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) 2000-2009 Torus Knot Software Ltd
00008 
00009 Permission is hereby granted, free of charge, to any person obtaining a copy
00010 of this software and associated documentation files (the "Software"), to deal
00011 in the Software without restriction, including without limitation the rights
00012 to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
00013 copies of the Software, and to permit persons to whom the Software is
00014 furnished to do so, subject to the following conditions:
00015 
00016 The above copyright notice and this permission notice shall be included in
00017 all copies or substantial portions of the Software.
00018 
00019 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
00020 IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
00021 FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
00022 AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
00023 LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
00024 OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
00025 THE SOFTWARE.
00026 -----------------------------------------------------------------------------
00027 */
00028 #ifndef __Matrix3_H__
00029 #define __Matrix3_H__
00030 
00031 #include "OgrePrerequisites.h"
00032 
00033 #include "OgreVector3.h"
00034 
00035 // NB All code adapted from Wild Magic 0.2 Matrix math (free source code)
00036 // http://www.geometrictools.com/
00037 
00038 // NOTE.  The (x,y,z) coordinate system is assumed to be right-handed.
00039 // Coordinate axis rotation matrices are of the form
00040 //   RX =    1       0       0
00041 //           0     cos(t) -sin(t)
00042 //           0     sin(t)  cos(t)
00043 // where t > 0 indicates a counterclockwise rotation in the yz-plane
00044 //   RY =  cos(t)    0     sin(t)
00045 //           0       1       0
00046 //        -sin(t)    0     cos(t)
00047 // where t > 0 indicates a counterclockwise rotation in the zx-plane
00048 //   RZ =  cos(t) -sin(t)    0
00049 //         sin(t)  cos(t)    0
00050 //           0       0       1
00051 // where t > 0 indicates a counterclockwise rotation in the xy-plane.
00052 
00053 namespace Ogre
00054 {
00068     class _OgreExport Matrix3
00069     {
00070     public:
00075         inline Matrix3 () {}
00076         inline explicit Matrix3 (const Real arr[3][3])
00077         {
00078             memcpy(m,arr,9*sizeof(Real));
00079         }
00080         inline Matrix3 (const Matrix3& rkMatrix)
00081         {
00082             memcpy(m,rkMatrix.m,9*sizeof(Real));
00083         }
00084         Matrix3 (Real fEntry00, Real fEntry01, Real fEntry02,
00085                     Real fEntry10, Real fEntry11, Real fEntry12,
00086                     Real fEntry20, Real fEntry21, Real fEntry22)
00087         {
00088             m[0][0] = fEntry00;
00089             m[0][1] = fEntry01;
00090             m[0][2] = fEntry02;
00091             m[1][0] = fEntry10;
00092             m[1][1] = fEntry11;
00093             m[1][2] = fEntry12;
00094             m[2][0] = fEntry20;
00095             m[2][1] = fEntry21;
00096             m[2][2] = fEntry22;
00097         }
00098 
00101         inline void swap(Matrix3& other)
00102         {
00103             std::swap(m[0][0], other.m[0][0]);
00104             std::swap(m[0][1], other.m[0][1]);
00105             std::swap(m[0][2], other.m[0][2]);
00106             std::swap(m[1][0], other.m[1][0]);
00107             std::swap(m[1][1], other.m[1][1]);
00108             std::swap(m[1][2], other.m[1][2]);
00109             std::swap(m[2][0], other.m[2][0]);
00110             std::swap(m[2][1], other.m[2][1]);
00111             std::swap(m[2][2], other.m[2][2]);
00112         }
00113 
00114         // member access, allows use of construct mat[r][c]
00115         inline Real* operator[] (size_t iRow) const
00116         {
00117             return (Real*)m[iRow];
00118         }
00119         /*inline operator Real* ()
00120         {
00121             return (Real*)m[0];
00122         }*/
00123         Vector3 GetColumn (size_t iCol) const;
00124         void SetColumn(size_t iCol, const Vector3& vec);
00125         void FromAxes(const Vector3& xAxis, const Vector3& yAxis, const Vector3& zAxis);
00126 
00127         // assignment and comparison
00128         inline Matrix3& operator= (const Matrix3& rkMatrix)
00129         {
00130             memcpy(m,rkMatrix.m,9*sizeof(Real));
00131             return *this;
00132         }
00133         bool operator== (const Matrix3& rkMatrix) const;
00134         inline bool operator!= (const Matrix3& rkMatrix) const
00135         {
00136             return !operator==(rkMatrix);
00137         }
00138 
00139         // arithmetic operations
00140         Matrix3 operator+ (const Matrix3& rkMatrix) const;
00141         Matrix3 operator- (const Matrix3& rkMatrix) const;
00142         Matrix3 operator* (const Matrix3& rkMatrix) const;
00143         Matrix3 operator- () const;
00144 
00145         // matrix * vector [3x3 * 3x1 = 3x1]
00146         Vector3 operator* (const Vector3& rkVector) const;
00147 
00148         // vector * matrix [1x3 * 3x3 = 1x3]
00149         _OgreExport friend Vector3 operator* (const Vector3& rkVector,
00150             const Matrix3& rkMatrix);
00151 
00152         // matrix * scalar
00153         Matrix3 operator* (Real fScalar) const;
00154 
00155         // scalar * matrix
00156         _OgreExport friend Matrix3 operator* (Real fScalar, const Matrix3& rkMatrix);
00157 
00158         // utilities
00159         Matrix3 Transpose () const;
00160         bool Inverse (Matrix3& rkInverse, Real fTolerance = 1e-06) const;
00161         Matrix3 Inverse (Real fTolerance = 1e-06) const;
00162         Real Determinant () const;
00163 
00164         // singular value decomposition
00165         void SingularValueDecomposition (Matrix3& rkL, Vector3& rkS,
00166             Matrix3& rkR) const;
00167         void SingularValueComposition (const Matrix3& rkL,
00168             const Vector3& rkS, const Matrix3& rkR);
00169 
00170         // Gram-Schmidt orthonormalization (applied to columns of rotation matrix)
00171         void Orthonormalize ();
00172 
00173         // orthogonal Q, diagonal D, upper triangular U stored as (u01,u02,u12)
00174         void QDUDecomposition (Matrix3& rkQ, Vector3& rkD,
00175             Vector3& rkU) const;
00176 
00177         Real SpectralNorm () const;
00178 
00179         // matrix must be orthonormal
00180         void ToAxisAngle (Vector3& rkAxis, Radian& rfAngle) const;
00181         inline void ToAxisAngle (Vector3& rkAxis, Degree& rfAngle) const {
00182             Radian r;
00183             ToAxisAngle ( rkAxis, r );
00184             rfAngle = r;
00185         }
00186         void FromAxisAngle (const Vector3& rkAxis, const Radian& fRadians);
00187 
00188         // The matrix must be orthonormal.  The decomposition is yaw*pitch*roll
00189         // where yaw is rotation about the Up vector, pitch is rotation about the
00190         // Right axis, and roll is rotation about the Direction axis.
