Posted 07 October 2001  05:46 PM
Posted 07 October 2001  11:28 PM
quote:
Now, if we want to transform a point in camera space to model space, we simple do this:
X = world_to_camera(T) * model_to_world(T) * X''
Posted 09 October 2001  03:17 AM
Posted 09 October 2001  04:33 AM
Posted 09 October 2001  02:11 PM
Posted 09 October 2001  09:03 PM
Posted 09 October 2001  11:55 PM
Posted 10 October 2001  12:23 AM
quote:
Original post by LilBudyWizer
I take it you mean rotations only and not rotations and translations since I don't think the transpose and inverse are the same when translations are included. I'm not particularly strong with matrices but when I tried multiplying a matrix that included translation by its transpose I didn't get the identity matrix.
Posted 10 October 2001  04:55 AM
quote:
Original post by silvren
You're right. Ortogonal matrices' inverses are simply the transposes.

Posted 10 October 2001  10:28 AM
quote:
Original post by grhodes_at_work
That's not exactly correct. For example, a scaling transformation matrix is orthogonal:
[sfx 0 0 ]
S = 0 sfy 0 
[ 0 0 sfz]
But its transpose and inverse are the same only if sfx = sfy = sfz = 1.
Posted 10 October 2001  10:31 AM
Posted 10 October 2001  12:13 PM
quote:
Original post by silvren
First, how can you determine that your matrix is orthogonal?
A matrix, if my memory''s still with me, is only called orthogonal if its inverse is the same as its transpose, and in your case the orthogonality depends on the variables'' values.
Second, the following properties must be true for your matrix to be orthogonal:
sfx = +1 sfy = +1 sfz = +1
So you can in fact get N=2^3=8 different matrices that are orthogonal, not only one.
To sum it up:
A*A(T)=I iff square matrix A is orthogonal.
Posted 10 October 2001  12:55 PM
Posted 10 October 2001  03:53 PM