[GeeTwo]

If space is bounded by a "rectangle", the easiest way to specify this is to have the first "obstacle" be space. Then, as long as the algorithm is insensitive to "inside" vs "outside" intersections, it's not a special case. If the algorithm is sensitive, you can just break it down into 2n separate obstacles and carry on.

Calculating angles in n-space.. I suppose the law of cosines applies, so that the dot product of two vectors divided by the product of their magnitudes is the cosine of the angle between them. That means that the greatest "turn" (an about face) is still pi radians, right?

And I understand that we're optimizing on "number of single turns + single segments that add up to no more than seven".