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I have two polygon layers I'd like to overlay using QGIS or another open source tool. What I want as output is a polygon layer with the extent of one polygon, but with each polygon in that layer subdivided into polygons based on overlapping polygons in the second layer.

This seems like a basic operation but I'm having trouble finding documentation on how to do it.

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    I think you have to describe your goal a little bit more precisely, or better still, include an image that shows what you're trying to do. At the moment, the phrasing is a bit confusing: You say you want "a polygon layer with the extent of one polygon", but "each polygon in that layer" should be subdivided. – Jake Oct 25 '13 at 14:37
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I believe you are looking for an 'intersect' operation. This leaves only the full extent covered by both inputs (where both overlap) but with polygons split and attributes combined from both.

In QGIS (v2.0) go to your 'Processing' menu and click 'toolbox'. Geoalgorithms > Vector > Overlay > Intersection

In QGIS (v1.8) Go to: 'Vector' menu > Geoprocessing Tools > Intersect.

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I seem to have gotten what I want by using the SEXTANTE Toolbox to run v.overlay from GRASS, with the "OR" operation selected.

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    If that gives you the correct results, then the native QGIS function you want is "Union". – Jake Oct 25 '13 at 14:41
  • Thanks. Unfortunately, having experimented with this a bit, it looks like fTools functions seem to be prohibitively slow for my datasets, whereas the GRASS function ran in just a few minutes. – user1521655 Oct 25 '13 at 15:03
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Check the identity tool from Saga Algorithms.

To perform the Identity operation with two polygon layers, you can use the Saga's algorithm "Indentity". Here you can find the documentation about the algorithm:

http://www.saga-gis.org/saga_module_doc/2.1.3/shapes_polygons_19.html

From the Qgis interface, you can find it in "Processing Toolbox" menu:

SAGA >- Shapes-Polygons >- Identity

enter image description here

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