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*
* Author: "Sjors H.W. Scheres"
* MRC Laboratory of Molecular Biology
*
* 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 2 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 General Public License for more details.
*
* This complete copyright notice must be included in any revised version of the
* source code. Additional authorship citations may be added, but existing
* author citations must be preserved.
***************************************************************************/
/***************************************************************************
*
* Authors: Carlos Oscar S. Sorzano (coss@cnb.csic.es)
*
* Unidad de Bioinformatica of Centro Nacional de Biotecnologia , CSIC
*
* 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 2 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 General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
* 02111-1307 USA
*
* All comments concerning this program package may be sent to the
* e-mail address 'xmipp@cnb.csic.es'
***************************************************************************/
#ifndef GEOMETRY_H
#define GEOMETRY_H
#include "src/multidim_array.h"
#include "src/transformations.h"
#ifndef FLT_EPSILON
#define FLT_EPSILON 1.19209e-07
#endif
/// @name Euler operations
/// @{
/** Euler angles --> "Euler" matrix
*
* This function returns the transformation matrix associated to the 3 given
* Euler angles (in degrees).
*
* As an implementation note you might like to know that this function calls
* always to Matrix2D::resize
*
* See http://xmipp.cnb.csic.es/twiki/bin/view/Xmipp/EulerAngles for a
* description of the Euler angles.
*/
void Euler_angles2matrix(DOUBLE a, DOUBLE b, DOUBLE g, Matrix2D< DOUBLE >& A,
bool homogeneous=false);
/** Euler angles2direction
*
* This function returns a vector parallel to the projection direction.
* Resizes v if needed
*/
void Euler_angles2direction(DOUBLE alpha,
DOUBLE beta,
Matrix1D< DOUBLE >& v);
/** Euler direction2angles
*
* This function returns the 2 Euler angles (rot&tilt) associated to the direction given by
* the vector v.
*/
void Euler_direction2angles(Matrix1D< DOUBLE >& v,
DOUBLE& alpha,
DOUBLE& beta);
/** "Euler" matrix --> angles
*
* This function compute a set of Euler angles which result in an "Euler" matrix
* as the one given. See \ref Euler_angles2matrix to know more about how this
* matrix is computed and what each row means. The result angles are in degrees.
* Alpha, beta and gamma are respectively the first, second and third rotation
* angles. If the input matrix is not 3x3 then an exception is thrown, the
* function doesn't check that the Euler matrix is truly representing a
* coordinate system.
*
* @code
* Euler_matrix2angles(Euler, alpha, beta, gamma);
* @endcode
*/
void Euler_matrix2angles(const Matrix2D< DOUBLE >& A,
DOUBLE& alpha,
DOUBLE& beta,
DOUBLE& gamma);
/** Up-Down projection equivalence
*
* As you know a projection view from a point has got its homologous from its
* diametrized point in the projection sphere. This function takes a projection
* defined by its 3 Euler angles and computes an equivalent set of Euler angles
* from which the view is exactly the same but in the other part of the sphere
* (if the projection is taken from the bottom then the new projection from the
* top, and viceversa). The defined projections are exactly the same except for
* a flip over X axis, ie, an up-down inversion. Exactly the correction
* performed is:
*
* @code
* newrot = rot;
* newtilt = tilt + 180;
* newpsi = -(180 + psi);
* @endcode
*
* @code
* Euler_up_down(rot, tilt, psi, newrot, newtilt, newpsi);
* @endcode
*/
void Euler_up_down(DOUBLE rot,
DOUBLE tilt,
DOUBLE psi,
DOUBLE& newrot,
DOUBLE& newtilt,
DOUBLE& newpsi);
/** The same view but differently expressed
*
* As you know a projection view from a point can be expressed with different
* sets of Euler angles. This function gives you another expression of the Euler
* angles for this point of view. Exactly the operation performed is:
*
* @code
* newrot = rot + 180;
* newtilt = -tilt;
* newpsi = -180 + psi;
* @endcode
*
* @code
* Euler_another_set(rot, tilt, psi, newrot, newtilt, newpsi);
* @endcode
*/
void Euler_another_set(DOUBLE rot,
DOUBLE tilt,
DOUBLE psi,
DOUBLE& newrot,
DOUBLE& newtilt,
DOUBLE& newpsi);
/** Mirror over Y axis
*
* Given a set of Euler angles this function returns a new set which define a
* mirrored (over Y axis) version of the former projection.
