As an alternative, we may use a global procedure to grid our data.
This approach, implemented in the program * surface*, represents
an improvement over standard minimum curvature algorithms by allowing
users to introduce some tension into the surface.
Physically, we are trying to force a thin elastic plate to go through
all our data points; the values of this surface at the grid points
become the gridded data. Mathematically, we want to find the function
that satisfies the following constraints:

where is the ``tension'',
. Basically, as
we obtain the minimum curvature solution, while as
we go towards a harmonic solution (which is linear
in cross-section). The theory behind all this is quite involved
and we do not have the time to explain it all here, please see
*Smith and Wessel* [1990] for details. Some of the most important
switches for this program are indicated in Table 3.3^{3.1}.