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/* Function is passed two vectors. It applies the rotation
* which moves first to second to the basis set, returning
* that in new_cell. For obfuscation, the input vectors are
* also passed in new_cell.
*/
/* Copyright (c) 2007 MJ Rutter
*
* This program is free software; you can redistribute it and/or
* modify it under the terms of the GNU General Public License as
* published by the Free Software Foundation, either version 3
* of the Licence, or (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, see http://www.gnu.org/licenses/
*/
#include <stdio.h>
#include <math.h>
#include "c2xsf.h"
int is_rhs(double b[3][3]); /* Found in basis.c */
void rotation(struct unit_cell *c, struct contents *m, double new_cell[3][3]){
double v1[3],v2[3],e[3],angle,tmp;
double rot_mat[3][3];
int i,j,k;
/* If new_cell[2] is not the zero vector, use it as Euler vector
* else determine our own Euler vector
*/
if ((new_cell[2][0]*new_cell[2][0]+new_cell[2][1]*new_cell[2][1]+
new_cell[2][2]*new_cell[2][2])==0.0){
/* Extract two vectors in absolute co-ords*/
for(i=0;i<3;i++){
v1[i]=new_cell[0][i];
v2[i]=new_cell[1][i];
}
/* euler is v1xv2 */
e[0]= v1[1]*v2[2]-v1[2]*v2[1];
e[1]=-v1[0]*v2[2]+v1[2]*v2[0];
e[2]= v1[0]*v2[1]-v1[1]*v2[0];
/* Which needs normalising */
tmp=sqrt(e[0]*e[0]+e[1]*e[1]+e[2]*e[2]);
if (tmp<1e-20) error_exit("Impossibly small cross product in rotation");
e[0]/=tmp;
e[1]/=tmp;
e[2]/=tmp;
}else{
e[0]=new_cell[2][0];
e[1]=new_cell[2][1];
e[2]=new_cell[2][2];
tmp=sqrt(e[0]*e[0]+e[1]*e[1]+e[2]*e[2]);
if (tmp<1e-20) error_exit("Impossibly small euler axis in rotation");
e[0]/=tmp;
e[1]/=tmp;
e[2]/=tmp;
/* project the vectors given onto plane perpendicular to euler axis */
tmp=e[0]*new_cell[0][0]+e[1]*new_cell[0][1]+e[2]*new_cell[0][2];
for(i=0;i<3;i++) v1[i]=new_cell[0][i]-tmp*e[i];
tmp=e[0]*new_cell[1][0]+e[1]*new_cell[1][1]+e[2]*new_cell[1][2];
for(i=0;i<3;i++) v2[i]=new_cell[1][i]-tmp*e[i];
}
/* angle is arccos(v1.v2 / mod(v1).mod(v2)) */
angle=acos((v1[0]*v2[0]+v1[1]*v2[1]+v1[2]*v2[2])/
sqrt((v1[0]*v1[0]+v1[1]*v1[1]+v1[2]*v1[2]) *
(v2[0]*v2[0]+v2[1]*v2[1]+v2[2]*v2[2])));
/* We have a sign ambiguity here, which we should try to resolve */
for(i=0;i<3;i++) rot_mat[0][i]=v1[i];
for(i=0;i<3;i++) rot_mat[1][i]=v2[i];
for(i=0;i<3;i++) rot_mat[2][i]=e[i];
if (debug>2) fprintf(stderr,"Sign is %s\n",is_rhs(rot_mat)?"+":"-");
if (!is_rhs(rot_mat)) angle*=-1;
if (debug>1) fprintf(stderr,"Rotating by %g degrees about (%g,%g,%g)\n",
angle*180/M_PI,e[0],e[1],e[2]);
/* Wikipedia says that the rotation matrix is:
*
* I cos(theta) + (1-cos(theta))ee^t - E sin(theta)
*
* ( 0 -e3 e2 )
* where E = ( e3 0 -e1 )
* ( -e2 e1 0 )
*
* with e=(e1,e2,e3) being the Euler vector (axis of rotation)
*/
for(i=0;i<3;i++)
for(j=0;j<3;j++)
rot_mat[i][j]=0;
for(i=0;i<3;i++) rot_mat[i][i]=cos(angle);
tmp=1-cos(angle);
for(i=0;i<3;i++)
for(j=0;j<3;j++)
rot_mat[i][j]+=tmp*e[i]*e[j];
tmp=sin(angle);
rot_mat[0][1]-=tmp*e[2];
rot_mat[0][2]+=tmp*e[1];
rot_mat[1][0]+=tmp*e[2];
rot_mat[1][2]-=tmp*e[0];
rot_mat[2][0]-=tmp*e[1];
rot_mat[2][1]+=tmp*e[0];
if (debug>2){
fprintf(stderr,"Rotation matrix\n");
for(i=0;i<=2;i++)
fprintf(stderr,"%f %f %f\n",
rot_mat[i][0],rot_mat[i][1],rot_mat[i][2]);
if (is_rhs(rot_mat)) fprintf(stderr,"(Determinant is >=0)\n");
else fprintf(stderr,"(Warning: determinant is <0\n");
fprintf(stderr,"(Old basis is a %shs)\n",is_rhs(c->basis)?"r":"l");
}
/* Now apply rotation to basis */
for(i=0;i<3;i++)
for(j=0;j<3;j++)
new_cell[i][j]=0;
for(i=0;i<3;i++)
for(j=0;j<3;j++)
for(k=0;k<3;k++)
new_cell[i][j]+=rot_mat[j][k]*c->basis[i][k];
if (debug>1){
fprintf(stderr,"New basis set\n");
for(i=0;i<=2;i++)
fprintf(stderr,"%f %f %f\n",
new_cell[i][0],new_cell[i][1],new_cell[i][2]);
}
for(i=0;i<3;i++)
for(j=0;j<3;j++)
c->basis[i][j]=new_cell[i][j];
if (debug>2)
fprintf(stderr,"(New basis is a %shs)\n",is_rhs(c->basis)?"r":"l");
/* Everything remains as was in relative co-ordinates, but the
* absolute co-ords of the atoms need recalculating, as does the
* reciprocal basis set
*/
addabs(m->atoms,m->n,c->basis);
real2rec(c);
}
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