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/*
* Project: The SPD Image correction and azimuthal regrouping
* http://forge.epn-campus.eu/projects/show/azimuthal
*
* Copyright (C) 2005-2010 European Synchrotron Radiation Facility
* Grenoble, France
*
* Principal authors: P. Boesecke (boesecke@esrf.fr)
* R. Wilcke (wilcke@esrf.fr)
*
* This program is free software: you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public License as published
* by the Free Software Foundation, either version 3 of the License, 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 Lesser General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* and the GNU Lesser General Public License along with this program.
* If not, see <http://www.gnu.org/licenses/>.
*/
# define ROT3D_VERSION "rot3d : V1.01 Peter Boesecke 2011-06-16"
/*---------------------------------------------------------------------------
NAME
rot3d - Conversion between rot1, rot2, rot3 and 3d rotation matrix.
SYNOPSIS
DESCRIPTION
Consecutive rotations, first around lab axis 1, second around lab axis 2 and
third around lab axis 3. The axes 1, 2 and 3 define a right-handed orthogonal
system in the laboratory space:
around lab axis 1:
| 1.0 0.0 0.0 |
R1(rot1) = | 0.0 cos(rot1) -sin(rot1) |
| 0.0 sin(rot1) cos(rot1) |
around lab axis 2:
| cos(rot2) 0.0 sin(rot2) |
R2(rot2) = | 0.0 1.0 0.0 |
| -sin(rot2) 0.0 cos(rot2) |
around lab axis 3:
| cos(rot3) -sin(rot3) 0.0 |
R3(rot3) = | sin(rot3) cos(rot3) 0.0 |
| 0.0 0.0 1.0 |
all rotations:
R(rot1,rot2,rot3) = R3(rot3).R2(rot2).R1(rot1)
r11 = R[0][0] = cos(rot2) cos(rot3)
r12 = R[1][0] = sin(rot1) sin(rot2) cos(rot3) - cos(rot1) sin(rot3)
r13 = R[2][0] = cos(rot1) sin(rot2) cos(rot3) + sin(rot1) sin(rot3)
r21 = R[0][1] = cos(rot2) sin(rot3)
r22 = R[1][1] = cos(rot1) cos(rot3) + sin(rot1) sin(rot2) sin(rot3)
r23 = R[2][1] = cos(rot1) sin(rot2) sin(rot3) - sin(rot1) cos(rot3)
r31 = R[0][2] = -sin(rot2)
r32 = R[1][2] = sin(rot1) cos(rot2)
r33 = R[2][2] = cos(rot1) cos(rot2)
| R[0][0] R[1][0] R[2][0] |
R(rot1,rot2,rot3) = | R[0][1] R[1][1] R[2][1] |
| R[0][2] R[1][2] R[2][2] |
| r11 r12 r13 |
= | r21 r22 r23 |
| r31 r32 r33 |
| c2 c3 s1 s2 c3 - c1 s3 c1 s2 c3 + s1 s3 |
= | c2 s3 c1 c3 + s1 s2 s3 c1 s2 s3 - s1 c3 |
| -s2 s1 c2 c1 c2 |
(c1=cos(rot1), s1=sin(rot1), c2=cos(rot2) etc.)
principal ranges of the angles rot1, rot2, rot3:
rot1 ] -Pi .. +Pi ]
rot2 [ -Pi/2 .. +Pi/2 ]
rot3 ] -Pi .. +Pi ]
History
2010-04-26 Peter Boesecke creation V0.0
2010-05-17 PB V1.0
2011-04-18 PB V1.0 rot3d_version() added
2011-05-17 PB V1.01 Suggested parentheses added
---------------------------------------------------------------------------*/
/***************************************************************************
* Include *
***************************************************************************/
# include "rot3d.h"
/***************************************************************************
* Internal *
***************************************************************************/
/****************************************************************************
* Static Variables and Numbers *
****************************************************************************/
static double rot3d_eps=1e-8;
static double rot3d_pi=3.1415926535897932384626;
/****************************************************************************
* Routines *
****************************************************************************/
/*--------------------------------------------------------------------------
NAME
rot3d_version --- returns pointer to the version string
SYNOPSIS
const char *rot3d_version ( void );
DESCRPTION
Returns pointer to the version string.
