On Thu, Jun 15, 2006 at 07:11:23PM +0200, Janek Kozicki wrote:
Your arguments did not convince me at all, because they are out of place.
Also - think about it - there is only one applicable definition of multiplication between vector<3> and vector<4> - and this definition will assume vector<4> to be quaternion which rotates vector<3>
I wish that were the case, but sadly, quaternion multiplication is slightly ambiguous. The problem is that the normal quaternion rotation is actually a conjugation: rotated_v = q v q^-1 where v = (x,y,z) is canonically viewed as the quaternion (0,x,y,z). rotated_v will come out looking like (0,rx,ry,rz), so we can drop the zero and view it as a vector again. This could be a problem if the conversion between vector<3> and quaternion was an actual C++ conversion, since q * v could mean two completely different things. I imagine most people handle this by disallowing that conversion.
Other definition for such multiplication doesn't exist, so there is no conflict with other math fields. It's specific just like cross product for vector<3>
So still I think that quaternion can be a template specialization for unitless (dimensionless) vector<4>. Also we can add a typedef quaternion<double> vector<4,double>; // etc...
That's bad for the following simple reason. If you give people two vector<4>'s and ask them to multiple them, they'll expect the answer to either not exist or be component-wise multiplication. There's very little chance they'll expect fancy quaternion multiplication. Quaternions need a multiplication operator to be useful, so they can't be the same as vector<4>. Geoffrey