I have a shapefile containing arcs representing the path travelled by a truck spreading fertiliser onto a farm.
Let's say I know the spread width is 30m, i.e. the truck can spread fertiliser 15m either side of the vehicle.
I want to generate a set of polygons, which show:
1) The total area that received fertiliser
2) The areas of overlap, i.e. where two separate passes were too close together, such that some parts of the farm received twice the correct "dose" of fertiliser.
A naive approach is to just create the coverage polygons as buffers around the arcs. This works in the special case where the spread lines are distinct from each other. However, the truck could conceivably travel around the farm in an ever-decreasing spiral, and a simple buffer would fail to show overlaps where two passes of the spiral were too close together (if the spiral is a single arc, I would end up with a single polygon with no overlapping parts).
If it's relevant, I'm using the TatukGIS VCL DK, but I'm really looking for an algorithm rather than a specific solution.
Some clarifications in response to the discussion so far:
1) I can't rely on the vector data having any particular metadata (e.g. GPS logs or spread rate). I allow the user to choose a layer and specify a spread width, then the report runs.
2) The purpose of the report is really to show the user how "skilled" the vehicle operator was, where "skilled" means "achieved the highest coverage with the lowest overlap".
3) I'm more comfortable in vector land than raster land, so will prefer vector-based solutions.