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) 2000-2012 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
    00136         bool operator== (const Matrix3& rkMatrix) const;
    00137
    00140         inline bool operator!= (const Matrix3& rkMatrix) const
    00141         {
    00142             return !operator==(rkMatrix);
    00143         }
    00144
    00145         // arithmetic operations
    00148         Matrix3 operator+ (const Matrix3& rkMatrix) const;
    00149
    00152         Matrix3 operator- (const Matrix3& rkMatrix) const;
    00153
    00156         Matrix3 operator* (const Matrix3& rkMatrix) const;
    00157         Matrix3 operator- () const;
    00158
    00160         Vector3 operator* (const Vector3& rkVector) const;
    00161
    00163         _OgreExport friend Vector3 operator* (const Vector3& rkVector,
    00164             const Matrix3& rkMatrix);
    00165
    00167         Matrix3 operator* (Real fScalar) const;
    00168
    00170         _OgreExport friend Matrix3 operator* (Real fScalar, const Matrix3& rkMatrix);
    00171
    00172         // utilities
    00173         Matrix3 Transpose () const;
    00174         bool Inverse (Matrix3& rkInverse, Real fTolerance = 1e-06) const;
    00175         Matrix3 Inverse (Real fTolerance = 1e-06) const;
    00176         Real Determinant () const;
    00177
    00178         // singular value decomposition
    00179         void SingularValueDecomposition (Matrix3& rkL, Vector3& rkS,
    00180             Matrix3& rkR) const;
    00181         void SingularValueComposition (const Matrix3& rkL,
    00182             const Vector3& rkS, const Matrix3& rkR);
    00183
    00185         void Orthonormalize ();
    00186
    00188         void QDUDecomposition (Matrix3& rkQ, Vector3& rkD,
    00189             Vector3& rkU) const;
    00190
    00191         Real SpectralNorm () const;
    00192
    00193         // matrix must be orthonormal
    00194         void ToAngleAxis (Vector3& rkAxis, Radian& rfAngle) const;
    00195         inline void ToAngleAxis (Vector3& rkAxis, Degree& rfAngle) const {
    00196             Radian r;
    00197             ToAngleAxis ( rkAxis, r );
    00198             rfAngle = r;
    00199         }
    00200         void FromAngleAxis (const Vector3& rkAxis, const Radian& fRadians);
    00201
    00202         // The matrix must be orthonormal.  The decomposition is yaw*pitch*roll
    00203         // where yaw is rotation about the Up vector, pitch is rotation about the
    00204         // Right axis, and roll is rotation about the Direction axis.
    00205         bool ToEulerAnglesXYZ (Radian& rfYAngle, Radian& rfPAngle,
    00206             Radian& rfRAngle) const;
    00207         bool ToEulerAnglesXZY (Radian& rfYAngle, Radian& rfPAngle,
    00208             Radian& rfRAngle) const;
    00209         bool ToEulerAnglesYXZ (Radian& rfYAngle, Radian& rfPAngle,
    00210             Radian& rfRAngle) const;
    00211         bool ToEulerAnglesYZX (Radian& rfYAngle, Radian& rfPAngle,
    00212             Radian& rfRAngle) const;
    00213         bool ToEulerAnglesZXY (Radian& rfYAngle, Radian& rfPAngle,
    00214             Radian& rfRAngle) const;
    00215         bool ToEulerAnglesZYX (Radian& rfYAngle, Radian& rfPAngle,
    00216             Radian& rfRAngle) const;
    00217         void FromEulerAnglesXYZ (const Radian& fYAngle, const Radian& fPAngle, const Radian& fRAngle);
    00218         void FromEulerAnglesXZY (const Radian& fYAngle, const Radian& fPAngle, const Radian& fRAngle);
    00219         void FromEulerAnglesYXZ (const Radian& fYAngle, const Radian& fPAngle, const Radian& fRAngle);
    00220         void FromEulerAnglesYZX (const Radian& fYAngle, const Radian& fPAngle, const Radian& fRAngle);
    00221         void FromEulerAnglesZXY (const Radian& fYAngle, const Radian& fPAngle, const Radian& fRAngle);
    00222         void FromEulerAnglesZYX (const Radian& fYAngle, const Radian& fPAngle, const Radian& fRAngle);
    00224         void EigenSolveSymmetric (Real afEigenvalue[3],
    00225             Vector3 akEigenvector[3]) const;
    00226
    00227         static void TensorProduct (const Vector3& rkU, const Vector3& rkV,
    00228             Matrix3& rkProduct);
    00229
    00231         inline bool hasScale() const
    00232         {
    00233             // check magnitude of column vectors (==local axes)
    00234             Real t = m[0][0] * m[0][0] + m[1][0] * m[1][0] + m[2][0] * m[2][0];
    00235             if (!Math::RealEqual(t, 1.0, (Real)1e-04))
    00236                 return true;
    00237             t = m[0][1] * m[0][1] + m[1][1] * m[1][1] + m[2][1] * m[2][1];
    00238             if (!Math::RealEqual(t, 1.0, (Real)1e-04))
    00239                 return true;
    00240             t = m[0][2] * m[0][2] + m[1][2] * m[1][2] + m[2][2] * m[2][2];
    00241             if (!Math::RealEqual(t, 1.0, (Real)1e-04))
    00242                 return true;
    00243
    00244             return false;
    00245         }
    00246
    00249         inline _OgreExport friend std::ostream& operator <<
    00250             ( std::ostream& o, const Matrix3& mat )
    00251         {
    00252             o << "Matrix3(" << mat[0][0] << ", " << mat[0][1] << ", " << mat[0][2] << ", "
    00253                             << mat[1][0] << ", " << mat[1][1] << ", " << mat[1][2] << ", "
    00254                             << mat[2][0] << ", " << mat[2][1] << ", " << mat[2][2] << ")";
    00255             return o;
    00256         }
    00257
    00258         static const Real EPSILON;
    00259         static const Matrix3 ZERO;
    00260         static const Matrix3 IDENTITY;
    00261
    00262     protected:
    00263         // support for eigensolver
    00264         void Tridiagonal (Real afDiag[3], Real afSubDiag[3]);
    00265         bool QLAlgorithm (Real afDiag[3], Real afSubDiag[3]);
    00266
    00267         // support for singular value decomposition
    00268         static const Real msSvdEpsilon;
    00269         static const unsigned int msSvdMaxIterations;
    00270         static void Bidiagonalize (Matrix3& kA, Matrix3& kL,
    00271             Matrix3& kR);
    00272         static void GolubKahanStep (Matrix3& kA, Matrix3& kL,
    00273             Matrix3& kR);
    00274
    00275         // support for spectral norm
    00276         static Real MaxCubicRoot (Real afCoeff[3]);
    00277
    00278         Real m[3][3];
    00279
    00280         // for faster access
    00281         friend class Matrix4;
    00282     };
    00285 }
    00286 #endif

Copyright © 2012 Torus Knot Software Ltd
This work is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License.
Last modified Sun Sep 2 2012 07:27:22