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I have a road layer of a country. What method or plugin would you suggest, to find a single point furthest from any road

(but as you can see, there is a coastline, so points in the sea can't count)

The road layer looks like this:

road layer

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    Your question isn't well specified. A large area could be a convex polygon (perhaps much longer than "wide") paralleling a road, but no point in the polygon may be very far from a road. What are you trying to show? What have you already looked at? – BradHards Dec 16 '13 at 9:56
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    I am looking for two things: area by size that is surrounded by roads, and also a single point that is furthest from any roads. – normis Dec 16 '13 at 9:58
  • That sounds like two questions so I recommend that you edit this one to focus on whichever of the two things is important to have answered first. meta.stackexchange.com/questions/39223/… – PolyGeo Dec 16 '13 at 10:20
  • sorry about that. in that case: single point furthest from any road (but as you can see, there is a coastline, so points in the sea can't count) – normis Dec 16 '13 at 10:22
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    The question is for points, but the approach is the same: gis.stackexchange.com/questions/21575/… – Matthias Kuhn Dec 16 '13 at 15:08
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First you need to rasterize the layer and then you can use proximity analysis from the GDAL Tools plugin: Raster > Analysis > Proximity.

More information can be found in the following related answer: Calculating distance to points in QGIS

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