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.