[Bioperl-l] torsion angle

[Giwrgos Tataetis]

Hi guys. I am an undergraduate student in Biology and I ve been assigned to
calculate the torsion angles in a molecule... The hole idea is that we have
4 points in a 3D system A-B-C-D and the only thing we know is their
coordinates, i.e. A(xa, ya, za). The wanted is to find tha torsion angle
among between A-B an C-D. I have repeatedly searched and asked around but I
still cant figure out what would a possible formula or algorithm would be. I
have found this in the archives of a mailing list but I really dont know if
it stands or is it true:

http://www.pikipimp.com/pp/pimped_ph...=1211535101226<http://www.pikipimp.com/pp/pimped_photo/s/image/29/876/862/1.JPG?ts=1211535101226>

even if this formula stands I have a lot of question.
1) how can I calculate r1, r2, r3 out of the coordinates of the points
2) how can I multipy them. well actually I think this is the cross product
but i am not sure..
3) I found how to calculate the cross product of two vectors and I think
that this is it

*a* × *b* = (a2b3 − a3b2) *i* + (a3b1 − a1b3) *j* + (a1b2 − a2b1) *k* =
(a2b3 − a3b2, a3b1 − a1b3, a1b2 − a2b1) however I still cant understand how
can a vector which -from what I understood- is not just a point, be defined
only by three coordinates, and if so how is this calculated out of its start
and endpoint...
4)in the third an fourth equation from what I can tell there are two or more
unknown elements so how can eaxh be calculated...
5) if I can find the cos or the sin of the angle what do I need atan for,
and what atan stands for, since tha only things I know is cos, sin and tan.
6) Last but not least I encounter two major problems which makes it even
harder to find an answer, since i am a biologist and maths was never of
first priority for me -regreatably i must admit- and english is not my
native language so the math terms are not easily understood.
Please can anyone help me finding some answers or even point some directions
here? thank you very much!!!