Exact and Smoothing Interpolators

Gridding methods included with Surfer are divided into two general categories: exact interpolators and smoothing interpolators. Some exact interpolators can incorporate a smoothing factor that causes them to become smoothing interpolators.

Exact Interpolators

Exact interpolators honor data points exactly when the point coincides with the grid node being interpolated. In other words, a coincident point carries a weight of essentially 1.0 and all other data points carry a weight of essentially zero. Even when using exact interpolators, it is possible that the grid file does not honor specific data points if the data points do not exactly coincide with the grid nodes. Refer to Weighted Averaging for more information on weights assigned during interpolation.

To increase the likelihood that your data are honored, you can increase the number of grid nodes in the X and Y direction. This increases the chance that grid nodes coincide with data points, thereby increasing the chance that the data values are applied directly to the grid file.

The following methods are exact interpolators:

Smoothing Interpolators

Smoothing interpolators or smoothing factors can be employed during gridding when you do not have strict confidence in the repeatability of your data measurements. This type of interpolation reduces the effects of small-scale variability between neighboring data points. Smoothing interpolators do not assign weights of 1.0 to any single point, even when a point is exactly coincident with the grid node. When smoothing is used, weighting factors are assigned so the map is smoother. In the extreme case, all data points are given equal weight and the surface becomes a horizontal plane at the average for all data in the data file.

The following methods are smoothing interpolators:

See Also

Grid Data

Introduction to Gridding Methods

General Gridding Recommendation

Choosing Methods Based on the Number of XYZ Data Points

Grid Function

Producing a Grid File from a Regular Array of XYZ Data

Weighted Averaging