OgreMatrix3.h

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00001 /*
00002 -----------------------------------------------------------------------------
00003 This source file is part of OGRE
00004     (Object-oriented Graphics Rendering Engine)
00005 For the latest info, see http://www.ogre3d.org/
00006 
00007 Copyright (c) 2000-2006 Torus Knot Software Ltd
00008 Also see acknowledgements in Readme.html
00009 
00010 This program is free software; you can redistribute it and/or modify it under
00011 the terms of the GNU Lesser General Public License as published by the Free Software
00012 Foundation; either version 2 of the License, or (at your option) any later
00013 version.
00014 
00015 This program is distributed in the hope that it will be useful, but WITHOUT
00016 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
00017 FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details.
00018 
00019 You should have received a copy of the GNU Lesser General Public License along with
00020 this program; if not, write to the Free Software Foundation, Inc., 59 Temple
00021 Place - Suite 330, Boston, MA 02111-1307, USA, or go to
00022 http://www.gnu.org/copyleft/lesser.txt.
00023 
00024 You may alternatively use this source under the terms of a specific version of
00025 the OGRE Unrestricted License provided you have obtained such a license from
00026 Torus Knot Software Ltd.
00027 -----------------------------------------------------------------------------
00028 */
00029 #ifndef __Matrix3_H__
00030 #define __Matrix3_H__
00031 
00032 #include "OgrePrerequisites.h"
00033 
00034 #include "OgreVector3.h"
00035 
00036 // NB All code adapted from Wild Magic 0.2 Matrix math (free source code)
00037 // http://www.geometrictools.com/
00038 
00039 // NOTE.  The (x,y,z) coordinate system is assumed to be right-handed.
00040 // Coordinate axis rotation matrices are of the form
00041 //   RX =    1       0       0
00042 //           0     cos(t) -sin(t)
00043 //           0     sin(t)  cos(t)
00044 // where t > 0 indicates a counterclockwise rotation in the yz-plane
00045 //   RY =  cos(t)    0     sin(t)
00046 //           0       1       0
00047 //        -sin(t)    0     cos(t)
00048 // where t > 0 indicates a counterclockwise rotation in the zx-plane
00049 //   RZ =  cos(t) -sin(t)    0
00050 //         sin(t)  cos(t)    0
00051 //           0       0       1
00052 // where t > 0 indicates a counterclockwise rotation in the xy-plane.
00053 
00054 namespace Ogre
00055 {
00063     class _OgreExport Matrix3
00064     {
00065     public:
00070         inline Matrix3 () {};
00071         inline explicit Matrix3 (const Real arr[3][3])
00072         {
00073             memcpy(m,arr,9*sizeof(Real));
00074         }
00075         inline Matrix3 (const Matrix3& rkMatrix)
00076         {
00077             memcpy(m,rkMatrix.m,9*sizeof(Real));
00078         }
00079         Matrix3 (Real fEntry00, Real fEntry01, Real fEntry02,
00080                     Real fEntry10, Real fEntry11, Real fEntry12,
00081                     Real fEntry20, Real fEntry21, Real fEntry22)
00082         {
00083             m[0][0] = fEntry00;
00084             m[0][1] = fEntry01;
00085             m[0][2] = fEntry02;
00086             m[1][0] = fEntry10;
00087             m[1][1] = fEntry11;
00088             m[1][2] = fEntry12;
00089             m[2][0] = fEntry20;
00090             m[2][1] = fEntry21;
00091             m[2][2] = fEntry22;
00092         }
00093 
00094         // member access, allows use of construct mat[r][c]
00095         inline Real* operator[] (size_t iRow) const
00096         {
00097             return (Real*)m[iRow];
00098         }
00099         /*inline operator Real* ()
00100         {
00101             return (Real*)m[0];
00102         }*/
00103         Vector3 GetColumn (size_t iCol) const;
00104         void SetColumn(size_t iCol, const Vector3& vec);
00105         void FromAxes(const Vector3& xAxis, const Vector3& yAxis, const Vector3& zAxis);
00106 
00107         // assignment and comparison
00108         inline Matrix3& operator= (const Matrix3& rkMatrix)
00109         {
00110             memcpy(m,rkMatrix.m,9*sizeof(Real));
00111             return *this;
00112         }
00113         bool operator== (const Matrix3& rkMatrix) const;
00114         inline bool operator!= (const Matrix3& rkMatrix) const
00115         {
00116             return !operator==(rkMatrix);
00117         }
00118 
00119         // arithmetic operations
00120         Matrix3 operator+ (const Matrix3& rkMatrix) const;
00121         Matrix3 operator- (const Matrix3& rkMatrix) const;
00122         Matrix3 operator* (const Matrix3& rkMatrix) const;
00123         Matrix3 operator- () const;
00124 
00125         // matrix * vector [3x3 * 3x1 = 3x1]
00126         Vector3 operator* (const Vector3& rkVector) const;
00127 
00128         // vector * matrix [1x3 * 3x3 = 1x3]
00129         _OgreExport friend Vector3 operator* (const Vector3& rkVector,
00130             const Matrix3& rkMatrix);
00131 
00132         // matrix * scalar
00133         Matrix3 operator* (Real fScalar) const;
00134 
00135         // scalar * matrix
00136         _OgreExport friend Matrix3 operator* (Real fScalar, const Matrix3& rkMatrix);
00137 
00138         // utilities
00139         Matrix3 Transpose () const;
00140         bool Inverse (Matrix3& rkInverse, Real fTolerance = 1e-06) const;
00141         Matrix3 Inverse (Real fTolerance = 1e-06) const;
00142         Real Determinant () const;
00143 
00144         // singular value decomposition
00145         void SingularValueDecomposition (Matrix3& rkL, Vector3& rkS,
00146             Matrix3& rkR) const;
00147         void SingularValueComposition (const Matrix3& rkL,
00148             const Vector3& rkS, const Matrix3& rkR);
00149 
00150         // Gram-Schmidt orthonormalization (applied to columns of rotation matrix)
00151         void Orthonormalize ();
00152 
00153         // orthogonal Q, diagonal D, upper triangular U stored as (u01,u02,u12)
00154         void QDUDecomposition (Matrix3& rkQ, Vector3& rkD,
00155             Vector3& rkU) const;
00156 
00157         Real SpectralNorm () const;
00158 
00159         // matrix must be orthonormal
00160         void ToAxisAngle (Vector3& rkAxis, Radian& rfAngle) const;
00161         inline void ToAxisAngle (Vector3& rkAxis, Degree& rfAngle) const {
00162             Radian r;
00163             ToAxisAngle ( rkAxis, r );
00164             rfAngle = r;
00165         }
00166         void FromAxisAngle (const Vector3& rkAxis, const Radian& fRadians);
00167 
00168         // The matrix must be orthonormal.  The decomposition is yaw*pitch*roll
00169         // where yaw is rotation about the Up vector, pitch is rotation about the
00170         // Right axis, and roll is rotation about the Direction axis.
