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/********************************************************************** |
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matrix3x3.cpp - Handle 3D rotation matrix. |
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|
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Copyright (C) 1998-2001 by OpenEye Scientific Software, Inc. |
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Some portions Copyright (C) 2001-2005 by Geoffrey R. Hutchison |
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|
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This file is part of the Open Babel project. |
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For more information, see <http://openbabel.sourceforge.net/> |
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|
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This program is free software; you can redistribute it and/or modify |
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it under the terms of the GNU General Public License as published by |
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the Free Software Foundation version 2 of the License. |
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|
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This program is distributed in the hope that it will be useful, |
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but WITHOUT ANY WARRANTY; without even the implied warranty of |
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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GNU General Public License for more details. |
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***********************************************************************/ |
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|
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#include <math.h> |
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|
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#include "mol.hpp" |
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#include "matrix3x3.hpp" |
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|
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#ifndef true |
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#define true 1 |
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#endif |
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|
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#ifndef false |
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#define false 0 |
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#endif |
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|
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using namespace std; |
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|
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namespace OpenBabel |
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{ |
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|
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/** \class matrix3x3 |
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\brief Represents a real 3x3 matrix. |
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|
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Rotating points in space can be performed by a vector-matrix |
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multiplication. The matrix3x3 class is designed as a helper to the |
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vector3 class for rotating points in space. The rotation matrix may be |
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initialised by passing in the array of floating point values, by |
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passing euler angles, or a rotation vector and angle of rotation about |
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that vector. Once set, the matrix3x3 class can be used to rotate |
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vectors by the overloaded multiplication operator. The following |
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demonstrates the usage of the matrix3x3 class: |
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|
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\code |
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matrix3x3 mat; |
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mat.SetupRotMat(0.0,180.0,0.0); //rotate theta by 180 degrees |
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vector3 v = VX; |
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v *= mat; //apply the rotation |
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\endcode |
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|
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*/ |
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|
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/*! the axis of the rotation will be uniformly distributed on |
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the unit sphere, the angle will be uniformly distributed in |
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the interval 0..360 degrees. */ |
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void matrix3x3::randomRotation(OBRandom &rnd) |
