Does anybody know of a way to find out where, physically on a CD or DVD a given piece of data would be located?

I am trying to watch a DVD at the moment, and am about half-way through, but it keeps dying at a specific spot in the film, presumably because of a scratch. I have a repair kit, but I don’t know where to focus my repair because there are several scuffs and scratches on the disc and I have no way of knowing which one is causing the issue.

Obviously, cleaning all of them is inadvisable because not only does it waste the consumable materials in the kit, but not all of them are a problem, and by working them, some may become unreadable. Moreover, just because I am half-way through the movie does not mean that it would be half-way from the hub to the edge for several reasons:

• Discs have more data towards the outer edge than the inner edge (circles are more mathematically complicated than rectangles)
• The disc is not completely filled up (and even if it were, the movie itself would be be using it all, there are extras and such)
• Because in this particular case it is a commercial DVD, it is also dual-layer which further complicates manual determination

As such, I am trying to find a program that can let me identify a file (or part thereof), cluster, etc. and show me a picture of where on the CD/DVD it would be located. That way, I can look at the disc and fix any scratches that correspond to that distance from the hub.

For example, the image below might indicate where on a disc a couple of files or range of clusters would be located, so by looking for anomalies in those areas (rotating as necessary), the correct one can be identified.

I’m sure it can be done since at least one form of copy protection (DPM) uses it and DVD-lab Pro includes a “DVD Topology” feature to do this.