I have a sphere with center O = (0,0,0) and radius r=1. I want to calculate "true" angles phi(i) between points Pi lying on this sphere.
From cartesian coordinate, I have :
$cos(phi) = x1 x2 + y1 y2 + z1 z2$
The problem is that this angle change according to positions of points on the sphere. For example, if severals points make a loop on the equator, my sum of phi(i) would be 360 degrees. If it's at the top of the sphere, the sum of phi(i) would be <360 degrees.
Does anyone knows how to correct that, a paper explaining this problem ? If points describe a rotation, what about changement of axis of rotation and angle calculation ?
We told me to estimate the plane containing the points and to project them on it. I used :
What do you thing about this ? I have correct angle for one example but bad results for others data.