qgis - Delineate polygonal catchment areas from a raster using open-source GIS

I'm 90% sure this basic question has been asked before but looking through the other posts I simply do not see a useful answer.

I need to calculate polygonal(vector) catchment areas from a raster based on minimum driving distance/cost from a set of points. I've already got the raster, and for that matter, the nodes(intersections with cost attribute) used to interpolate it. What I need now are polygons for each point describing the area nearer it than any other point. This is basically like a voronoi diagram but based on network distance rather than euclidean space.

How exactly can I do this using only open-source tools? I'm comfortable with the command line if I just know what I'm looking for. I feel like GDAL is going to be the answer, but if so, what exactly is the command I'm looking for?

Thanks!