[3] | 1 | /* |
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| 2 | ----------------------------------------------------------------------------- |
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| 3 | This source file is part of OGRE |
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| 4 | (Object-oriented Graphics Rendering Engine) |
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| 5 | For the latest info, see http://www.ogre3d.org/ |
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| 6 | |
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| 7 | Copyright (c) 2000-2006 Torus Knot Software Ltd |
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| 8 | Also see acknowledgements in Readme.html |
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| 9 | |
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| 10 | This program is free software; you can redistribute it and/or modify it under |
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| 11 | the terms of the GNU Lesser General Public License as published by the Free Software |
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| 12 | Foundation; either version 2 of the License, or (at your option) any later |
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| 13 | version. |
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| 14 | |
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| 15 | This program is distributed in the hope that it will be useful, but WITHOUT |
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| 16 | ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS |
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| 17 | FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details. |
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| 18 | |
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| 19 | You should have received a copy of the GNU Lesser General Public License along with |
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| 20 | this program; if not, write to the Free Software Foundation, Inc., 59 Temple |
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| 21 | Place - Suite 330, Boston, MA 02111-1307, USA, or go to |
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| 22 | http://www.gnu.org/copyleft/lesser.txt. |
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| 23 | |
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| 24 | You may alternatively use this source under the terms of a specific version of |
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| 25 | the OGRE Unrestricted License provided you have obtained such a license from |
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| 26 | Torus Knot Software Ltd. |
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| 27 | ----------------------------------------------------------------------------- |
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| 28 | */ |
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| 29 | #ifndef __Matrix3_H__ |
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| 30 | #define __Matrix3_H__ |
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| 31 | |
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| 32 | #include "OgrePrerequisites.h" |
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| 33 | |
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| 34 | #include "OgreVector3.h" |
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| 35 | |
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| 36 | // NB All code adapted from Wild Magic 0.2 Matrix math (free source code) |
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| 37 | // http://www.geometrictools.com/ |
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| 38 | |
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| 39 | // NOTE. The (x,y,z) coordinate system is assumed to be right-handed. |
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| 40 | // Coordinate axis rotation matrices are of the form |
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| 41 | // RX = 1 0 0 |
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| 42 | // 0 cos(t) -sin(t) |
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| 43 | // 0 sin(t) cos(t) |
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| 44 | // where t > 0 indicates a counterclockwise rotation in the yz-plane |
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| 45 | // RY = cos(t) 0 sin(t) |
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| 46 | // 0 1 0 |
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| 47 | // -sin(t) 0 cos(t) |
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| 48 | // where t > 0 indicates a counterclockwise rotation in the zx-plane |
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| 49 | // RZ = cos(t) -sin(t) 0 |
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| 50 | // sin(t) cos(t) 0 |
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| 51 | // 0 0 1 |
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| 52 | // where t > 0 indicates a counterclockwise rotation in the xy-plane. |
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| 53 | |
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| 54 | namespace Ogre |
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| 55 | { |
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| 56 | /** A 3x3 matrix which can represent rotations around axes. |
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| 57 | @note |
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| 58 | <b>All the code is adapted from the Wild Magic 0.2 Matrix |
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| 59 | library (http://www.geometrictools.com/).</b> |
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| 60 | @par |
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| 61 | The coordinate system is assumed to be <b>right-handed</b>. |
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| 62 | */ |
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| 63 | class _OgreExport Matrix3 |
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| 64 | { |
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| 65 | public: |
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| 66 | /** Default constructor. |
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| 67 | @note |
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| 68 | It does <b>NOT</b> initialize the matrix for efficiency. |
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| 69 | */ |
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| 70 | inline Matrix3 () {}; |
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| 71 | inline explicit Matrix3 (const Real arr[3][3]) |
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| 72 | { |
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| 73 | memcpy(m,arr,9*sizeof(Real)); |
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| 74 | } |
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| 75 | inline Matrix3 (const Matrix3& rkMatrix) |
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| 76 | { |
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| 77 | memcpy(m,rkMatrix.m,9*sizeof(Real)); |
