Maths and physics is the quaternion questions forum.
The point transform operation pointout = q * pointin * q-1 (where the point is pure imaginary i.e. the w component is 0) maps the origin to the origin so to rotate around a point you need to translate the object so its centre of rotation is at the origin, rotate the object and rotate the translation you applied, then apply the negated rotated translation to the object again.
Matrix multiplication also maps the origin to the origin, but in homogeneous coordinates the origin is actually (0, 0, 0, 1) and translation is possible. (Note the "real" origin (0, 0, 0, 0) isn't a valid element of homogeneous space and is indeed mapped to (0, 0, 0, 0) by multiplication by any 4x4 matrix).
EDIT: That is because matrix multiplication is a linear mapping, i.e.
f(k * a) = k * f(a)
and f(a + b) = f(a) + f(b)
from which we see f(0) = f(0 * a) = 0 * f(a) = 0. (Alternatively, f(0) = f(a + (-a)) = f(a) + f(-a) = f(a) - f(a) = 0)
Edited by Paradigm Shifter, 08 October 2013 - 06:12 AM.
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