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{ |
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double rotAngle; |
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vector3 v1; |
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|
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v1.randomUnitVector(&rnd); |
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rotAngle = 360.0 * rnd.NextFloat(); |
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this->RotAboutAxisByAngle(v1,rotAngle); |
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} |
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|
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void matrix3x3::SetupRotMat(double phi,double theta,double psi) |
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{ |
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double p = phi * DEG_TO_RAD; |
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double h = theta * DEG_TO_RAD; |
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double b = psi * DEG_TO_RAD; |
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|
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double cx = cos(p); |
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double sx = sin(p); |
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double cy = cos(h); |
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double sy = sin(h); |
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double cz = cos(b); |
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double sz = sin(b); |
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|
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ele[0][0] = cy*cz; |
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ele[0][1] = cy*sz; |
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ele[0][2] = -sy; |
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|
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ele[1][0] = sx*sy*cz-cx*sz; |
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ele[1][1] = sx*sy*sz+cx*cz; |
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ele[1][2] = sx*cy; |
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|
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ele[2][0] = cx*sy*cz+sx*sz; |
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ele[2][1] = cx*sy*sz-sx*cz; |
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ele[2][2] = cx*cy; |
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} |
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|
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/*! Replaces *this with a matrix that represents reflection on |
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the plane through 0 which is given by the normal vector norm. |
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|
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\warning If the vector norm has length zero, this method will |
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generate the 0-matrix. If the length of the axis is close to |
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zero, but not == 0.0, this method may behave in unexpected |
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ways and return almost random results; details may depend on |
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your particular floating point implementation. The use of this |
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method is therefore highly discouraged, unless you are certain |
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that the length is in a reasonable range, away from 0.0 |
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(Stefan Kebekus) |
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|
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\deprecated This method will probably replaced by a safer |
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algorithm in the future. |
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|
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\todo Replace this method with a more fool-proof version. |
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|
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@param norm specifies the normal to the plane |
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*/ |
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void matrix3x3::PlaneReflection(const vector3 &norm) |
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{ |
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//@@@ add a safety net |
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|
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vector3 normtmp = norm; |
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normtmp.normalize(); |
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|
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SetColumn(0, vector3(1,0,0) - 2*normtmp.x()*normtmp); |
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SetColumn(1, vector3(0,1,0) - 2*normtmp.y()*normtmp); |
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SetColumn(2, vector3(0,0,1) - 2*normtmp.z()*normtmp); |
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} |
