OGRE: OgreMatrix3.h Source File - OGRE Documentation

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# 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 #ifndef OGRE_FORCE_ANGLE_TYPES
    00168         inline void ToAxisAngle (Vector3& rkAxis, Real& rfRadians) const {
    00169             Radian r;
    00170             ToAxisAngle ( rkAxis, r );
    00171             rfRadians = r.valueRadians();
    00172         }
    00173         inline void FromAxisAngle (const Vector3& rkAxis, Real fRadians) {
    00174             FromAxisAngle ( rkAxis, Radian(fRadians) );
    00175         }
    00176 #endif//OGRE_FORCE_ANGLE_TYPES
    00177
    00178         // The matrix must be orthonormal.  The decomposition is yaw*pitch*roll
    00179         // where yaw is rotation about the Up vector, pitch is rotation about the
    00180         // Right axis, and roll is rotation about the Direction axis.
    00181         bool ToEulerAnglesXYZ (Radian& rfYAngle, Radian& rfPAngle,
    00182             Radian& rfRAngle) const;
    00183         bool ToEulerAnglesXZY (Radian& rfYAngle, Radian& rfPAngle,
    00184             Radian& rfRAngle) const;
    00185         bool ToEulerAnglesYXZ (Radian& rfYAngle, Radian& rfPAngle,
    00186             Radian& rfRAngle) const;
    00187         bool ToEulerAnglesYZX (Radian& rfYAngle, Radian& rfPAngle,
    00188             Radian& rfRAngle) const;
    00189         bool ToEulerAnglesZXY (Radian& rfYAngle, Radian& rfPAngle,
    00190             Radian& rfRAngle) const;
    00191         bool ToEulerAnglesZYX (Radian& rfYAngle, Radian& rfPAngle,
    00192             Radian& rfRAngle) const;
    00193         void FromEulerAnglesXYZ (const Radian& fYAngle, const Radian& fPAngle, const Radian& fRAngle);
    00194         void FromEulerAnglesXZY (const Radian& fYAngle, const Radian& fPAngle, const Radian& fRAngle);
    00195         void FromEulerAnglesYXZ (const Radian& fYAngle, const Radian& fPAngle, const Radian& fRAngle);
    00196         void FromEulerAnglesYZX (const Radian& fYAngle, const Radian& fPAngle, const Radian& fRAngle);
    00197         void FromEulerAnglesZXY (const Radian& fYAngle, const Radian& fPAngle, const Radian& fRAngle);
    00198         void FromEulerAnglesZYX (const Radian& fYAngle, const Radian& fPAngle, const Radian& fRAngle);
    00199 #ifndef OGRE_FORCE_ANGLE_TYPES
    00200         inline bool ToEulerAnglesXYZ (float& rfYAngle, float& rfPAngle,
    00201             float& rfRAngle) const {
    00202             Radian y, p, r;
    00203             bool b = ToEulerAnglesXYZ(y,p,r);
    00204             rfYAngle = y.valueRadians();
    00205             rfPAngle = p.valueRadians();
    00206             rfRAngle = r.valueRadians();
    00207             return b;
    00208         }
    00209         inline bool ToEulerAnglesXZY (float& rfYAngle, float& rfPAngle,
    00210             float& rfRAngle) const {
    00211             Radian y, p, r;
    00212             bool b = ToEulerAnglesXZY(y,p,r);
    00213             rfYAngle = y.valueRadians();
    00214             rfPAngle = p.valueRadians();
    00215             rfRAngle = r.valueRadians();
    00216             return b;
    00217         }
    00218         inline bool ToEulerAnglesYXZ (float& rfYAngle, float& rfPAngle,
    00219             float& rfRAngle) const {
    00220             Radian y, p, r;
    00221             bool b = ToEulerAnglesYXZ(y,p,r);
    00222             rfYAngle = y.valueRadians();
    00223             rfPAngle = p.valueRadians();
    00224             rfRAngle = r.valueRadians();
    00225             return b;
    00226         }
    00227         inline bool ToEulerAnglesYZX (float& rfYAngle, float& rfPAngle,
    00228             float& rfRAngle) const {
    00229             Radian y, p, r;
    00230             bool b = ToEulerAnglesYZX(y,p,r);
