16 Jun
2006
16 Jun
'06
4:46 a.m.
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