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|
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#define x vtmp.x() |
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#define y vtmp.y() |
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#define z vtmp.z() |
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|
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/*! Replaces *this with a matrix that represents rotation about the |
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axis by a an angle. |
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|
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\warning If the vector axis has length zero, this method will |
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generate the 0-matrix. If the length of the axis is close to |
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zero, but not == 0.0, this method may behave in unexpected ways |
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and return almost random results; details may depend on your |
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particular floating point implementation. The use of this method |
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is therefore highly discouraged, unless you are certain that the |
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length is in a reasonable range, away from 0.0 (Stefan |
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Kebekus) |
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|
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\deprecated This method will probably replaced by a safer |
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algorithm in the future. |
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|
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\todo Replace this method with a more fool-proof version. |
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|
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@param v specifies the axis of the rotation |
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@param angle angle in degrees (0..360) |
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*/ |
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void matrix3x3::RotAboutAxisByAngle(const vector3 &v,const double angle) |
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{ |
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double theta = angle*DEG_TO_RAD; |
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double s = sin(theta); |
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double c = cos(theta); |
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double t = 1 - c; |
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|
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vector3 vtmp = v; |
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vtmp.normalize(); |
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|
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ele[0][0] = t*x*x + c; |
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ele[0][1] = t*x*y + s*z; |
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ele[0][2] = t*x*z - s*y; |
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|
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ele[1][0] = t*x*y - s*z; |
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ele[1][1] = t*y*y + c; |
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ele[1][2] = t*y*z + s*x; |
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|
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ele[2][0] = t*x*z + s*y; |
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ele[2][1] = t*y*z - s*x; |
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ele[2][2] = t*z*z + c; |
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} |
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|
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#undef x |
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#undef y |
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#undef z |
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|
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void matrix3x3::SetColumn(int col, const vector3 &v) throw(OBError) |
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{ |
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if (col > 2) |
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{ |
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OBError er("matrix3x3::SetColumn(int col, const vector3 &v)", |
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"The method was called with col > 2.", |
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"This is a programming error in your application."); |
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throw er; |
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} |
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|
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ele[0][col] = v.x(); |
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ele[1][col] = v.y(); |
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ele[2][col] = v.z(); |
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} |
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|
