[1809] | 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) 2000-2005 The OGRE Team
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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 | */
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| 25 | #ifndef __Matrix3_H__
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| 26 | #define __Matrix3_H__
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| 27 |
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| 28 | #include "OgrePrerequisites.h"
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| 29 |
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| 30 | #include "OgreVector3.h"
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| 31 |
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| 32 | // NB All code adapted from Wild Magic 0.2 Matrix math (free source code)
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| 33 | // http://www.geometrictools.com/
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| 34 |
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| 35 | // NOTE. The (x,y,z) coordinate system is assumed to be right-handed.
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| 36 | // Coordinate axis rotation matrices are of the form
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| 37 | // RX = 1 0 0
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| 38 | // 0 cos(t) -sin(t)
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| 39 | // 0 sin(t) cos(t)
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| 40 | // where t > 0 indicates a counterclockwise rotation in the yz-plane
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| 41 | // RY = cos(t) 0 sin(t)
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| 42 | // 0 1 0
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| 43 | // -sin(t) 0 cos(t)
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| 44 | // where t > 0 indicates a counterclockwise rotation in the zx-plane
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| 45 | // RZ = cos(t) -sin(t) 0
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| 46 | // sin(t) cos(t) 0
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| 47 | // 0 0 1
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| 48 | // where t > 0 indicates a counterclockwise rotation in the xy-plane.
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| 49 |
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| 50 | namespace Ogre
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| 51 | {
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| 52 | /** A 3x3 matrix which can represent rotations around axes.
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| 53 | @note
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| 54 | <b>All the code is adapted from the Wild Magic 0.2 Matrix
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| 55 | library (http://www.geometrictools.com/).</b>
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| 56 | @par
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| 57 | The coordinate system is assumed to be <b>right-handed</b>.
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| 58 | */
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| 59 | class _OgreExport Matrix3
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| 60 | {
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| 61 | public:
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| 62 | /** Default constructor.
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| 63 | @note
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| 64 | It does <b>NOT</b> initialize the matrix for efficiency.
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| 65 | */
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| 66 | inline Matrix3 () {};
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| 67 | inline explicit Matrix3 (const Real arr[3][3])
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| 68 | {
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| 69 | memcpy(m,arr,9*sizeof(Real));
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| 70 | }
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| 71 | inline Matrix3 (const Matrix3& rkMatrix)
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| 72 | {
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| 73 | memcpy(m,rkMatrix.m,9*sizeof(Real));
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| 74 | }
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| 75 | Matrix3 (Real fEntry00, Real fEntry01, Real fEntry02,
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| 76 | Real fEntry10, Real fEntry11, Real fEntry12,
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| 77 | Real fEntry20, Real fEntry21, Real fEntry22)
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| 78 | {
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| 79 | m[0][0] = fEntry00;
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| 80 | m[0][1] = fEntry01;
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| 81 | m[0][2] = fEntry02;
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| 82 | m[1][0] = fEntry10;
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| 83 | m[1][1] = fEntry11;
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| 84 | m[1][2] = fEntry12;
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| 85 | m[2][0] = fEntry20;
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| 86 | m[2][1] = fEntry21;
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| 87 | m[2][2] = fEntry22;
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| 88 | }
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| 89 |
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| 90 | // member access, allows use of construct mat[r][c]
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| 91 | inline Real* operator[] (size_t iRow) const
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| 92 | {
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| 93 | return (Real*)m[iRow];
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| 94 | }
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| 95 | /*inline operator Real* ()
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| 96 | {
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| 97 | return (Real*)m[0];
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| 98 | }*/
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| 99 | Vector3 GetColumn (size_t iCol) const;
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| 100 | void SetColumn(size_t iCol, const Vector3& vec);
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| 101 | void FromAxes(const Vector3& xAxis, const Vector3& yAxis, const Vector3& zAxis);
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| 102 |
