TorCoor.c

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/************************************************************************/
/**

   \file       TorCoor.c
   
   \version    V1.1
   \date       07.07.14
   \brief      Calculate cartesian coordinates from torsion angle
   
   \copyright  (c) UCL / Dr. Andrew C. R. Martin 1989-2014
   \author     Dr. Andrew C. R. Martin
   \par
               Institute of Structural & Molecular Biology,
               University College London,
               Gower Street,
               London.
               WC1E 6BT.
   \par
               andrew@bioinf.org.uk
               andrew.martin@ucl.ac.uk
               
**************************************************************************

   This code is NOT IN THE PUBLIC DOMAIN, but it may be copied
   according to the conditions laid out in the accompanying file
   COPYING.DOC.

   The code may be modified as required, but any modifications must be
   documented so that the person responsible can be identified.

   The code may not be sold commercially or included as part of a 
   commercial product except as described in the file COPYING.DOC.

**************************************************************************

   Description:
   ============


**************************************************************************

   Usage:
   ======

**************************************************************************

   Revision History:
   =================

*************************************************************************/
/* Doxygen
   -------
   #GROUP    Maths
   #SUBGROUP Geometry
   #FUNCTION  blTorToCoor()
   Calculates cartesian coordinates for an atom given the coordinates of
   three antecedant atoms and the bond length, angle and torsion angle
*/
/************************************************************************/
/* Includes
*/
#include <math.h>
#include <stdio.h>

#include "MathType.h"
#include "SysDefs.h"

/************************************************************************/
/* Defines and macros
*/
#define ETA (1.07e-7)

/************************************************************************/
/* Globals
*/

/************************************************************************/
/* Prototypes
*/

/************************************************************************/
/*>BOOL blTorToCoor(VEC3F ant1, VEC3F ant2, VEC3F ant3, 
                    REAL bond, REAL theta, REAL torsion,
                    VEC3F *coords)
   -----------------------------------------------------
*//**

   \param[in]     ant1      First antecedent atom coordinates
   \param[in]     ant2      Second antecedent atom coordinates
   \param[in]     ant3      Third antecedent atom coordinates
   \param[in]     bond      Bond length from ant3 to new atom
   \param[in]     theta     Bond angle ant2-ant3-new
   \param[in]     torsion   Torsion angle ant1-ant2-ant3-new
   \param[out]    *coords   Coordinates of new atom
   \return                        TRUE if distance between atoms 2 and 3
                                is < ETA (1.07e-7)

   Calculates cartesian coordinates for an atom given the coordinates of
   three antecedant atoms and the bond length, angle and torsion angle

-  08.07.96 Original By: ACRM based on earlier FORTRAN code
-  07.07.14 Use bl prefix for functions By: CTP
*/
BOOL blTorToCoor(VEC3F ant1, VEC3F ant2, VEC3F ant3, 
                 REAL bond, REAL theta, REAL torsion,
                 VEC3F *coords)
{
   REAL x1,  y1,  z1,
        x2,  y2,  z2,
        x3,  y3,  z3,
        xx4, yy4, zz4,
        x2o, y2o, z2o,
        CosTheta, SinTheta,
        CosTor,   SinTor,
        DistYZ1,  InvDistYZ1,
        DistXZ2,  DistSqXZ2,
        Dist2,    InvDist2,
        y1o,      z1o,
        xz2o,     xx1,
        BondSinTheta,
        InvDistXZ2;
   BOOL RetVal = FALSE;

   /* Generate pretend position of new atom if all other atoms were
      easily lined up.
   */
   SinTheta = sin(PI-theta);
   CosTheta = cos(PI-theta);
   SinTor = sin(torsion);
   CosTor = cos(torsion);
   BondSinTheta = bond * SinTheta;
   coords->x = bond * CosTheta;
   coords->y = BondSinTheta * CosTor;
   coords->z = BondSinTheta * SinTor;

   /* Translate ant1 and ant2 such that ant3 is at the origin.          */
   x3 = ant3.x;
   y3 = ant3.y;
   z3 = ant3.z;
   x1 = ant1.x - x3;
   y1 = ant1.y - y3;
   z1 = ant1.z - z3;
   x2 = ant2.x - x3;
   y2 = ant2.y - y3;
   z2 = ant2.z - z3;

   /* Rotate ant1 by rotation of ant2 to the origin.                    */
   DistSqXZ2 = x2*x2 + z2*z2;
   Dist2     = sqrt(DistSqXZ2+y2*y2);
   DistXZ2   = sqrt(DistSqXZ2);
   
   if (Dist2 < ETA)
   {
      RetVal   = TRUE;
      InvDist2 = 1.0/ETA;
   }
   else
   {
      InvDist2 = 1.0/Dist2;
   }

   if (DistXZ2 < ETA)
   {
      xx1 = x1;
      x2o = 1.0;
      z2o = 0.0;
   }
   else
   {
      InvDistXZ2 = 1.0/DistXZ2;
      x2o        = x2*InvDistXZ2;
      z2o        = z2*InvDistXZ2;
      xx1        = x1*x2o + z1*z2o;
      z1         = z1*x2o - x1*z2o;
   }

   xz2o = DistXZ2 * InvDist2;
   y2o  = y2 * InvDist2;
   x1   = (-xx1*xz2o) - y1*y2o;
   y1   = xx1*y2o - y1*xz2o;
   
   /* Rotate new atom by inverse of rotation which takes the transformed 
      ant1 atom to the xy plane by rotation about the x axis.
   */
   DistYZ1    = sqrt(y1*y1 + z1*z1);
   InvDistYZ1 = 1.0 / DistYZ1;
   y1o        = y1 * InvDistYZ1;
   z1o        = z1 * InvDistYZ1;
   yy4        = y1o*coords->y - z1o*coords->z;
   zz4        = y1o*coords->z + z1o*coords->y;

   /* Rotate new atom by inverse of ant2 rotation to -x axis.           */
   xx4       = y2o*yy4 - xz2o*coords->x;
   coords->y = (-xz2o*yy4) - y2o*coords->x;
   coords->x = x2o*xx4 - z2o*zz4;
   coords->z = z2o*xx4 + x2o*zz4;

   /* Move back since we translated such that ant3 was at the origin    */
   coords->x += x3;
   coords->y += y3;
   coords->z += z3;

   return(RetVal);
}