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void matrix3x3::SetRow(int row, const vector3 &v) throw(OBError) |
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{ |
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if (row > 2) |
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{ |
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OBError er("matrix3x3::SetRow(int row, const vector3 &v)", |
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"The method was called with row > 2.", |
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"This is a programming error in your application."); |
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throw er; |
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} |
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|
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ele[row][0] = v.x(); |
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ele[row][1] = v.y(); |
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ele[row][2] = v.z(); |
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} |
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|
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vector3 matrix3x3::GetColumn(unsigned int col) const throw(OBError) |
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{ |
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if (col > 2) |
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{ |
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OBError er("matrix3x3::GetColumn(unsigned int col) const", |
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"The method was called with col > 2.", |
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"This is a programming error in your application."); |
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throw er; |
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} |
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|
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return vector3(ele[0][col], ele[1][col], ele[2][col]); |
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} |
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|
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vector3 matrix3x3::GetRow(unsigned int row) const throw(OBError) |
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{ |
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if (row > 2) |
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{ |
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OBError er("matrix3x3::GetRow(unsigned int row) const", |
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"The method was called with row > 2.", |
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"This is a programming error in your application."); |
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throw er; |
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} |
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|
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return vector3(ele[row][0], ele[row][1], ele[row][2]); |
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} |
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|
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/*! calculates the product m*v of the matrix m and the column |
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vector represented by v |
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*/ |
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vector3 operator *(const matrix3x3 &m,const vector3 &v) |
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{ |
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vector3 vv; |
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|
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vv._vx = v._vx*m.ele[0][0] + v._vy*m.ele[0][1] + v._vz*m.ele[0][2]; |
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vv._vy = v._vx*m.ele[1][0] + v._vy*m.ele[1][1] + v._vz*m.ele[1][2]; |
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vv._vz = v._vx*m.ele[2][0] + v._vy*m.ele[2][1] + v._vz*m.ele[2][2]; |
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|
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return(vv); |
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} |
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|
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matrix3x3 operator *(const matrix3x3 &A,const matrix3x3 &B) |
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{ |
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matrix3x3 result; |
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|
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result.ele[0][0] = A.ele[0][0]*B.ele[0][0] + A.ele[0][1]*B.ele[1][0] + A.ele[0][2]*B.ele[2][0]; |
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result.ele[0][1] = A.ele[0][0]*B.ele[0][1] + A.ele[0][1]*B.ele[1][1] + A.ele[0][2]*B.ele[2][1]; |
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result.ele[0][2] = A.ele[0][0]*B.ele[0][2] + A.ele[0][1]*B.ele[1][2] + A.ele[0][2]*B.ele[2][2]; |
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|
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result.ele[1][0] = A.ele[1][0]*B.ele[0][0] + A.ele[1][1]*B.ele[1][0] + A.ele[1][2]*B.ele[2][0]; |
