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## Gridding with Splines in Tension

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 z(x, y) that satisfies the following constraints:

where t 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.

Table 3.3: Some of the options in surface
Option | Purpose
-–A aspect | Sets aspect ratio for anisotropic grids.
-–C limit | Sets convergence limit. Default is 1/1000 of data range.
-–T tension | Sets the tension [Default is 0]

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