A long distance drivers technique for saving time is to drive the width of the road you are on. To do this you drive so that you are placing you car on the inside of all turns as much as possible. I want to know how much distance is saved.
From the point of view of a math problem it could be presented as two parralel curves in 3space forming a ribbon and you want to know the difference in length of the edges compared to a radius minimizing path. The problem can have a simplified presentation of two curves in a plane.
I am not sure of the best equation form for the edges to make it possible to calculate the radius min line between.