Spline
Instead of averaging
values, like IDW does, the Spline interpolation
method fits a flexible surface, as if it were stretching a rubber sheet across
all the known point values.
The Spline
method of interpolation estimates unknown values by bending a surface through
known values.
This stretching effect is
useful if you want estimated values that are below the minimum or above the
maximum values found in the sample data. This makes the Spline
interpolation method good for estimating lows and highs where they are not
included in the sample data.
A surface created with Spline interpolation passes through each sample point and
may exceed the value range of the sample point set.
However, when
the sample points are close together and have extreme differences in value, Spline interpolation doesn't work as well. This is because Spline uses slope calculations (change over distance) to
figure out the shape of the flexible rubber sheet.
Phenomena that cause
surface values to change suddenly, such as a cliff face or a fault line, are
not represented well by a smooth-curving surface. In such cases, you might
prefer to use IDW interpolation, where barriers can be used to deal with these
types of abrupt changes in local values.
There are two types of Spline: Regularized and Tension. A Tension Spline is flatter than a Regularized Spline
of the same sample points, forcing the estimates to stay closer to the sample
data. You might say that the Tension Spline method
produces a surface more rigid in character, while the Regularized Spline method creates one that's more elastic.