Geoffrey Irving said: (by the date of Thu, 15 Jun 2006 10:23:24 -0700)
On Thu, Jun 15, 2006 at 07:11:23PM +0200, Janek Kozicki wrote:
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>.
You are absolutely right, I forgot about this one when I was talking about quaternions. So it means that quaternions will be implementad as separate class. Though it is possible that quaternion will use vector<4> inside as a backend to store data...
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.
IMHO it's a good solution. Such conversion would not be used anyway. Also the documentation must explicitly state that q*v is actually a conjugation. In fact when I started working with yade, and had some problems. One of the questions I asked myself was - what actually q*v is doing - does it perform rotation (full conjugation)? Or maybe it's just multiplication? I had to check that in the source, because I was using third party math library, not a one written by me. -- Janek Kozicki |