On: Beautiful maths simplification: quaternion from two vectors (2013)

[panic]

Is there a connection to geometric algebra here? The similarity of the final result to the geometric product (a dot b + a cross b) seems like it can't just be a coincidence.

[grondilu → panic]

Check out my implementation of a trackball with GA : http://grondilu.github.io/cube.html

[mattnewport → panic]

Yes, a quaternion is basically equivalent to a rotor in geometric algebra which is the geometric product of two vectors from what I remember.

[mattnewport → mattnewport]

More specifically, the rotor that rotates (unit) vector a to vector b is the geometric product of a and the half angle vector between a and b. Barring a sign change that works out equivalent to the quaternion given in the article.