I have a non-uniform grid within which velocity data is known at each grid point. This velocity data is to be interpolated to allow for evaluation of velocity at an arbitrary point inside the grid.(adsbygoogle = window.adsbygoogle || []).push({});

I am wondering about the correct approach to this problem. In actuality I want to evaluate the velocity using tri-cubic interpolation but considering the grid is non-uniform I would start with basics.

In the image you can sort of see what the grid looks like. I have for example points [1 2 3 4] and I want to evaluate the velocity at point X (x, y). dx is constant but dy is different between (x) and (x+1) therefore two different dy exist to account for this; dy1 and dy2.

So bilinear interpolation:

interpolate normally between 1 and 2 using dy1, interpolate between 3 and 4 using dy2, here comes the problem. I assume simply interpolating between the two found values using dx is enough? Possibly dx could be extended by the fact that it is now somewhat tilted (simple trigonometry). But then again the same tilt would apply to the position of X, i.e. the distance it is in x from point 1 and 2.

What is the correct way of doing this? I suppose if I figure out this it should not be too hard to extend to tri-cubic.

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# Non-uniform bi-linear interpolation

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