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result.ele[1][1] = A.ele[1][0]*B.ele[0][1] + A.ele[1][1]*B.ele[1][1] + A.ele[1][2]*B.ele[2][1]; |
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result.ele[1][2] = A.ele[1][0]*B.ele[0][2] + A.ele[1][1]*B.ele[1][2] + A.ele[1][2]*B.ele[2][2]; |
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|
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result.ele[2][0] = A.ele[2][0]*B.ele[0][0] + A.ele[2][1]*B.ele[1][0] + A.ele[2][2]*B.ele[2][0]; |
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result.ele[2][1] = A.ele[2][0]*B.ele[0][1] + A.ele[2][1]*B.ele[1][1] + A.ele[2][2]*B.ele[2][1]; |
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result.ele[2][2] = A.ele[2][0]*B.ele[0][2] + A.ele[2][1]*B.ele[1][2] + A.ele[2][2]*B.ele[2][2]; |
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|
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return(result); |
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} |
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|
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/*! calculates the product m*(*this) of the matrix m and the |
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column vector represented by *this |
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*/ |
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vector3 &vector3::operator *= (const matrix3x3 &m) |
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{ |
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vector3 vv; |
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|
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vv.SetX(_vx*m.Get(0,0) + _vy*m.Get(0,1) + _vz*m.Get(0,2)); |
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vv.SetY(_vx*m.Get(1,0) + _vy*m.Get(1,1) + _vz*m.Get(1,2)); |
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vv.SetZ(_vx*m.Get(2,0) + _vy*m.Get(2,1) + _vz*m.Get(2,2)); |
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_vx = vv.x(); |
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_vy = vv.y(); |
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_vz = vv.z(); |
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|
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return(*this); |
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} |
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|
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/*! This method checks if the absolute value of the determinant is smaller than 1e-6. If |
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so, nothing is done and an exception is thrown. Otherwise, the |
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inverse matrix is calculated and returned. *this is not changed. |
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|
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\warning If the determinant is close to zero, but not == 0.0, |
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this method may behave in unexpected ways and return almost |
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random results; details may depend on your particular floating |
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point implementation. The use of this method is therefore highly |
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discouraged, unless you are certain that the determinant is in a |
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reasonable range, away from 0.0 (Stefan Kebekus) |
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*/ |
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matrix3x3 matrix3x3::inverse(void) const throw(OBError) |
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{ |
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double det = determinant(); |
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if (fabs(det) <= 1e-6) |
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{ |
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OBError er("matrix3x3::invert(void)", |
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"The method was called on a matrix with |determinant| <= 1e-6.", |
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"This is a runtime or a programming error in your application."); |
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throw er; |
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} |
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|
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matrix3x3 inverse; |
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inverse.ele[0][0] = ele[1][1]*ele[2][2] - ele[1][2]*ele[2][1]; |
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inverse.ele[1][0] = ele[1][2]*ele[2][0] - ele[1][0]*ele[2][2]; |
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inverse.ele[2][0] = ele[1][0]*ele[2][1] - ele[1][1]*ele[2][0]; |
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inverse.ele[0][1] = ele[2][1]*ele[0][2] - ele[2][2]*ele[0][1]; |
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inverse.ele[1][1] = ele[2][2]*ele[0][0] - ele[2][0]*ele[0][2]; |
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inverse.ele[2][1] = ele[2][0]*ele[0][1] - ele[2][1]*ele[0][0]; |