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| 103 | // assignment and comparison
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| 104 | inline Matrix3& operator= (const Matrix3& rkMatrix)
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| 105 | {
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| 106 | memcpy(m,rkMatrix.m,9*sizeof(Real));
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| 107 | return *this;
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| 108 | }
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| 109 | bool operator== (const Matrix3& rkMatrix) const;
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| 110 | inline bool operator!= (const Matrix3& rkMatrix) const
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| 111 | {
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| 112 | return !operator==(rkMatrix);
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| 113 | }
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| 114 |
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| 115 | // arithmetic operations
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| 116 | Matrix3 operator+ (const Matrix3& rkMatrix) const;
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| 117 | Matrix3 operator- (const Matrix3& rkMatrix) const;
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| 118 | Matrix3 operator* (const Matrix3& rkMatrix) const;
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| 119 | Matrix3 operator- () const;
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| 120 |
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| 121 | // matrix * vector [3x3 * 3x1 = 3x1]
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| 122 | Vector3 operator* (const Vector3& rkVector) const;
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| 123 |
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| 124 | // vector * matrix [1x3 * 3x3 = 1x3]
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| 125 | _OgreExport friend Vector3 operator* (const Vector3& rkVector,
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| 126 | const Matrix3& rkMatrix);
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| 127 |
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| 128 | // matrix * scalar
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| 129 | Matrix3 operator* (Real fScalar) const;
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| 130 |
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| 131 | // scalar * matrix
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| 132 | _OgreExport friend Matrix3 operator* (Real fScalar, const Matrix3& rkMatrix);
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| 133 |
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| 134 | // utilities
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| 135 | Matrix3 Transpose () const;
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| 136 | bool Inverse (Matrix3& rkInverse, Real fTolerance = 1e-06) const;
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| 137 | Matrix3 Inverse (Real fTolerance = 1e-06) const;
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| 138 | Real Determinant () const;
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| 139 |
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| 140 | // singular value decomposition
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| 141 | void SingularValueDecomposition (Matrix3& rkL, Vector3& rkS,
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| 142 | Matrix3& rkR) const;
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| 143 | void SingularValueComposition (const Matrix3& rkL,
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| 144 | const Vector3& rkS, const Matrix3& rkR);
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| 145 |
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| 146 | // Gram-Schmidt orthonormalization (applied to columns of rotation matrix)
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| 147 | void Orthonormalize ();
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| 148 |
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| 149 | // orthogonal Q, diagonal D, upper triangular U stored as (u01,u02,u12)
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| 150 | void QDUDecomposition (Matrix3& rkQ, Vector3& rkD,
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| 151 | Vector3& rkU) const;
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| 152 |
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| 153 | Real SpectralNorm () const;
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| 154 |
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| 155 | // matrix must be orthonormal
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| 156 | void ToAxisAngle (Vector3& rkAxis, Radian& rfAngle) const;
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| 157 | inline void ToAxisAngle (Vector3& rkAxis, Degree& rfAngle) const {
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| 158 | Radian r;
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| 159 | ToAxisAngle ( rkAxis, r );
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| 160 | rfAngle = r;
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| 161 | }
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| 162 | void FromAxisAngle (const Vector3& rkAxis, const Radian& fRadians);
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| 163 | #ifndef OGRE_FORCE_ANGLE_TYPES
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| 164 | inline void ToAxisAngle (Vector3& rkAxis, Real& rfRadians) const {
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| 165 | Radian r;
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| 166 | ToAxisAngle ( rkAxis, r );
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| 167 | rfRadians = r.valueRadians();
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| 168 | }
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| 169 | inline void FromAxisAngle (const Vector3& rkAxis, Real fRadians) {
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| 170 | FromAxisAngle ( rkAxis, Radian(fRadians) );
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| 171 | }
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| 172 | #endif//OGRE_FORCE_ANGLE_TYPES
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| 173 |
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| 174 | // The matrix must be orthonormal. The decomposition is yaw*pitch*roll
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| 175 | // where yaw is rotation about the Up vector, pitch is rotation about the
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| 176 | // Right axis, and roll is rotation about the Direction axis.
