# [Chimera-users] Transformation matrices

Greg Couch gregc at cgl.ucsf.edu
Fri Jun 29 02:26:45 PDT 2007

```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

```