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inverse.ele[0][2] = ele[0][1]*ele[1][2] - ele[0][2]*ele[1][1]; |
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inverse.ele[1][2] = ele[0][2]*ele[1][0] - ele[0][0]*ele[1][2]; |
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inverse.ele[2][2] = ele[0][0]*ele[1][1] - ele[0][1]*ele[1][0]; |
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|
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inverse /= det; |
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|
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return(inverse); |
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} |
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|
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/* This method returns the transpose of a matrix. The original |
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matrix remains unchanged. */ |
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matrix3x3 matrix3x3::transpose(void) const |
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{ |
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matrix3x3 transpose; |
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|
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for(unsigned int i=0; i<3; i++) |
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for(unsigned int j=0; j<3; j++) |
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transpose.ele[i][j] = ele[j][i]; |
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|
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return(transpose); |
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} |
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|
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double matrix3x3::determinant(void) const |
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{ |
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double x,y,z; |
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|
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x = ele[0][0] * (ele[1][1] * ele[2][2] - ele[1][2] * ele[2][1]); |
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y = ele[0][1] * (ele[1][2] * ele[2][0] - ele[1][0] * ele[2][2]); |
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z = ele[0][2] * (ele[1][0] * ele[2][1] - ele[1][1] * ele[2][0]); |
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|
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return(x + y + z); |
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} |
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|
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/*! This method returns false if there are indices i,j such that |
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fabs(*this[i][j]-*this[j][i]) > 1e-6. Otherwise, it returns |
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true. */ |
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bool matrix3x3::isSymmetric(void) const |
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{ |
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if (fabs(ele[0][1] - ele[1][0]) > 1e-6) |
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return false; |
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if (fabs(ele[0][2] - ele[2][0]) > 1e-6) |
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return false; |
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if (fabs(ele[1][2] - ele[2][1]) > 1e-6) |
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return false; |
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return true; |
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} |
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|
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/*! This method returns false if there are indices i != j such |
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that fabs(*this[i][j]) > 1e-6. Otherwise, it returns true. */ |
| 364 |
bool matrix3x3::isDiagonal(void) const |
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{ |
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if (fabs(ele[0][1]) > 1e-6) |
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return false; |
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if (fabs(ele[0][2]) > 1e-6) |
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return false; |
| 370 |
if (fabs(ele[1][2]) > 1e-6) |
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return false; |
| 372 |
|
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if (fabs(ele[1][0]) > 1e-6) |
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return false; |
| 375 |
if (fabs(ele[2][0]) > 1e-6) |
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return false; |
| 377 |
if (fabs(ele[2][1]) > 1e-6) |
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return false; |
| 379 |
|
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return true; |
| 381 |
} |
| 382 |
|
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/*! This method returns false if there are indices i != j such |
| 384 |
that fabs(*this[i][j]) > 1e-6, or if there is an index i such |
| 385 |
that fabs(*this[i][j]-1) > 1e-6. Otherwise, it returns |
| 386 |
true. */ |
