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Splitting by overlap

I need to find a way to split features based on overlap within the same layer. If, for example, I have two circles that overlap partially, I would have an output of three features (ideally with the number of overlaps - that would be 1 or 0 for the parts with no overlap and 1 or 2 for the middle overlapping part - I wrote 0 or 1 and 1 or 2 because it does not batter if it counts the number of overlaps or the number of features that overlap).

Figure 1: Basic principle Visualised basic principle of overlap

Real example: I have isochrones of walking distances and I want to differentiate areas with more that one isochrone overlapping. One way to do this is to create a fine grid where I use Join attributes by location (summary), but that is more steps and more computational power, that I would like to avoid. Ideally I would also like to add some values to this overlap - for example if one isochrone has potential 5 customers and the other has 10, I would like to have 15 customers in the overlapping part. I need this for around 900 features, so this cannot be done by hand.

To sum up:

  • How can I split features based on overlap?
  • How can I add values that are the sum of a selected attributes for all overlapping features?
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