How do I calculate arc angle between two points on a circle?

Question

Given a circle with a known center point and two points on the circle (thus known radius), how do I determine the angle of the minimum arc between the two points on the circle?

Answer 1

Turn the center to the two points into a pair of vectors, then shove through this.

So, cos^-1 ((x₁x₂ + y₁y₂ + z₁z₂) / r²).