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| 78 | } |
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| 79 | Matrix3 (Real fEntry00, Real fEntry01, Real fEntry02, |
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| 80 | Real fEntry10, Real fEntry11, Real fEntry12, |
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| 81 | Real fEntry20, Real fEntry21, Real fEntry22) |
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| 82 | { |
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| 83 | m[0][0] = fEntry00; |
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| 84 | m[0][1] = fEntry01; |
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| 85 | m[0][2] = fEntry02; |
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| 86 | m[1][0] = fEntry10; |
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| 87 | m[1][1] = fEntry11; |
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| 88 | m[1][2] = fEntry12; |
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| 89 | m[2][0] = fEntry20; |
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| 90 | m[2][1] = fEntry21; |
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| 91 | m[2][2] = fEntry22; |
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| 92 | } |
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| 93 | |
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| 94 | // member access, allows use of construct mat[r][c] |
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| 95 | inline Real* operator[] (size_t iRow) const |
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| 96 | { |
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| 97 | return (Real*)m[iRow]; |
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| 98 | } |
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| 99 | /*inline operator Real* () |
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| 100 | { |
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| 101 | return (Real*)m[0]; |
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| 102 | }*/ |
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| 103 | Vector3 GetColumn (size_t iCol) const; |
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| 104 | void SetColumn(size_t iCol, const Vector3& vec); |
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| 105 | void FromAxes(const Vector3& xAxis, const Vector3& yAxis, const Vector3& zAxis); |
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| 106 | |
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| 107 | // assignment and comparison |
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| 108 | inline Matrix3& operator= (const Matrix3& rkMatrix) |
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| 109 | { |
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| 110 | memcpy(m,rkMatrix.m,9*sizeof(Real)); |
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| 111 | return *this; |
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| 112 | } |
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| 113 | bool operator== (const Matrix3& rkMatrix) const; |
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| 114 | inline bool operator!= (const Matrix3& rkMatrix) const |
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| 115 | { |
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| 116 | return !operator==(rkMatrix); |
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| 117 | } |
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| 118 | |
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| 119 | // arithmetic operations |
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| 120 | Matrix3 operator+ (const Matrix3& rkMatrix) const; |
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| 121 | Matrix3 operator- (const Matrix3& rkMatrix) const; |
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| 122 | Matrix3 operator* (const Matrix3& rkMatrix) const; |
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| 123 | Matrix3 operator- () const; |
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| 124 | |
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| 125 | // matrix * vector [3x3 * 3x1 = 3x1] |
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| 126 | Vector3 operator* (const Vector3& rkVector) const; |
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| 127 | |
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| 128 | // vector * matrix [1x3 * 3x3 = 1x3] |
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| 129 | _OgreExport friend Vector3 operator* (const Vector3& rkVector, |
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| 130 | const Matrix3& rkMatrix); |
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| 131 | |
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| 132 | // matrix * scalar |
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| 133 | Matrix3 operator* (Real fScalar) const; |
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| 134 | |
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| 135 | // scalar * matrix |
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| 136 | _OgreExport friend Matrix3 operator* (Real fScalar, const Matrix3& rkMatrix); |
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| 137 | |
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| 138 | // utilities |
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| 139 | Matrix3 Transpose () const; |
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| 140 | bool Inverse (Matrix3& rkInverse, Real fTolerance = 1e-06) const; |
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| 141 | Matrix3 Inverse (Real fTolerance = 1e-06) const; |
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| 142 | Real Determinant () const; |
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| 143 | |
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| 144 | // singular value decomposition |
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| 145 | void SingularValueDecomposition (Matrix3& rkL, Vector3& rkS, |
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| 146 | Matrix3& rkR) const; |
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| 147 | void SingularValueComposition (const Matrix3& rkL, |
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| 148 | const Vector3& rkS, const Matrix3& rkR); |
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| 149 | |
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| 150 | // Gram-Schmidt orthonormalization (applied to columns of rotation matrix) |
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| 151 | void Orthonormalize (); |
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| 152 | |
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| 153 | // orthogonal Q, diagonal D, upper triangular U stored as (u01,u02,u12) |
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| 154 | void QDUDecomposition (Matrix3& rkQ, Vector3& rkD, |
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| 155 | Vector3& rkU) const; |
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| 156 | |
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| 157 | Real SpectralNorm () const; |
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| 158 | |
