Re: [boost] [pqs] Vector<3>

From: Geoffrey Irving (irving_at_[hidden])
Date: 2006-06-16 00:46:14

On Thu, Jun 15, 2006 at 04:38:48PM -0400, Hickerson, David A wrote:
> <snip>
> 
> Geoffrey wrote:
> > And it is not true that "when doing transformations on vectors, you
> must use 1 dimension 
> > higher than the level you are working in."
> 
> He would right had I said rotations. Transformations are rotations and
> translations requiring the extra dimension.
> 
> [ x1, x2, x3, 0]
> [ y1, y2, y3, 0]
> [ z1, z2, z3, 0]
> [ t1, t2, t3, 1]

The fact that you have three 0's and a 1 there shows that that
representation is nonoptimal.  I don't recall any standard place where
those zeros and ones get filled in except the last (and increasingly
fastest) stage of scan line renderers, so it would be a terrible shame
if 4x4 matrices were the only kind of transform supported.

Geoffrey