[Chimera-users] Transformation matrices

[Greg Couch]

On Fri, 29 Jun 2007, Eduardo Sanz-Garcia wrote:

> I am getting the rotation matrices (I am not interested in the
> translation column) using matrixget command.
> My naive question: Should I use in this way:
>
> x'                    x
> y' = [3x3 matrix]     y
> z'                    z
>
>
> or in this other way?
>
> z'                   z
> y' = [3x3 matrix']   y
> x'                   x
>
>
> Thank you very much.

It's the first way.  The coordinate system is right-handed with column 
vectors for Points and Vectors (eg., normals) which would be on the right 
hand side of the matrix matrixset/matrixget uses.  An additional row of
[0 0 0 1] could be added on if you wanted a 4x4 matrix.  For Point or 
Vector transformations, Points have an implicit forth value of one:

     Px'     R00 R01 R01 Tx     Px
     Py'  =  R10 R11 R12 Ty  *  Py
     Pz'     R20 R21 R22 Tz     Pz
                                1

And Vectors and an implicit forth value of zero:

     Vx'     R00 R01 R01 Tx     Vx
     Vy'  =  R10 R11 R12 Ty  *  Vy
     Vz'     R20 R21 R22 Tz     Vz
                                0

So Vector transformations ignore the translation part.

 	Greg Couch
 	UCSF Computer Graphics Lab