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:
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) also what is the difference betwenn p1 an |p1| and how are they calculated?
7) 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!!!