00191         bool ToEulerAnglesXYZ (Radian& rfYAngle, Radian& rfPAngle,
00192             Radian& rfRAngle) const;
00193         bool ToEulerAnglesXZY (Radian& rfYAngle, Radian& rfPAngle,
00194             Radian& rfRAngle) const;
00195         bool ToEulerAnglesYXZ (Radian& rfYAngle, Radian& rfPAngle,
00196             Radian& rfRAngle) const;
00197         bool ToEulerAnglesYZX (Radian& rfYAngle, Radian& rfPAngle,
00198             Radian& rfRAngle) const;
00199         bool ToEulerAnglesZXY (Radian& rfYAngle, Radian& rfPAngle,
00200             Radian& rfRAngle) const;
00201         bool ToEulerAnglesZYX (Radian& rfYAngle, Radian& rfPAngle,
00202             Radian& rfRAngle) const;
00203         void FromEulerAnglesXYZ (const Radian& fYAngle, const Radian& fPAngle, const Radian& fRAngle);
00204         void FromEulerAnglesXZY (const Radian& fYAngle, const Radian& fPAngle, const Radian& fRAngle);
00205         void FromEulerAnglesYXZ (const Radian& fYAngle, const Radian& fPAngle, const Radian& fRAngle);
00206         void FromEulerAnglesYZX (const Radian& fYAngle, const Radian& fPAngle, const Radian& fRAngle);
00207         void FromEulerAnglesZXY (const Radian& fYAngle, const Radian& fPAngle, const Radian& fRAngle);
00208         void FromEulerAnglesZYX (const Radian& fYAngle, const Radian& fPAngle, const Radian& fRAngle);
00209         // eigensolver, matrix must be symmetric
00210         void EigenSolveSymmetric (Real afEigenvalue[3],
00211             Vector3 akEigenvector[3]) const;
00212 
00213         static void TensorProduct (const Vector3& rkU, const Vector3& rkV,
00214             Matrix3& rkProduct);
00215 
00217         inline bool hasScale() const
00218         {
00219             // check magnitude of column vectors (==local axes)
00220             Real t = m[0][0] * m[0][0] + m[1][0] * m[1][0] + m[2][0] * m[2][0];
00221             if (!Math::RealEqual(t, 1.0, (Real)1e-04))
00222                 return true;
00223             t = m[0][1] * m[0][1] + m[1][1] * m[1][1] + m[2][1] * m[2][1];
00224             if (!Math::RealEqual(t, 1.0, (Real)1e-04))
00225                 return true;
00226             t = m[0][2] * m[0][2] + m[1][2] * m[1][2] + m[2][2] * m[2][2];
00227             if (!Math::RealEqual(t, 1.0, (Real)1e-04))
00228                 return true;
00229 
00230             return false;
00231         }
00232 
00235         inline _OgreExport friend std::ostream& operator <<
00236             ( std::ostream& o, const Matrix3& mat )
00237         {
00238             o << "Matrix3(" << mat[0][0] << ", " << mat[0][1] << ", " << mat[0][2] << ", " 
00239                             << mat[1][0] << ", " << mat[1][1] << ", " << mat[1][2] << ", " 
00240                             << mat[2][0] << ", " << mat[2][1] << ", " << mat[2][2] << ")";
00241             return o;
00242         }
00243 
00244         static const Real EPSILON;
00245         static const Matrix3 ZERO;
00246         static const Matrix3 IDENTITY;
00247 
00248     protected:
00249         // support for eigensolver
00250         void Tridiagonal (Real afDiag[3], Real afSubDiag[3]);
00251         bool QLAlgorithm (Real afDiag[3], Real afSubDiag[3]);
00252 
00253         // support for singular value decomposition
00254         static const Real ms_fSvdEpsilon;
00255         static const unsigned int ms_iSvdMaxIterations;
00256         static void Bidiagonalize (Matrix3& kA, Matrix3& kL,
00257             Matrix3& kR);
00258         static void GolubKahanStep (Matrix3& kA, Matrix3& kL,
00259             Matrix3& kR);
00260 
00261         // support for spectral norm
00262         static Real MaxCubicRoot (Real afCoeff[3]);
00263 
00264         Real m[3][3];
00265 
00266         // for faster access
00267         friend class Matrix4;
00268     };
00271 }
00272 #endif

Copyright © 2008 Torus Knot Software Ltd
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This work is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License.
Last modified Wed Nov 3 2010 19:24:52