Vector to raster conversion

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I'm using GRASS but, in case, I'm also familiar with R and Qgis.

I'm trying to convert a vector area map into a raster one. My problem is that the resolution of the raster is too low (and I can't change it for other reasons) so many areas disppear.

I need each raster cell covered by the vector to be converted and to associate to the cell the coverage (i.e. if the 20% of the cell is covered by the vector map its value will be 20).

Thanks and sorry for my english.



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