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

From: Michael Marcin (mmarcin_at_[hidden])
Date: 2006-06-16 12:55:18

> 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

The last column is used when you need the inverse or transpose of a 
transformation matrix.

Mike