Spline is an interpolation method that estimates values using a mathematical function that minimizes overall surface curvature, resulting in a smooth surface that passes exactly through the input points.
Conceptually, the sample points are extruded to the height of their magnitude; Spline bends a sheet of rubber that passes through the input points while minimizing the total curvature of the surface. It fits a mathematical function to a specified number of nearest input points while passing through the sample points. This method is best for generating gently varying surfaces such as elevation, water table heights, or pollution concentrations.
Spine methods—regularized and tension
There are two Spline methods: Regularized and Tension.
The Regularized method creates a smooth, gradually changing surface with values that can lie outside the sample data range.
The Tension method controls the stiffness of the surface according to the character of the modeled phenomenon. It creates a less smooth surface with values more closely constrained by the sample data range.
Additional parameters
Further control of the output surface is accomplished through two additional parameters—weight and number of points.
For the Regularized Spline method, the Weight parameter defines the weight of the third derivative of the surface in the curvature minimization expression. The higher the weight, the smoother the output surface. The values entered for this parameter must be equal to or greater than zero. The typical values that can be used are 0, .001, .01, .1, and .5.
For the Tension Spline method, the Weight parameter defines the weight of tension. The higher the weight, the coarser the output surface. The values entered have to be equal to or greater than zero. The typical values are 0, 1, 5, and 10.
The Number of Points parameter identifies the number of points used in the calculation of each interpolated cell. The more input points you specify, the more each cell is influenced by distant points and the smoother the output surface is. The larger the number of points, the longer it will take to process the output raster.