00171         bool ToEulerAnglesXYZ (Radian& rfYAngle, Radian& rfPAngle,
00172             Radian& rfRAngle) const;
00173         bool ToEulerAnglesXZY (Radian& rfYAngle, Radian& rfPAngle,
00174             Radian& rfRAngle) const;
00175         bool ToEulerAnglesYXZ (Radian& rfYAngle, Radian& rfPAngle,
00176             Radian& rfRAngle) const;
00177         bool ToEulerAnglesYZX (Radian& rfYAngle, Radian& rfPAngle,
00178             Radian& rfRAngle) const;
00179         bool ToEulerAnglesZXY (Radian& rfYAngle, Radian& rfPAngle,
00180             Radian& rfRAngle) const;
00181         bool ToEulerAnglesZYX (Radian& rfYAngle, Radian& rfPAngle,
00182             Radian& rfRAngle) const;
00183         void FromEulerAnglesXYZ (const Radian& fYAngle, const Radian& fPAngle, const Radian& fRAngle);
00184         void FromEulerAnglesXZY (const Radian& fYAngle, const Radian& fPAngle, const Radian& fRAngle);
00185         void FromEulerAnglesYXZ (const Radian& fYAngle, const Radian& fPAngle, const Radian& fRAngle);
00186         void FromEulerAnglesYZX (const Radian& fYAngle, const Radian& fPAngle, const Radian& fRAngle);
00187         void FromEulerAnglesZXY (const Radian& fYAngle, const Radian& fPAngle, const Radian& fRAngle);
00188         void FromEulerAnglesZYX (const Radian& fYAngle, const Radian& fPAngle, const Radian& fRAngle);
00189         // eigensolver, matrix must be symmetric
00190         void EigenSolveSymmetric (Real afEigenvalue[3],
00191             Vector3 akEigenvector[3]) const;
00192 
00193         static void TensorProduct (const Vector3& rkU, const Vector3& rkV,
00194             Matrix3& rkProduct);
00195 
00197         inline bool hasScale() const
00198         {
00199             // check magnitude of column vectors (==local axes)
00200             Real t = m[0][0] * m[0][0] + m[1][0] * m[1][0] + m[2][0] * m[2][0];
00201             if (!Math::RealEqual(t, 1.0, 1e-04))
00202                 return true;
00203             t = m[0][1] * m[0][1] + m[1][1] * m[1][1] + m[2][1] * m[2][1];
00204             if (!Math::RealEqual(t, 1.0, 1e-04))
00205                 return true;
00206             t = m[0][2] * m[0][2] + m[1][2] * m[1][2] + m[2][2] * m[2][2];
00207             if (!Math::RealEqual(t, 1.0, 1e-04))
00208                 return true;
00209 
00210             return false;
00211         }
00212 
00213 
00214         static const Real EPSILON;
00215         static const Matrix3 ZERO;
00216         static const Matrix3 IDENTITY;
00217 
00218     protected:
00219         // support for eigensolver
00220         void Tridiagonal (Real afDiag[3], Real afSubDiag[3]);
00221         bool QLAlgorithm (Real afDiag[3], Real afSubDiag[3]);
00222 
00223         // support for singular value decomposition
00224         static const Real ms_fSvdEpsilon;
00225         static const unsigned int ms_iSvdMaxIterations;
00226         static void Bidiagonalize (Matrix3& kA, Matrix3& kL,
00227             Matrix3& kR);
00228         static void GolubKahanStep (Matrix3& kA, Matrix3& kL,
00229             Matrix3& kR);
00230 
00231         // support for spectral norm
00232         static Real MaxCubicRoot (Real afCoeff[3]);
00233 
00234         Real m[3][3];
00235 
00236         // for faster access
00237         friend class Matrix4;
00238     };
00239 }
00240 #endif

Copyright © 2008 Torus Knot Software Ltd
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This work is licensed under a Creative Commons Attribution-ShareAlike 2.5 License.
Last modified Sun Sep 27 22:02:24 2009