| 387 |
bool matrix3x3::isUnitMatrix(void) const |
| 388 |
{ |
| 389 |
if (!isDiagonal()) |
| 390 |
return false; |
| 391 |
|
| 392 |
if (fabs(ele[0][0]-1) > 1e-6) |
| 393 |
return false; |
| 394 |
if (fabs(ele[1][1]-1) > 1e-6) |
| 395 |
return false; |
| 396 |
if (fabs(ele[2][2]-1) > 1e-6) |
| 397 |
return false; |
| 398 |
|
| 399 |
return true; |
| 400 |
} |
| 401 |
|
| 402 |
/*! This method employs the static method matrix3x3::jacobi(...) |
| 403 |
to find the eigenvalues and eigenvectors of a symmetric |
| 404 |
matrix. On entry it is checked if the matrix really is |
| 405 |
symmetric: if isSymmetric() returns 'false', an OBError is |
| 406 |
thrown. |
| 407 |
|
| 408 |
\note The jacobi algorithm is should work great for all |
| 409 |
symmetric 3x3 matrices. If you need to find the eigenvectors |
| 410 |
of a non-symmetric matrix, you might want to resort to the |
| 411 |
sophisticated routines of LAPACK. |
| 412 |
|
| 413 |
@param eigenvals a reference to a vector3 where the |
| 414 |
eigenvalues will be stored. The eigenvalues are ordered so |
| 415 |
that eigenvals[0] <= eigenvals[1] <= eigenvals[2]. |
| 416 |
|
| 417 |
@return an orthogonal matrix whose ith column is an |
| 418 |
eigenvector for the eigenvalue eigenvals[i]. Here 'orthogonal' |
| 419 |
means that all eigenvectors have length one and are mutually |
| 420 |
orthogonal. The ith eigenvector can thus be conveniently |
| 421 |
accessed by the GetColumn() method, as in the following |
| 422 |
example. |
| 423 |
\code |
| 424 |
// Calculate eigenvectors and -values |
| 425 |
vector3 eigenvals; |
| 426 |
matrix3x3 eigenmatrix = somematrix.findEigenvectorsIfSymmetric(eigenvals); |
| 427 |
|
| 428 |
// Print the 2nd eigenvector |
| 429 |
cout << eigenmatrix.GetColumn(1) << endl; |
| 430 |
\endcode |
| 431 |
With these conventions, a matrix is diagonalized in the following way: |
| 432 |
\code |
| 433 |
// Diagonalize the matrix |
| 434 |
matrix3x3 diagonalMatrix = eigenmatrix.inverse() * somematrix * eigenmatrix; |
| 435 |
\endcode |
| 436 |
|
| 437 |
*/ |
| 438 |
matrix3x3 matrix3x3::findEigenvectorsIfSymmetric(vector3 &eigenvals) const throw(OBError) |
| 439 |
{ |
| 440 |
matrix3x3 result; |
| 441 |
|
| 442 |
if (!isSymmetric()) |
| 443 |
{ |
| 444 |
OBError er("matrix3x3::findEigenvectorsIfSymmetric(vector3 &eigenvals) const throw(OBError)", |
| 445 |
"The method was called on a matrix that was not symmetric, i.e. where isSymetric() == false.", |
| 446 |
"This is a runtime or a programming error in your application."); |
| 447 |
throw er; |
| 448 |
} |
| 449 |
|
| 450 |
double d[3]; |
| 451 |
matrix3x3 copyOfThis = *this; |
| 452 |
|
| 453 |
jacobi(3, copyOfThis.ele[0], d, result.ele[0]); |
| 454 |
eigenvals.Set(d); |
| 455 |
|
| 456 |
return result; |
| 457 |
} |
| 458 |
|
| 459 |
matrix3x3 &matrix3x3::operator/=(const double &c) |
| 460 |
{ |
| 461 |
for (int row = 0;row < 3; row++) |
| 462 |
for (int col = 0;col < 3; col++) |
| 463 |
ele[row][col] /= c; |
| 464 |
|
| 465 |
return(*this); |
| 466 |
} |
| 467 |
|
| 468 |
#ifndef SQUARE |
| 469 |
#define SQUARE(x) ((x)*(x)) |
| 470 |
#endif |
| 471 |
|
| 472 |
void matrix3x3::FillOrth(double Alpha,double Beta, double Gamma, |
| 473 |
double A, double B, double C) |
| 474 |
{ |
| 475 |
double V; |
| 476 |
|
| 477 |
Alpha *= DEG_TO_RAD; |
| 478 |
Beta *= DEG_TO_RAD; |
| 479 |
Gamma *= DEG_TO_RAD; |
| 480 |
|
| 481 |
// from the PDB specification: |
| 482 |
// http://www.rcsb.org/pdb/docs/format/pdbguide2.2/part_75.html |
| 483 |
|
| 484 |
|
| 485 |
// since we'll ultimately divide by (a * b), we've factored those out here |
| 486 |
V = C * sqrt(1 - SQUARE(cos(Alpha)) - SQUARE(cos(Beta)) - SQUARE(cos(Gamma)) |
| 487 |
+ 2 * cos(Alpha) * cos(Beta) * cos(Gamma)); |
| 488 |
|
| 489 |
ele[0][0] = A; |
| 490 |
ele[0][1] = B*cos(Gamma); |
| 491 |
ele[0][2] = C*cos(Beta); |
| 492 |
|
| 493 |
ele[1][0] = 0.0; |
| 494 |
ele[1][1] = B*sin(Gamma); |
| 495 |
ele[1][2] = C*(cos(Alpha)-cos(Beta)*cos(Gamma))/sin(Gamma); |
| 496 |
|
| 497 |
ele[2][0] = 0.0; |
| 498 |
ele[2][1] = 0.0; |
| 499 |
ele[2][2] = V / (sin(Gamma)); // again, we factored out A * B when defining V |
| 500 |
} |
| 501 |
|
| 502 |
ostream& operator<< ( ostream& co, const matrix3x3& m ) |
| 503 |
|
| 504 |
{ |
| 505 |
co << "[ " |
| 506 |
<< m.ele[0][0] |
| 507 |
<< ", " |
| 508 |
<< m.ele[0][1] |
| 509 |
<< ", " |
| 510 |
<< m.ele[0][2] |
| 511 |
<< " ]" << endl; |
| 512 |
|
| 513 |
co << "[ " |
| 514 |
<< m.ele[1][0] |
| 515 |
<< ", " |
| 516 |
<< m.ele[1][1] |
| 517 |
<< ", " |
| 518 |
<< m.ele[1][2] |
| 519 |
<< " ]" << endl; |
| 520 |
|
| 521 |
co << "[ " |
| 522 |
<< m.ele[2][0] |
| 523 |
<< ", " |
| 524 |
<< m.ele[2][1] |
| 525 |
<< ", " |
| 526 |
<< m.ele[2][2] |
| 527 |
<< " ]" << endl; |
| 528 |
|
| 529 |
return co ; |
| 530 |
} |
| 531 |
|
| 532 |
/*! This static function computes the eigenvalues and |
| 533 |
eigenvectors of a SYMMETRIC nxn matrix. This method is used |
| 534 |
internally by OpenBabel, but may be useful as a general |
| 535 |
eigenvalue finder. |
| 536 |
|
| 537 |
The algorithm uses Jacobi transformations. It is described |
| 538 |
e.g. in Wilkinson, Reinsch "Handbook for automatic computation, |
| 539 |
Volume II: Linear Algebra", part II, contribution II/1. The |
