normalize - Properly normalizing a dual quaternion -

i'm having trouble dual quaternions, , believe it's because they're not normalized. a, b , a' dual quaternions latter conjugated. when doing this: q = * b * a' should theoretically end q = b if , b normalized. in cases, don't, , it's messing whole skeletal hierarchy.

many pages show norm of dual quaternion ||q|| = sqrt(qq'), means taking square root of dual number, , have no idea how that. right i'm dividing whole thing length of real part.

i've been searching around days, still have yet find code example on how use dual quaternions. feel know theory pretty well, still can't work.

not difficult. of interest computer graphics unit dual quaternions, i.e. ||q|| = 1. leads to:

qq' = (r, d)(r*, d*) = (rr*, rd* + dr*) = (1, 0) 

q = dual quaternion. r = real part, d = dual part. see, unit dual quaternions dual part vanishes. need calculate magnitude real part. problem reduced calculating magnitude of simple quaternion. , calculated analogous done complex numbers:

||r|| = sqrt(r1^2+r2^2+r3^2+r4^2) 

(r1 - r4 components of 4d vector r)

now divide r/||r|| , d/||r|| , have normalized q.