--------------------------------------------------------------------------*/
const char *rot3d_version ( void )
{
return ( ROT3D_VERSION );
} /* rot3d_version */
/*---------------------------------------------------------------------------
NAME
rot3d_determinante
SYNOPSIS
double rot3d_determinante ( double A[3][3] )
DESCRIPTION
input: double A[3][3] (3d matrix)
RETURN VALUE
determinante of A
---------------------------------------------------------------------------*/
double rot3d_determinante ( double A[3][3] )
{ double determinante=0.0;
if (!A) {
fprintf( stderr, "ERROR: rot3d_determinante: NULL pointer\n" );
goto rot3d_determinante_error;
}
determinante = A[0][0]*(A[1][1]*A[2][2]-A[2][1]*A[1][2]);
determinante -= A[0][1]*(A[1][0]*A[2][2]-A[1][2]*A[2][0]);
determinante += A[0][2]*(A[1][0]*A[2][1]-A[1][1]*A[2][0]);
rot3d_determinante_error:
return( determinante );
} // rot3d_determinante
/*---------------------------------------------------------------------------
NAME
rot3d_mat_scale
SYNOPSIS
int rot3d_mat_scale ( double A[3][3], double scale )
DESCRIPTION
Multiplies each element of A with scale.
input: double A[3][3] (3d matrix)
double scale (scale factor)
updated: A
RETURN VALUE
status
---------------------------------------------------------------------------*/
int rot3d_mat_scale ( double A[3][3], double scale )
{ int status=-1;
int i,j;
if (!A) {
fprintf( stderr, "ERROR: rot3d_mat_scale: NULL pointer\n" );
goto rot3d_mat_scale_error;
}
if (scale!=1.0)
for (i=0;i<3;i++)
for (j=0;j<3;j++)
A[i][j] *= scale;
status = 0;
rot3d_mat_scale_error:
return( status );
} // rot3d_mat_scale
/*+++------------------------------------------------------------------------
NAME
rot3d_mat_transpose --- transpose a 3-dimensional matrix
SYNOPSIS
int rot3d_mat_transpose ( double A[3][3] )
DESCRIPTION
A[3][3] = Transpose(A[3][3])
RETURN VALUE
status
----------------------------------------------------------------------------*/
int rot3d_mat_transpose ( double A[3][3] )
{ int j,k;
double tmp;
for (j=0;j<3;j++)
for (k=0;k<j;k++) {
tmp=A[j][k];
A[j][k] = A[k][j];
A[k][j] = tmp;
}
return(0);
} // rot3d_mat_transpose
/*---------------------------------------------------------------------------
NAME
rot3d_isnotrot
SYNOPSIS
int rot3d_isnotrot ( double R[3][3] )
DESCRIPTION
Returns 1 if R is a rotation
RETURN VALUE
is rotation 0
no rotation 1
error -1
---------------------------------------------------------------------------*/
int rot3d_isnotrot ( double R[3][3] )
{ int is_not_rot=-1;
int i,j;
double len;
if (!R) {
fprintf( stderr, "ERROR: rot3d_isnotrot: NULL pointer\n" );
goto rot3d_isnotrot_error;
}
if ( fabs(rot3d_determinante(R)-1.0)>rot3d_eps )
is_not_rot=1;
else {
is_not_rot=0;
for (i=0;i<3;i++) {
len=0.0;
for (j=0;j<3;j++)
len+=R[i][j]*R[i][j];
if (fabs(len-1.0)>rot3d_eps) {
is_not_rot=1;
break;
}
}
}
rot3d_isnotrot_error:
return( is_not_rot );
} // rot3d_isnotrot
/*---------------------------------------------------------------------------
NAME
rot3d_matrix
SYNOPSIS
int rot3d_matrix(double ROT[3], double R[3][3]);
DESCRIPTION
input: double ROT[3] (angles rot1, rot2, rot3)
updated: double R[3][3] (3d rotation matrix)
RETURN VALUE
status
---------------------------------------------------------------------------*/
int rot3d_matrix(double ROT[3], double R[3][3])
{ int status=-1;
double c1, c2, c3;
double s1, s2, s3;
if ((!ROT)||(!R)) {
fprintf( stderr, "ERROR: rot3d_matrix: NULL pointer\n" );
goto rot3d_matrix_error;
}
c1 = cos(ROT[0]); c2 = cos(ROT[1]); c3 = cos(ROT[2]);
s1 = sin(ROT[0]); s2 = sin(ROT[1]); s3 = sin(ROT[2]);
R[0][0] = c2 * c3;
R[1][0] = s1 * s2 * c3 - c1 * s3;
R[2][0] = c1 * s2 * c3 + s1 * s3;
R[0][1] = c2 * s3;
R[1][1] = c1 * c3 + s1 * s2 * s3;
R[2][1] = c1 * s2 * s3 - s1 * c3;
R[0][2] = -s2;
R[1][2] = s1 * c2;
R[2][2] = c1 * c2;
status = 0;
rot3d_matrix_error:
return( status );
} // rot3d_matrix
/*---------------------------------------------------------------------------
NAME
rot3d_inverse_matrix
SYNOPSIS
int rot3d_inverse_matrix(double ROT[3], double R[3][3]);
DESCRIPTION
input: double ROT[3] (angles rot1, rot2, rot3)
updated: double R[3][3] (inverse 3d rotation matrix)
RETURN VALUE
status
---------------------------------------------------------------------------*/
int rot3d_inverse_matrix(double ROT[3], double R[3][3])
{ int status=-1;
if ( (status=rot3d_matrix(ROT, R)) ) goto rot3d_inverse_matrix_error;
if ( (status=rot3d_mat_transpose (R)) ) goto rot3d_inverse_matrix_error;
return( status );
rot3d_inverse_matrix_error:
return( status );
} // rot3d_inverse_matrix
/*---------------------------------------------------------------------------
NAME
rot3d_angles
SYNOPSIS
int rot3d_angles(double ROT[3], double R[3][3]);
DESCRIPTION
Calculate rot1, rot2 and rot3 for an arbitrary 3d rotation matrix.
