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Interpolation::udeg

Details

  • This message is generated when an attempt is made to create a higher-order interpolation on an unstructured point dataset.
  • Off[message] switches off the message; On[message] switches it on. For example: Off[Interpolation::udeg].

Examples

Basic Examples  (1)

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

Wolfram Language code: pts = Flatten[Table[RandomReal[1, {2}], {i, 10}, {j, 10}], 1]; f = RandomReal[1, 100]; Interpolation[Transpose[{pts, f}]]

Internally a mesh needs to be created:

Wolfram Language code: Needs["NDSolve`FEM`"] mesh = ToElementMesh[pts]

This mesh is of first order:

Wolfram Language code: mesh["MeshOrder"]

Visualize the mesh coordinates:

Wolfram Language code: HighlightMesh[MeshRegion[mesh], {0, All}]

A mesh can be converted to a higher order:

Wolfram Language code: mesh2 = MeshOrderAlteration[mesh, 2]; mesh2["MeshOrder"]

A second-order mesh introduces midside nodes:

Wolfram Language code: HighlightMesh[MeshRegion[mesh2], {0, All}]

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:

Wolfram Language code: g = Function[{x, y}, Sqrt[x ^ +y ^ 2]]@@@mesh2["Coordinates"];

A second-order interpolating function is generated:

Wolfram Language code: if = ListInterpolation[g, mesh2]

Inspect the mesh order of the interpolating function:

Wolfram Language code: if["ElementMesh"]["MeshOrder"]