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How can I get the value of a point that falls between 2 points of another layer?

I have a Shapefile of points with values representing the distance from an origin (blue in the example bellow) at equal interval along a polyline and a Shapefile of points that I want to get the values (red in the example bellow).

I'm thinking of using the IDW interpolation, but I'm not quite sure...

EDIT 1 : Made a more accurate example

EDIT 2 : Would a TIN (linear interpolation) and then a TIN to Raster give me a better result?

enter image description here

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IDW interpolation will not be good because it will not calculate the distance along the polyline.

IDW will interpolate from the blue point values and give more weight to those blue points that are closest.

For example if your situation was like the one below the red points between 200 and 300 might well receive values greater than 300 because of the proximity to the blue 400.

enter image description here

What you can do is use the Point Distance tool. It will build a table of distances from all your input points (red point layer) to all the near feature points (blue point layer).

You can then use Join to move the data between attribute tables as you see fit. (You may need to do a field calculation to get the exact distances you want. For example if you find that the first red point after the blue 200 is 60 units from it then the number you want is 260. You cannot take the distance from the origin as this will be a direct distance and not along your polyline.)

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