Fitting irregular data to a mesh
main topics 

Contour plots, 3D surface plots, and 3D wireframe plots are always constructed on a grid of evenly spaced x- and y-values called a mesh.

·    If your x- and y-values are evenly spaced, Minitab uses the regular mesh defined by your data and plots the z-values at the mesh 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. You can choose the interpolation method Minitab uses to determine the z-values for the mesh intersections.

image\Regulgnu.gif

image\Irreggnu.gif

Mesh created from regular data – the x- and y-values form a regular grid.

Mesh interpolated based on irregular data - x- and y-values do not form a regular grid; therefore, data points are not always at the intersections of the mesh.

Note

Symbols and projection lines always display the actual (rather than interpolated) data points.

Interpolation methods

If your data are irregular, Minitab interpolates the z-value at each grid intersection using one of two methods: Distance or Akima's polynomial.

·    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 works well in some cases, but can have undesired effects in others. Because it uses a fifth-order polynomial, it can estimate unacceptably large or small z-values at x-y positions beyond those you have sampled.

Note

If your data form a regular grid, the interpolation method has no effect on your plot.

  Use the following chart to help you decide which method to use:

Use the Distance method if...

Use Akima's polynomial method if...

·    Your surface has isolated extreme values or abrupt 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 capture smooth surface transitions

·    Sampling error is large

·    sampling error is small relative to the surface

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.

Tip

Show the locations of your x- and y- data by adding symbols to the plot (Editor > Add > Data Display > check Symbols). Akima's polynomial method sometimes shows steep changes just outside the x- and y-data that may not be supported if you had sampled there. If you use the Distance method, showing the symbols can also help you in choosing a distance power because you can see how predictions extend beyond your x- and y-data.