What is a 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 plots response (z) values at the x-y intersections of the mesh.

3D wireframe and surface plots
Contour plot

Usually, the mesh is not displayed on a graph. These graphs illustrate what the mesh might look like.

Tip

Choose Calc > Make Mesh Data to create a regular grid of x-y sample locations or factor combinations. You can then add your own z columns or choose from a list of functions.

How does Minitab plot response data on the mesh?

Minitab plots response (z) values at the x-y intersections of an evenly-spaced mesh. If your x- and y-values are evenly spaced, Minitab plots the z-values at the x-y intersections. If your x- and y-values 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.

Data on a regular mesh
Data on an irregular mesh

The symbols on these graphs represent the actual, not interpolated, data points. With a regular mesh the z-values are plotted at the x-y intersections. But when the x- and y-values do not form a regular mesh the z-values are not plotted at the intersections.

Note

Symbols and project lines always display the actual, not the interpolated, data points.

Change the interpolation method for an irregular mesh

If your x- and y-values 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.

Note

If your x- and y- values form an evenly-spaced grid, the interpolation method has no effect on your plot.

  1. In the dialog box for the graph you are creating, click Surface Options or Contour Options, then click the Method tab.
  2. Choose an interpolation method.
    Distance method
    The Distance method (default) works well in a wide range of circumstances. It is conservative in that it will always give estimates of z within the range of your data.
    Akima’s polynomial method
    This method works well in some cases, but can have undesired effects in others. Because it 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 the Distance method if the following are true Use Akima's polynomial method if the following are true
    Your surface has isolated extreme values or sudden transitions Your surface smoothly changes over the x- and y-range of your data
    Sampling is not intensive enough to capture smooth surface transitions Sampling is intensive enough to catch smooth surface transitions
    Sampling error is large Sampling error is small relative to the surface
  3. Click OK.
  4. (Optional) Show the locations of your x- and y- data by adding symbols to the plot.
    1. With the graph active, choose Editor > Add > Data Display.
    2. Choose Symbols, then click OK.
    Tip

    Show the locations of your x- and y- data for the following reasons:

    • If you use Akima's polynomial method, showing symbols can help you look for steep changes just outside the x- and y-data that may not be supported if you had sampled in that area.
    • If you use the Distance method, showing the symbols can help you choose a distance power because you can see how predictions extend beyond your x- and y-data.

What is the mesh resolution?

The number of x- and y-values on a mesh determines its resolution. A higher resolution mesh (one with more x- and y-values) will result in a finer interpolation of the surface or contours. The following wireframe and contour plots show the same data but use different mesh resolutions. (Gridlines on the contour plots show approximate mesh location.)

5 by 5 mesh with wireframe plots
15 by 15 mesh with wireframe plots
5 by 5 mesh with contour plots
15 by 15 mesh with contour plots

Adjust the mesh resolution

When x-y data do not form a regular grid, the mesh resolution could have a large effect on a contour or surface plot. If your data were sampled such that your x-y points are close to a regular grid, you might enhance the fit by specifying a mesh similar to that of your data.

For example, you want to investigate the effect of temperature and pressure on cook time. You have four temperature settings (325, 350, 375, 400) and three pressure settings (5, 10, 15). When you run the experiment, however, the temperature was slightly different than the desired setting for several runs; thus, the data won't quite form a regular grid. However, because your temperature values are close to regular, a 4 x 3 mesh (temperature x pressure) might give good results for your contour and 3D surface plots.

Note

Using a mesh with more and smaller intervals than exist between data points may seem to add more resolution to the graph, but the detail is probably only background noise.

  1. Double-click the 3D surface plot or contour plot and click the Method tab.
  2. Under Mesh for Interpolating Surface, choose Custom.
  3. Enter X-Mesh Number and Y-Mesh Number for the resolution of mesh you want.
  4. Click OK.
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