| 540 |
implementation is also similar to the implementation in this |
| 541 |
book. This method is adequate to solve the eigenproblem for |
| 542 |
small matrices, of size perhaps up to 10x10. For bigger |
| 543 |
problems, you might want to resort to the sophisticated routines |
| 544 |
of LAPACK. |
| 545 |
|
| 546 |
\note If you plan to find the eigenvalues of a symmetric 3x3 |
| 547 |
matrix, you will probably prefer to use the more convenient |
| 548 |
method findEigenvectorsIfSymmetric() |
| 549 |
|
| 550 |
@param n the size of the matrix that should be diagonalized |
| 551 |
|
| 552 |
@param a array of size n^2 which holds the symmetric matrix |
| 553 |
whose eigenvectors are to be computed. The convention is that |
| 554 |
the entry in row r and column c is addressed as a[n*r+c] where, |
| 555 |
of course, 0 <= r < n and 0 <= c < n. There is no check that the |
| 556 |
matrix is actually symmetric. If it is not, the behaviour of |
| 557 |
this function is undefined. On return, the matrix is |
| 558 |
overwritten with junk. |
| 559 |
|
| 560 |
@param d pointer to a field of at least n doubles which will be |
| 561 |
overwritten. On return of this function, the entries d[0]..d[n-1] |
| 562 |
will contain the eigenvalues of the matrix. |
| 563 |
|
| 564 |
@param v an array of size n^2 where the eigenvectors will be |
| 565 |
stored. On return, the columns of this matrix will contain the |
| 566 |
eigenvectors. The eigenvectors are normalized and mutually |
| 567 |
orthogonal. |
| 568 |
*/ |
| 569 |
void matrix3x3::jacobi(unsigned int n, double *a, double *d, double *v) |
| 570 |
{ |
| 571 |
double onorm, dnorm; |
| 572 |
double b, dma, q, t, c, s; |
| 573 |
double atemp, vtemp, dtemp; |
| 574 |
register int i, j, k, l; |
| 575 |
int nrot; |
| 576 |
|
| 577 |
int MAX_SWEEPS=50; |
| 578 |
|
| 579 |
// Set v to the identity matrix, set the vector d to contain the |
| 580 |
// diagonal elements of the matrix a |
| 581 |
for (j = 0; j < static_cast<int>(n); j++) |
| 582 |
{ |
| 583 |
for (i = 0; i < static_cast<int>(n); i++) |
| 584 |
v[n*i+j] = 0.0; |
| 585 |
v[n*j+j] = 1.0; |
| 586 |
d[j] = a[n*j+j]; |
| 587 |
} |
| 588 |
|
| 589 |
nrot = MAX_SWEEPS; |
| 590 |
for (l = 1; l <= nrot; l++) |
| 591 |
{ |
| 592 |
// Set dnorm to be the maximum norm of the diagonal elements, set |
| 593 |
// onorm to the maximum norm of the off-diagonal elements |
| 594 |
dnorm = 0.0; |
| 595 |
onorm = 0.0; |
| 596 |
for (j = 0; j < static_cast<int>(n); j++) |
| 597 |
{ |
| 598 |
dnorm += (double)fabs(d[j]); |
| 599 |
for (i = 0; i < j; i++) |
| 600 |
onorm += (double)fabs(a[n*i+j]); |
| 601 |
} |
| 602 |
// Normal end point of this algorithm. |
| 603 |
if((onorm/dnorm) <= 1.0e-12) |
| 604 |
goto Exit_now; |
| 605 |
|
| 606 |
for (j = 1; j < static_cast<int>(n); j++) |
| 607 |
{ |
| 608 |
for (i = 0; i <= j - 1; i++) |
| 609 |
{ |
| 610 |
|
| 611 |
b = a[n*i+j]; |
| 612 |
if(fabs(b) > 0.0) |
| 613 |
{ |
| 614 |
dma = d[j] - d[i]; |
| 615 |
if((fabs(dma) + fabs(b)) <= fabs(dma)) |
| 616 |
t = b / dma; |
| 617 |
else |
| 618 |
{ |
| 619 |
q = 0.5 * dma / b; |
| 620 |
t = 1.0/((double)fabs(q) + (double)sqrt(1.0+q*q)); |
| 621 |
if (q < 0.0) |
| 622 |
t = -t; |
| 623 |
} |
| 624 |
|
| 625 |
c = 1.0/(double)sqrt(t*t + 1.0); |
| 626 |
s = t * c; |
| 627 |
a[n*i+j] = 0.0; |
| 628 |
|
| 629 |
for (k = 0; k <= i-1; k++) |
| 630 |
{ |
| 631 |
atemp = c * a[n*k+i] - s * a[n*k+j]; |
| 632 |
a[n*k+j] = s * a[n*k+i] + c * a[n*k+j]; |
| 633 |
a[n*k+i] = atemp; |
| 634 |
} |
| 635 |
|
| 636 |
for (k = i+1; k <= j-1; k++) |
| 637 |
{ |
| 638 |
atemp = c * a[n*i+k] - s * a[n*k+j]; |
| 639 |
a[n*k+j] = s * a[n*i+k] + c * a[n*k+j]; |
| 640 |
a[n*i+k] = atemp; |
| 641 |
} |
| 642 |
|
| 643 |
for (k = j+1; k < static_cast<int>(n); k++) |
| 644 |
{ |
| 645 |
atemp = c * a[n*i+k] - s * a[n*j+k]; |
| 646 |
a[n*j+k] = s * a[n*i+k] + c * a[n*j+k]; |
| 647 |
a[n*i+k] = atemp; |
| 648 |
} |
| 649 |
|
| 650 |
for (k = 0; k < static_cast<int>(n); k++) |
| 651 |
{ |
| 652 |
vtemp = c * v[n*k+i] - s * v[n*k+j]; |
| 653 |
v[n*k+j] = s * v[n*k+i] + c * v[n*k+j]; |
| 654 |
v[n*k+i] = vtemp; |
| 655 |
} |
| 656 |
|
| 657 |
dtemp = c*c*d[i] + s*s*d[j] - 2.0*c*s*b; |
| 658 |
d[j] = s*s*d[i] + c*c*d[j] + 2.0*c*s*b; |
| 659 |
d[i] = dtemp; |
| 660 |
} /* end if */ |
| 661 |
} /* end for i */ |
| 662 |
} /* end for j */ |
| 663 |
} /* end for l */ |
| 664 |
|
| 665 |
Exit_now: |
| 666 |
|
| 667 |
// Now sort the eigenvalues (and the eigenvectors) so that the |
| 668 |
// smallest eigenvalues come first. |
| 669 |
nrot = l; |
| 670 |
|
| 671 |
for (j = 0; j < static_cast<int>(n)-1; j++) |
| 672 |
{ |
| 673 |
k = j; |
| 674 |
dtemp = d[k]; |
| 675 |
for (i = j+1; i < static_cast<int>(n); i++) |
| 676 |
if(d[i] < dtemp) |
| 677 |
{ |
| 678 |
k = i; |
| 679 |
dtemp = d[k]; |
| 680 |
} |
| 681 |
|
| 682 |
if(k > j) |
| 683 |
{ |
| 684 |
d[k] = d[j]; |
| 685 |
d[j] = dtemp; |
| 686 |
for (i = 0; i < static_cast<int>(n); i++) |
| 687 |
{ |
| 688 |
dtemp = v[n*i+k]; |
| 689 |
v[n*i+k] = v[n*i+j]; |
| 690 |
v[n*i+j] = dtemp; |
| 691 |
} |
| 692 |
} |
| 693 |
} |
| 694 |
} |
| 695 |
|
| 696 |
} // end namespace OpenBabel |
| 697 |
|
| 698 |
//! \file matrix3x3.cpp |
| 699 |
//! \brief Handle 3D rotation matrix. |
| 700 |
|
