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Let's say I have a set of points representing bridges. I want to create a kind of "heat" map that would highlight areas within my study area that has many bridges in good or bad condition. I have a rating attribute for each bridge point.

I've tried the spline interpolation method (in ArcGIS spatial analyst) which seems to work okay but it interpolates values for the entire area. I only want raster values for areas that within a certain distance of a bridge point (say one mile for example). How would I go about doing this?

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"Many bridges" tells us you want a density map. (After all, interpolating the bridges makes no sense: you know where all the bridges are and don't want to project that there are any more lying in the hills between them! Therefore splines are definitely out.)

SA provides two forms of a kernel density operation along with weighted focal means, which are also a form of density map. The simplest solution is to select all good bridges and run a kernel density calculation for them. Experiment with the kernel radius to make a map that conforms to your expectations (starting with one mile, for example). Repeat for the bad bridges.

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