*
* @code
* -----> X X<------
* | |
* | |
* | ======> |
* v v
* Y Y
* @endcode
*
* The operation performed is
*
* @code
* newrot = rot;
* newtilt = tilt + 180;
* newpsi = -psi;
* @endcode
*
* @code
* Euler_mirrorY(rot, tilt, psi, newrot, newtilt, newpsi);
* @endcode
*/
void Euler_mirrorY(DOUBLE rot,
DOUBLE tilt,
DOUBLE psi,
DOUBLE& newrot,
DOUBLE& newtilt,
DOUBLE& newpsi);
/** Mirror over X axis
*
* Given a set of Euler angles this function returns a new set which define a
* mirrored (over X axis) version of the former projection.
*
* @code
* -----> X Y
* | ^
* | |
* | ======> |
* v |
* Y -----> X
* @endcode
*
* The operation performed is
*
* @code
* newrot = rot;
* newtilt = tilt + 180;
* newpsi = 180 - psi;
* @endcode
*
* @code
* Euler_mirrorX(rot, tilt, psi, newrot, newtilt, newpsi);
* @endcode
*/
void Euler_mirrorX(DOUBLE rot,
DOUBLE tilt,
DOUBLE psi,
DOUBLE& newrot,
DOUBLE& newtilt,
DOUBLE& newpsi);
/** Mirror over X and Y axes
*
* Given a set of Euler angles this function returns a new set which define a
* mirrored (over X and Y axes at the same time) version of the former
* projection.
*
* @code
* -----> X Y
* | ^
* | |
* | ======> |
* v |
* Y X<-----
* @endcode
*
* The operation performed is
*
* @code
* newrot = rot;
* newtilt = tilt;
* newpsi = 180 + psi;
* @endcode
*
* @code
* Euler_mirrorX(rot, tilt, psi, newrot, newtilt, newpsi);
* @endcode
*/
void Euler_mirrorXY(DOUBLE rot,
DOUBLE tilt,
DOUBLE psi,
DOUBLE& newrot,
DOUBLE& newtilt,
DOUBLE& newpsi);
/** Apply a geometrical transformation
*
* The idea behind this function is the following. 3 Euler angles define a point
* of view for a projection, but also a coordinate system. You might apply a
* geometrical transformation to this system, and then compute back what the
* Euler angles for the new system are. This could be used to "mirror" points of
* view, rotate them and all the stuff. The transformation matrix must be 3x3
* but it must transform R3 vectors into R3 vectors (that is a normal 3D
* transformation matrix when vector coordinates are not homogeneous) and it
* will be applied in the sense:
*
* @code
* New Euler matrix = L * Old Euler matrix * R
* @endcode
*
* where you know that the Euler matrix rows represent the different system
* axes. See Euler_angles2matrix for more information about the Euler coordinate
* system.
*
* @code
* Matrix2D< DOUBLE > R60 = rotation3DMatrix(60, 'Z');
* R60.resize(3, 3); // Get rid of homogeneous part
* Matrix2D< DOUBLE > I(3, 3);
* I.initIdentity();
* Euler_apply_transf(I, R60, rot, tilt, psi, newrot, newtilt, newpsi);
* @endcode
*/
void Euler_apply_transf(const Matrix2D< DOUBLE >& L,
const Matrix2D< DOUBLE >& R,
DOUBLE rot,
DOUBLE tilt,
DOUBLE psi,
DOUBLE& newrot,
DOUBLE& newtilt,
DOUBLE& newpsi);
/** 3D Rotation matrix after 3 Euler angles
*
* Creates a rotational matrix (4x4) for volumes around the combination of the 3
* rotations around ZYZ. All angles are in degrees. You must use it with
* IS_NOT_INV in applyGeometry.
*
* @code
* Matrix2D< float > euler = Euler_rotation3DMatrix(60, 30, 60);
* @endcode
*/
void Euler_rotation3DMatrix(DOUBLE rot, DOUBLE tilt, DOUBLE psi,
Matrix2D<DOUBLE> &result);
//@}
#endif
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