A warning occurs because currently no algorithm is implemented that allows to recover a higher-order interpolation on a list of unstructured points:

Internally a mesh needs to be created:

This mesh is of first order:

Visualize the mesh coordinates:

A mesh can be converted to a higher order:

A second-order mesh introduces midside nodes:

The remaining question is to find the correct values at the midside nodes from the given (linear) point set f. If such values can be found then a second-order interpolation is possible. Currently no such algorithm is implemented.

If more information about the dataset is available and values for the midside nodes can be generated, a second-order interpolation can be constructed in the following manner. To generate a set of values for the second-order mesh, a function is evaluated at the second-order mesh coordinates:

A second-order interpolating function is generated:

Inspect the mesh order of the interpolating function: