If the edge is straight (or close to it) you can cut a section through the point of interest. If the edge is curved, it gets a little trickier.
If you have only defined 2 radii on the edge, it does a linear change along the 2 points. If you know how far down the edge you are you can calculate it from that. If more than 2 points have been specified (with different radii) then it does a cubic interpolation between them and again it gets tricky.