# Interpolation method for mesh

A mesh is a grid of regularly spaced x- and y-values on which a 3D surface, 3D wireframe, or contour plot is based. Minitab calculates response (z) values at the x-y intersections of the mesh. The mesh is not displayed on a graph. The following graphs illustrate what the mesh might look like.

If the x- and y-values on a plot are not evenly spaced, Minitab interpolates (estimates) the z-values at the intersections of a regular 15 by 15 mesh with the same x- and y-ranges as your data. You can change the interpolation method that Minitab uses. If you are unsure of which method to use, you may want to try both and pick the one that works best for your data. For more information, go to Working with mesh on contour plots and 3D graphs.

To edit the method when you create a graph, click Surface Options or Contour Options, and then select the options on the Method tab. To edit the surface on an existing graph, double-click the surface, and click the Method tab.

Change the interpolation method for an irregular mesh
If the x- and y- values form an evenly-spaced grid, the interpolation method has no effect on the plot.
Distance method
The distance method (default) works well in a wide range of circumstances. It is a conservative method because it always provides estimates of z within the range of your data. Use the distance method if the following are true:
• Your surface has isolated extreme values or sudden transitions
• Sampling is not intensive enough to capture smooth surface transitions
• Sampling error is large

In Distance power, enter a number greater than 0 and less than or equal to 12 to indicate the amount of local variation smoothing. The closer to 0, the closer the fits are to the overall mean. The farther from 0, the more weight is placed on local variation.

Select Standardize x- and y-data to standardize the x- and y-data if the data are measured on different scales. (The graph scale does not change.)

Akima’s polynomial method
This method works well in some cases, but can produce misleading results in other cases. Because this method uses a fifth-order polynomial, it can estimate z-values at x-y positions beyond those you have sampled that are too large or small. Use Akima's polynomial method if the following are true:
• Your surface smoothly changes over the x- and y-range of your data
• Sampling is intensive enough to catch smooth surface transitions
• Sampling error is small relative to the surface

In Boundary z-value, enter a z-value to use at the boundaries (corners and edges) of the plot. By default, Minitab uses the minimum z-value.