Hmm, I think I got my math wrong too. What is a proper distance function is (1 - |a*b|). That's proportional to the distance between those points on the plane

Hmm, I think I got my math wrong too. What is a proper distance function is (1 - |a*b|). That's proportional to the distance between those points on the plane spanned along the circumference of the circle/sphere/hypersphere as it's projected onto that plane.