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Does qgis have the ability to compare and quantify existing versus proposed elevations?

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I will suppose your points and lines have Z values, so you would need to convert them to a DEM, probably points are masspoints and lines being hard or soft lines (breaks). After that you will need a second DEM with the proposed elevations.

Having both DEMS 1. The original DEM 2. The proposed elevation DEM

You can now do raster calculations to determine where you have cuts and fills, for the quantity you can do some volumetric calculations also

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