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| 159 | // matrix must be orthonormal |
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| 160 | void ToAxisAngle (Vector3& rkAxis, Radian& rfAngle) const; |
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| 161 | inline void ToAxisAngle (Vector3& rkAxis, Degree& rfAngle) const { |
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| 162 | Radian r; |
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| 163 | ToAxisAngle ( rkAxis, r ); |
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| 164 | rfAngle = r; |
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| 165 | } |
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| 166 | void FromAxisAngle (const Vector3& rkAxis, const Radian& fRadians); |
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| 167 | #ifndef OGRE_FORCE_ANGLE_TYPES |
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| 168 | inline void ToAxisAngle (Vector3& rkAxis, Real& rfRadians) const { |
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| 169 | Radian r; |
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| 170 | ToAxisAngle ( rkAxis, r ); |
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| 171 | rfRadians = r.valueRadians(); |
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| 172 | } |
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| 173 | inline void FromAxisAngle (const Vector3& rkAxis, Real fRadians) { |
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| 174 | FromAxisAngle ( rkAxis, Radian(fRadians) ); |
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| 175 | } |
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| 176 | #endif//OGRE_FORCE_ANGLE_TYPES |
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| 177 | |
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| 178 | // The matrix must be orthonormal. The decomposition is yaw*pitch*roll |
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| 179 | // where yaw is rotation about the Up vector, pitch is rotation about the |
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| 180 | // Right axis, and roll is rotation about the Direction axis. |
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| 181 | bool ToEulerAnglesXYZ (Radian& rfYAngle, Radian& rfPAngle, |
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| 182 | Radian& rfRAngle) const; |
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| 183 | bool ToEulerAnglesXZY (Radian& rfYAngle, Radian& rfPAngle, |
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| 184 | Radian& rfRAngle) const; |
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| 185 | bool ToEulerAnglesYXZ (Radian& rfYAngle, Radian& rfPAngle, |
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| 186 | Radian& rfRAngle) const; |
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| 187 | bool ToEulerAnglesYZX (Radian& rfYAngle, Radian& rfPAngle, |
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| 188 | Radian& rfRAngle) const; |
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| 189 | bool ToEulerAnglesZXY (Radian& rfYAngle, Radian& rfPAngle, |
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| 190 | Radian& rfRAngle) const; |
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| 191 | bool ToEulerAnglesZYX (Radian& rfYAngle, Radian& rfPAngle, |
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| 192 | Radian& rfRAngle) const; |
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| 193 | void FromEulerAnglesXYZ (const Radian& fYAngle, const Radian& fPAngle, const Radian& fRAngle); |
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| 194 | void FromEulerAnglesXZY (const Radian& fYAngle, const Radian& fPAngle, const Radian& fRAngle); |
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| 195 | void FromEulerAnglesYXZ (const Radian& fYAngle, const Radian& fPAngle, const Radian& fRAngle); |
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| 196 | void FromEulerAnglesYZX (const Radian& fYAngle, const Radian& fPAngle, const Radian& fRAngle); |
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| 197 | void FromEulerAnglesZXY (const Radian& fYAngle, const Radian& fPAngle, const Radian& fRAngle); |
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| 198 | void FromEulerAnglesZYX (const Radian& fYAngle, const Radian& fPAngle, const Radian& fRAngle); |
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| 199 | #ifndef OGRE_FORCE_ANGLE_TYPES |
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| 200 | inline bool ToEulerAnglesXYZ (float& rfYAngle, float& rfPAngle, |
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| 201 | float& rfRAngle) const { |
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| 202 | Radian y, p, r; |
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| 203 | bool b = ToEulerAnglesXYZ(y,p,r); |
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| 204 | rfYAngle = y.valueRadians(); |
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| 205 | rfPAngle = p.valueRadians(); |
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| 206 | rfRAngle = r.valueRadians(); |
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| 207 | return b; |
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| 208 | } |
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| 209 | inline bool ToEulerAnglesXZY (float& rfYAngle, float& rfPAngle, |
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| 210 | float& rfRAngle) const { |
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| 211 | Radian y, p, r; |
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| 212 | bool b = ToEulerAnglesXZY(y,p,r); |
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| 213 | rfYAngle = y.valueRadians(); |
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| 214 | rfPAngle = p.valueRadians(); |
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| 215 | rfRAngle = r.valueRadians(); |
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| 216 | return b; |
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| 217 | } |
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| 218 | inline bool ToEulerAnglesYXZ (float& rfYAngle, float& rfPAngle, |
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| 219 | float& rfRAngle) const { |
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| 220 | Radian y, p, r; |
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| 221 | bool b = ToEulerAnglesYXZ(y,p,r); |
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| 222 | rfYAngle = y.valueRadians(); |
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| 223 | rfPAngle = p.valueRadians(); |
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| 224 | rfRAngle = r.valueRadians(); |
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| 225 | return b; |
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| 226 | } |
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| 227 | inline bool ToEulerAnglesYZX (float& rfYAngle, float& rfPAngle, |
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| 228 | float& rfRAngle) const { |
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| 229 | Radian y, p, r; |
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| 230 | bool b = ToEulerAnglesYZX(y,p,r); |
