OGRE: OgreMatrix3.h Source File - OGRE Documentation

# 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
This work is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License.
Last modified Wed Nov 3 2010 19:24:52