Hi Burr - basically if you want to find the shortest distance that you can move the curve in one specific direction until it first touches another one, that is a totally different problem than finding closest or furthest points along shared perpendicular lines.

For something like that instead of finding the shared perp/perp lines it would instead involve shooting a ray out along that move direction on every point from the base curve and then intersecting that ray with the target object and finding which spot has the smallest distance between the start of the ray and the intersection point.

That's a different problem than what CrvDeviation in Rhino is doing - CrvDeviation in Rhino will find the shortest and furthest global distances between the 2 curves (which will include perp/perp lines).

For a directed one I'm not sure where you would find that already done - maybe as a collision detection mechanism in some physics simulation stuff...

But a direction constrained one doesn't really have anything to do with perp/perp lines like you were originally asking about here.

- Michael