# Finding Joint Angle from Motion Capture

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Mary on 12 Dec 2012
Commented: Suranjita Ganguly on 23 Jun 2020
Hi!
I'm working right now with data from a motion capture device, essentially picking up data for three markers placed on the head neck and shoulder in an x y z plane.
My difficulty trying to develop a code to calculate the joint angles between these three markers. I am able to animate the three coordinates to play as an animation, but I'm more interested in the calculation of the angles between these points changing over time.
Thanks

Roger Stafford on 12 Dec 2012
At any time, let H = [x,y,z], N = [x,y,z], S = [x,y,z] be coordinate vectors of the head, neck, and shoulder markers at that time. Then the three respective inner angles within the triangle HNS then are:
h = atan2(norm(cross(N-H,S-H)),dot(N-H,S-H));
n = atan2(norm(cross(S-N,H-N)),dot(S-N,H-N));
s = atan2(norm(cross(H-S,N-S)),dot(H-S,N-S));
(The sum of these should always be pi to within round-off accuracy.)
Roger Stafford
Suranjita Ganguly on 23 Jun 2020
The sum of the angles should be Pi (approx), because the three angles are forming a triangle, and sum of all internal angles in a triangle is 180 degrees i.e. pi