    00231             rfYAngle = y.valueRadians();
    00232             rfPAngle = p.valueRadians();
    00233             rfRAngle = r.valueRadians();
    00234             return b;
    00235         }
    00236         inline bool ToEulerAnglesZXY (float& rfYAngle, float& rfPAngle,
    00237             float& rfRAngle) const {
    00238             Radian y, p, r;
    00239             bool b = ToEulerAnglesZXY(y,p,r);
    00240             rfYAngle = y.valueRadians();
    00241             rfPAngle = p.valueRadians();
    00242             rfRAngle = r.valueRadians();
    00243             return b;
    00244         }
    00245         inline bool ToEulerAnglesZYX (float& rfYAngle, float& rfPAngle,
    00246             float& rfRAngle) const {
    00247             Radian y, p, r;
    00248             bool b = ToEulerAnglesZYX(y,p,r);
    00249             rfYAngle = y.valueRadians();
    00250             rfPAngle = p.valueRadians();
    00251             rfRAngle = r.valueRadians();
    00252             return b;
    00253         }
    00254         inline void FromEulerAnglesXYZ (float fYAngle, float fPAngle, float fRAngle) {
    00255             FromEulerAnglesXYZ ( Radian(fYAngle), Radian(fPAngle), Radian(fRAngle) );
    00256         }
    00257         inline void FromEulerAnglesXZY (float fYAngle, float fPAngle, float fRAngle) {
    00258             FromEulerAnglesXZY ( Radian(fYAngle), Radian(fPAngle), Radian(fRAngle) );
    00259         }
    00260         inline void FromEulerAnglesYXZ (float fYAngle, float fPAngle, float fRAngle) {
    00261             FromEulerAnglesYXZ ( Radian(fYAngle), Radian(fPAngle), Radian(fRAngle) );
    00262         }
    00263         inline void FromEulerAnglesYZX (float fYAngle, float fPAngle, float fRAngle) {
    00264             FromEulerAnglesYZX ( Radian(fYAngle), Radian(fPAngle), Radian(fRAngle) );
    00265         }
    00266         inline void FromEulerAnglesZXY (float fYAngle, float fPAngle, float fRAngle) {
    00267             FromEulerAnglesZXY ( Radian(fYAngle), Radian(fPAngle), Radian(fRAngle) );
    00268         }
    00269         inline void FromEulerAnglesZYX (float fYAngle, float fPAngle, float fRAngle) {
    00270             FromEulerAnglesZYX ( Radian(fYAngle), Radian(fPAngle), Radian(fRAngle) );
    00271         }
    00272 #endif//OGRE_FORCE_ANGLE_TYPES
    00273         // eigensolver, matrix must be symmetric
    00274         void EigenSolveSymmetric (Real afEigenvalue[3],
    00275             Vector3 akEigenvector[3]) const;
    00276
    00277         static void TensorProduct (const Vector3& rkU, const Vector3& rkV,
    00278             Matrix3& rkProduct);
    00279
    00280         static const Real EPSILON;
    00281         static const Matrix3 ZERO;
    00282         static const Matrix3 IDENTITY;
    00283
    00284     protected:
    00285         // support for eigensolver
    00286         void Tridiagonal (Real afDiag[3], Real afSubDiag[3]);
    00287         bool QLAlgorithm (Real afDiag[3], Real afSubDiag[3]);
    00288
    00289         // support for singular value decomposition
    00290         static const Real ms_fSvdEpsilon;
    00291         static const unsigned int ms_iSvdMaxIterations;
    00292         static void Bidiagonalize (Matrix3& kA, Matrix3& kL,
    00293             Matrix3& kR);
    00294         static void GolubKahanStep (Matrix3& kA, Matrix3& kL,
    00295             Matrix3& kR);
    00296
    00297         // support for spectral norm
    00298         static Real MaxCubicRoot (Real afCoeff[3]);
    00299
    00300         Real m[3][3];
    00301
    00302         // for faster access
    00303         friend class Matrix4;
    00304     };
    00305 }
    00306 #endif

Copyright © 2000-2005 by The OGRE Team
This work is licensed under a Creative Commons Attribution-ShareAlike 2.5 License.
Last modified Thu Mar 6 09:46:25 2008