Suppose that I have a GIS grid.

I need to do linear interpolation for a given point located inside a cell of the GIS grid.

The locations and values of the vertices of each cell in the grid are known.

I am also given the location and value of the centroid of each cell.

For a given point, I need to use linear interpolation to find the value.

If the given point is located on the centroid, I do not need to do any linear interpolation. I just pick up the value of the centroid.

But, if the given point is close to the centroid but not located on it, I want the value of the centroid to play an important role in the interpolation with the 4 vertices of the cell and the centroid.

How to implement this idea ?

I do not want to define a fixed value as a radius. If the given point distance from the centroid is less than the centroid, the centroid value will be used as the given point value. This may cause some "jumps" in the interpolation.

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