I have a line shapefile where the lines form a closed polygon. Using QGIS (2.8 on OSX 10.7) I would like to add lines to the layer, basically splitting the polygon into quadrants. Then, I will need to convert the line shapefile to a polygon shapefile, so that the newly formed quadrants will be separate polygons.
I am encountering some difficulties, and am hoping I can be pointed in the right direction. First, when I add the new lines, they don't "split" the existing boundary lines of the polygon where the new lines intersect (I am snapping the new lines to existing vertices of the boundary lines). Second, where the new lines cross in the middle, they also don't split/intersect.
In order to create a polygon shapefile with the necessary quadrants, it seems that the lines need to be intersected, or else I only get the main original polygon as a result (using the Polygonize process). I have tried the "Split lines with lines" option (using my line shapefile as both the input and output layer), and I have tried v.clean from the GRASS processes, but neither of these approaches split the lines where they intersect (either in the middle, or on the boundary) in all cases, only some.
I feel that the easiest way would be if the new lines would split the existing lines when I add them (and also split each other where they cross), but I can't figure out how to do that.