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| 231 | rfYAngle = y.valueRadians(); |
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| 232 | rfPAngle = p.valueRadians(); |
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| 233 | rfRAngle = r.valueRadians(); |
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| 234 | return b; |
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| 235 | } |
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| 236 | inline bool ToEulerAnglesZXY (float& rfYAngle, float& rfPAngle, |
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| 237 | float& rfRAngle) const { |
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| 238 | Radian y, p, r; |
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| 239 | bool b = ToEulerAnglesZXY(y,p,r); |
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| 240 | rfYAngle = y.valueRadians(); |
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| 241 | rfPAngle = p.valueRadians(); |
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| 242 | rfRAngle = r.valueRadians(); |
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| 243 | return b; |
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| 244 | } |
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| 245 | inline bool ToEulerAnglesZYX (float& rfYAngle, float& rfPAngle, |
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| 246 | float& rfRAngle) const { |
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| 247 | Radian y, p, r; |
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| 248 | bool b = ToEulerAnglesZYX(y,p,r); |
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| 249 | rfYAngle = y.valueRadians(); |
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| 250 | rfPAngle = p.valueRadians(); |
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| 251 | rfRAngle = r.valueRadians(); |
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| 252 | return b; |
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| 253 | } |
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| 254 | inline void FromEulerAnglesXYZ (float fYAngle, float fPAngle, float fRAngle) { |
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| 255 | FromEulerAnglesXYZ ( Radian(fYAngle), Radian(fPAngle), Radian(fRAngle) ); |
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| 256 | } |
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| 257 | inline void FromEulerAnglesXZY (float fYAngle, float fPAngle, float fRAngle) { |
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| 258 | FromEulerAnglesXZY ( Radian(fYAngle), Radian(fPAngle), Radian(fRAngle) ); |
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| 259 | } |
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| 260 | inline void FromEulerAnglesYXZ (float fYAngle, float fPAngle, float fRAngle) { |
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| 261 | FromEulerAnglesYXZ ( Radian(fYAngle), Radian(fPAngle), Radian(fRAngle) ); |
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| 262 | } |
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| 263 | inline void FromEulerAnglesYZX (float fYAngle, float fPAngle, float fRAngle) { |
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| 264 | FromEulerAnglesYZX ( Radian(fYAngle), Radian(fPAngle), Radian(fRAngle) ); |
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| 265 | } |
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| 266 | inline void FromEulerAnglesZXY (float fYAngle, float fPAngle, float fRAngle) { |
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| 267 | FromEulerAnglesZXY ( Radian(fYAngle), Radian(fPAngle), Radian(fRAngle) ); |
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| 268 | } |
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| 269 | inline void FromEulerAnglesZYX (float fYAngle, float fPAngle, float fRAngle) { |
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| 270 | FromEulerAnglesZYX ( Radian(fYAngle), Radian(fPAngle), Radian(fRAngle) ); |
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| 271 | } |
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| 272 | #endif//OGRE_FORCE_ANGLE_TYPES |
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| 273 | // eigensolver, matrix must be symmetric |
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| 274 | void EigenSolveSymmetric (Real afEigenvalue[3], |
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| 275 | Vector3 akEigenvector[3]) const; |
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| 276 | |
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| 277 | static void TensorProduct (const Vector3& rkU, const Vector3& rkV, |
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| 278 | Matrix3& rkProduct); |
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| 279 | |
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| 280 | static const Real EPSILON; |
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| 281 | static const Matrix3 ZERO; |
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| 282 | static const Matrix3 IDENTITY; |
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| 283 | |
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| 284 | protected: |
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| 285 | // support for eigensolver |
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| 286 | void Tridiagonal (Real afDiag[3], Real afSubDiag[3]); |
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| 287 | bool QLAlgorithm (Real afDiag[3], Real afSubDiag[3]); |
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| 288 | |
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| 289 | // support for singular value decomposition |
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| 290 | static const Real ms_fSvdEpsilon; |
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| 291 | static const unsigned int ms_iSvdMaxIterations; |
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| 292 | static void Bidiagonalize (Matrix3& kA, Matrix3& kL, |
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| 293 | Matrix3& kR); |
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| 294 | static void GolubKahanStep (Matrix3& kA, Matrix3& kL, |
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| 295 | Matrix3& kR); |
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| 296 | |
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| 297 | // support for spectral norm |
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| 298 | static Real MaxCubicRoot (Real afCoeff[3]); |
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| 299 | |
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| 300 | Real m[3][3]; |
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| 301 | |
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| 302 | // for faster access |
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| 303 | friend class Matrix4; |
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| 304 | }; |
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| 305 | } |
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| 306 | #endif |
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