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I need a raster coverage of distances from points outside the geographic region of interest, and am having trouble doing this with QGIS.

Questions like this one (Calculating distance to points in QGIS) seem close to what I want, but I'm getting hung up on the first step. The raster that I create with the QGIS "Rasterize" tool has an extent that does not overlap with the region of interest (because all of the points I want the distance from are outside of that region). I don't see any option for changing the extent of the generated raster.

I am then unable to generate a Proximity raster with the extent I need. How can I get the correct extent?

In addition, when I run "Proximity", I consistently get an error that my raster cells are not square and so distance calculations may not be accurate. I don't know how to make square cells because the tool asks for how many cells I want in the x and y directions, not the x and y dimensions of each cell. Is there a way of fixing this?

Ultimately, I'm a bit uncomfortable with the necessity of converting point data to raster in order to calculate proximity, and wonder whether there is an open source tool that can do what I want without the "Rasterize" step...

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The answer to the first part of my question (how to rasterize with pre-specified extents and resolution) is here: Rasterize vector layers with different extents into identical raster grids with QGIS

For this purpose, I'm finding working with gdal from the command line more useful than using the QGIS gdal interface.

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