Sperical splines


Project description

A spherical spline is a piecewise-polynomial function f defined on the sphere Sd, 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 Prg 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 locally-supported basis for it.

We are currently improving the basis construction algorithms, and testing the suitability of spline spaces for least-squares approximation and integration of partial differential equations on the sphere, especially for non-uniform 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.

More details

Main publications:

Additional publications (superseded by the above):

Last edited on 2003-06-10 00:45:09 by stolfi