# Dihedral angles - how to calculate

Martyn Winn m.d.winn at dl.ac.uk
Fri Feb 21 04:41:13 EST 1997

```Andrew Dalke wrote:
>
>   // angle between them
>   return(geomValue = angle(n1, n2));
> }
>
> and the funtions used here are defined as:
>
> extern float angle(float *a, float *b) {
>   register float amag = sqrtf(a[0] * a[0] + a[1] * a[1] + a[2] * a[2]);
>   register float bmag = sqrtf(b[0] * b[0] + b[1] * b[1] + b[2] * b[2]);
>   register float dotprot = a[0] * b[0] + a[1] * b[1] + a[2] * b[2];
>   if (amag == 0 || bmag == 0) {
>     return 180;
>   }
>   return (57.2958 * acosf(dotprot / (amag * bmag)));
> }
>
>                                                 Andrew
>                                                 dalke at ks.uiuc.edu

Here you calculate cos(angle), and when you do the acos there will be an
ambiguity in the sign of the angle, no?  And I think this is what the
original

The way we do it, is to calculate (in your notation):

(n1 x n2) . r2   = |n1| |n2| |r2| sin(angle)
(n1 . n2) * |r2| = |n1| |n2| |r2| cos(angle)

and then use the Fortram atan2 function which takes the atan of the
ratio. Having
both arguments removes the sign ambiguity.

Think that's right....

Martyn

```