Recently a "U" shaped scratch appeared on my car's front tire. It looks like someone rolled past a curb and scraped it. This has led me to the following problem:
Generate a plot (ideally polar) of a scratch pattern on a tire given tire radius and the ground height of a protrusion. Assume the protrusion is a single point and remains stationary while the tire rolls past. Also assume that the tire rolls straight past the protrusion, which scratches the side of the tire (i.e. hubcap, trim, etc).
If I wasn't so rusty on this material I would have taken a stab at it myself. So, any help in setting up and solving this problem would be greatly appreciated.