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The IDW tool's documentation states that using barrier lines will significantly extend the processing time. It does not explain why this happen. Is anyone able to provide an insight into the inner workings of this tool?

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This blog has some explanations, here is a brief excerpt from one of the answers:

When you use a barrier, every IDW calculation--that's one per output grid cell--has to involve a check against the barrier file for every possible neighbor. The more features there are (you have 1088) and the more vertices they have (you have 23,938), the longer it takes. Your calculation is going to take a long time!

If you simply must use a barrier, then (a) simplify the features as much as possible and (b) use only those features or portions of features absolutely necessary to affect the interpolation. Use an output cell size that is as large as you can tolerate--you can resample it later if need be. Test on a small subset of your study area so that you can anticipate what the total calculation time will be.

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