.. _example_29:

(29) Gridding spherical surface data using splines
--------------------------------------------------

Finally, we demonstrate how gridding on a spherical surface can be
accomplished using Green's functions of surface splines, with or without
tension. Global gridding does not work particularly well in Cartesian
coordinates hence the chosen approach. We use
:doc:`greenspline </greenspline>` to produce a crude
topography grid for Mars based on radii estimates from the Mariner 9 and
Viking Orbiter spacecrafts. This data comes from *Smith and Zuber*
[Science, 1996] and is used here as a small (*N* = 370) data set we can
use to demonstrate spherical surface gridding. Since
:doc:`greenspline </greenspline>` must solve a *N* by
*N* matrix system your system memory may impose limits on how large data
sets you can handle; also note that the spherical surface spline in
tension is particularly slow to compute.

Our script must first estimate the ellipsoidal shape of Mars from the
parameters given by *Smith and Zuber* so that we can remove this
reference surface from the gridded radii. We run the gridding twice:
First with no tension using *Parker*\ 's [1990] method and then with
tension using the *Wessel and Becker* [2008] method. The grids are then
imaged with :doc:`grdimage </grdimage>` and
:doc:`grdcontour </grdcontour>` and a color scale is placed between them.

.. literalinclude:: /_verbatim/example_29.txt
   :language: bash

.. figure:: /_images/example_29.*
   :width: 500 px
   :align: center

   Gridding of spherical surface data using Green's function splines.