updated: double ROT[3] (angles rot1, rot2, rot3)
input: double R[3][3] (3d rotation matrix)
principal ranges of the angles rot1, rot2, rot3:
rot1 ] -Pi .. +Pi ]
rot2 [ -Pi/2 .. +Pi/2 ] => c2 >= 0.0
rot3 ] -Pi .. +Pi ]
RETURN VALUE
status
---------------------------------------------------------------------------*/
int rot3d_angles(double ROT[3], double R[3][3])
{ int status=-1;
double rot1=0.0, rot2=0.0, rot3=0.0; // set defaults
double c1, c2;
double s1;
double determinante=0.0, scale=1.0;
if ((!ROT)||(!R)) {
fprintf( stderr, "ERROR: rot3d_angles: NULL pointer\n" );
goto rot3d_angle_error;
}
determinante = rot3d_determinante( R );
if ( determinante < rot3d_eps ) {
fprintf( stderr, "ERROR: rot3d_angles: Det(R) = %lg is not positive\n",
determinante );
goto rot3d_angle_error;
}
scale = pow( determinante, 1.0/3.0 );
ROT[0] = rot1;
ROT[1] = rot2;
ROT[2] = rot3;
if ( (status=rot3d_mat_scale ( R, scale )) ) {
goto rot3d_angle_error;
}
if ( rot3d_isnotrot ( R ) ) {
fprintf( stderr, "ERROR: rot3d_angles: R is not a rotation matrix\n");
goto rot3d_angle_error;
}
// rot1
if ( (1.0-fabs(R[0][2])) > rot3d_eps ) { // c2 > 0
rot1 = atan2( R[1][2], R[2][2]);
} else { // c2 == 0
if ( R[0][2] < 0) { // sin(rot2)==+1.0
rot1 = atan2( R[1][0],R[2][0])+rot3;
} else { // sin(rot2)==-1.0
rot1 = atan2( -R[1][0],-R[2][0])-rot3;
}
}
c1 = cos(rot1); s1 = sin(rot1);
if (fabs(rot1+rot3d_pi)<rot3d_eps) rot1=-rot3d_pi;
if (rot1>rot3d_pi) rot1-=rot3d_pi*2.0;
if (rot1<=-rot3d_pi) rot1+=rot3d_pi*2.0;
// rot2
if ( fabs(s1) > rot3d_eps ) { // s1 != 0.0
rot2 = atan2(-R[0][2],R[1][2]/s1);
} else { // c2 != 0.0
rot2 = atan2(-R[0][2],R[2][2]/c1);
}
c2 = cos(rot2);
if (fabs(rot2+rot3d_pi)<rot3d_eps) rot2=-rot3d_pi;
if (rot2>rot3d_pi) rot2-=rot3d_pi*2.0;
if (rot2<=-rot3d_pi) rot2+=rot3d_pi*2.0;
// rot3
if ( fabs(c2) > rot3d_eps ) {
rot3 = atan2(R[0][1]/c2,R[0][0]/c2);
} else { // default of rot3
rot3 = atan2(-(R[1][1]*s1+R[2][1]*c1)/R[0][2],
-(R[1][0]*s1+R[2][0]*c1)/R[0][2]);
}
if (fabs(rot3+rot3d_pi)<rot3d_eps) rot3=-rot3d_pi;
if (rot3>rot3d_pi) rot3-=rot3d_pi*2.0;
if (rot3<=-rot3d_pi) rot3+=rot3d_pi*2.0;
ROT[0] = rot1;
ROT[1] = rot2;
ROT[2] = rot3;
status = 0;
rot3d_angle_error:
return( status );
} // rot3d_angles
|
