No PS]
[bib]

Nonhomogeneous spline bases for approximation on the sphere.
A. Gomide and J. Stolfi
Abstracts of the 4th International Conference on Curves and Surfaces,
SaintMalo, France, page 27.
July 1999.
[No PS]
[bib]
 Bases para splines polinomiais não homogêneos C_{k} na esfera.
A. Gomide and J. Stolfi. (In Portuguese.)
Technical report IC9710, Institute of Computing, Univ. of Campinas;
August 1997.
[PS,9p,39kB]
[bib]

NonHomogeneous Spline Bases for Approximation on the Sphere.
A. Gomide and J. Stolfi. (Full version; see the published
[abstract].)
July 2000.
[PS,??p,??KB]
[bib]
Last edited on 20030610 00:45:09 by stolfi