# [Chimera-users] Get angles in degree out of Rotation matrix

Thomas Goddard goddard at cgl.ucsf.edu
Mon Nov 27 14:38:31 PST 2006

```Hi Michael,

Perhaps you can compare the orientation between the exact symmetric
placement of a chain and the actual position by measuring the
translation and rotation angle needed to align the two.  By rotation
angle I mean that any rotation can be represented as a rotation about
a single axis (which depends on the rotation).  I do not understand
what you mean by rotation angles about x, y and z axes.  As I
mentioned that depends on the order of the rotations and therefore is
rarely used.  In the Chimera match command or matchmaker tool the
optimal rotation matrix is computed -- it is *not* decomposed into
separate x, y and z rotations during that calculation.  I suppose if
your system has symmetry about the z axis you could ask what rotation
about z best aligns a chain with the exact symmetric chain location.
In other words, only a z-axis rotation rather then rotation about an
arbitrary axis would be allowed.  Chimera does not have code for that
and I have never heard that number reported.

If you spell out precisely what angle is needed I can give better
advice on how to get it from Chimera.

Tom

> From: "Stohr, Michael" <stohr at uni-mainz.de>
> To: "Thomas Goddard" <goddard at cgl.ucsf.edu>
> Date: Mon, 27 Nov 2006 09:51:31 +0100
> Subject: AW: Get angles in degree out of Rotation matrix
>
> Hi Tom,
>
> Thanks a lot for your description. It does not fit completely my demand. I will rephrase my question, is there a simple way to determine the three angles between the two 3d-structures of two identical chains? The background is that my molecule is not absolutely symmetrical and I want to quantify the asymmetry. So, I want to be able to say, this angle between this two chains differs from ideal symmetry angle by X degrees for different directions (x, y, z). I thought the rotation matrix would be the way to do so, but it does not seem so. I've found a not very precise method by using the distance tool and trigonometric functions. Therefore, if there is no answer for my question it will be ok at first especially I have to finish my theses very soon. By the way, in which order does for example the tool match or matchmaker rotates a structure or is this not predictable?
>
> Thanks for your afford,
> Michael

```