How to perform interpolation using inverse of the square of distance

Please can someone assist with how to interpolate using the inverse of the square of the distance from points of known values to the point of value you wish to interpolate for?

I am trying to get the pressure at the vertex points of my triangulation by interpolating the pressure at the neighboring control volume midpoints using the inverse of the square of the distance between the center of the neighboring control volume and the vertex.

Answer 1

[Walter Roberson]

You might want to use something like pdist to get the pairwise distances between your target points and the control points; then square those, take reciprocal, multiply by the pressures at those points (this part is a guess), sum the result.

[Mark]

Thanks Walter for your response, that was my initial guess too but the interpolated values I get as a result are too large to be correct.

[Walter Roberson]

If a point is 2 units away from each of two sources that have values A and B, then what would be the expected pressure at that location? A/4 + B/4 ?

[Mark]

Yes I guess so, but my entire domain is 1mX1m so distances are well less than 1 which makes squaring it lower and so increases the result of A/4 and B/4.

[Walter Roberson]

But the physical processes involved are scale-invariant, so you should be able to multiply them by an arbitrary scale factor. In particular you should be able to substitute Euclidean distance based upon indices (provided that your x and y scales are the same.)