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| 177 | bool ToEulerAnglesXYZ (Radian& rfYAngle, Radian& rfPAngle,
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| 178 | Radian& rfRAngle) const;
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| 179 | bool ToEulerAnglesXZY (Radian& rfYAngle, Radian& rfPAngle,
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| 180 | Radian& rfRAngle) const;
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| 181 | bool ToEulerAnglesYXZ (Radian& rfYAngle, Radian& rfPAngle,
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| 182 | Radian& rfRAngle) const;
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| 183 | bool ToEulerAnglesYZX (Radian& rfYAngle, Radian& rfPAngle,
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| 184 | Radian& rfRAngle) const;
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| 185 | bool ToEulerAnglesZXY (Radian& rfYAngle, Radian& rfPAngle,
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| 186 | Radian& rfRAngle) const;
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| 187 | bool ToEulerAnglesZYX (Radian& rfYAngle, Radian& rfPAngle,
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| 188 | Radian& rfRAngle) const;
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| 189 | void FromEulerAnglesXYZ (const Radian& fYAngle, const Radian& fPAngle, const Radian& fRAngle);
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| 190 | void FromEulerAnglesXZY (const Radian& fYAngle, const Radian& fPAngle, const Radian& fRAngle);
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| 191 | void FromEulerAnglesYXZ (const Radian& fYAngle, const Radian& fPAngle, const Radian& fRAngle);
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| 192 | void FromEulerAnglesYZX (const Radian& fYAngle, const Radian& fPAngle, const Radian& fRAngle);
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| 193 | void FromEulerAnglesZXY (const Radian& fYAngle, const Radian& fPAngle, const Radian& fRAngle);
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| 194 | void FromEulerAnglesZYX (const Radian& fYAngle, const Radian& fPAngle, const Radian& fRAngle);
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| 195 | #ifndef OGRE_FORCE_ANGLE_TYPES
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| 196 | inline bool ToEulerAnglesXYZ (float& rfYAngle, float& rfPAngle,
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| 197 | float& rfRAngle) const {
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| 198 | Radian y, p, r;
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| 199 | bool b = ToEulerAnglesXYZ(y,p,r);
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| 200 | rfYAngle = y.valueRadians();
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| 201 | rfPAngle = p.valueRadians();
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| 202 | rfRAngle = r.valueRadians();
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| 203 | return b;
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| 204 | }
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| 205 | inline bool ToEulerAnglesXZY (float& rfYAngle, float& rfPAngle,
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| 206 | float& rfRAngle) const {
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| 207 | Radian y, p, r;
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| 208 | bool b = ToEulerAnglesXZY(y,p,r);
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| 209 | rfYAngle = y.valueRadians();
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| 210 | rfPAngle = p.valueRadians();
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| 211 | rfRAngle = r.valueRadians();
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| 212 | return b;
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| 213 | }
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| 214 | inline bool ToEulerAnglesYXZ (float& rfYAngle, float& rfPAngle,
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| 215 | float& rfRAngle) const {
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| 216 | Radian y, p, r;
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| 217 | bool b = ToEulerAnglesYXZ(y,p,r);
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| 218 | rfYAngle = y.valueRadians();
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| 219 | rfPAngle = p.valueRadians();
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| 220 | rfRAngle = r.valueRadians();
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| 221 | return b;
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| 222 | }
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| 223 | inline bool ToEulerAnglesYZX (float& rfYAngle, float& rfPAngle,
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| 224 | float& rfRAngle) const {
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| 225 | Radian y, p, r;
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| 226 | bool b = ToEulerAnglesYZX(y,p,r);
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| 227 | rfYAngle = y.valueRadians();
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| 228 | rfPAngle = p.valueRadians();
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| 229 | rfRAngle = r.valueRadians();
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| 230 | return b;
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| 231 | }
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| 232 | inline bool ToEulerAnglesZXY (float& rfYAngle, float& rfPAngle,
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| 233 | float& rfRAngle) const {
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| 234 | Radian y, p, r;
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| 235 | bool b = ToEulerAnglesZXY(y,p,r);
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| 236 | rfYAngle = y.valueRadians();
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| 237 | rfPAngle = p.valueRadians();
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| 238 | rfRAngle = r.valueRadians();
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| 239 | return b;
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| 240 | }
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| 241 | inline bool ToEulerAnglesZYX (float& rfYAngle, float& rfPAngle,
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| 242 | float& rfRAngle) const {
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| 243 | Radian y, p, r;
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| 244 | bool b = ToEulerAnglesZYX(y,p,r);
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| 245 | rfYAngle = y.valueRadians();
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| 246 | rfPAngle = p.valueRadians();
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| 247 | rfRAngle = r.valueRadians();
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| 248 | return b;
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| 249 | }
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| 250 | inline void FromEulerAnglesXYZ (float fYAngle, float fPAngle, float fRAngle) {
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| 251 | FromEulerAnglesXYZ ( Radian(fYAngle), Radian(fPAngle), Radian(fRAngle) );
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| 252 | }
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| 253 | inline void FromEulerAnglesXZY (float fYAngle, float fPAngle, float fRAngle) {
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| 254 | FromEulerAnglesXZY ( Radian(fYAngle), Radian(fPAngle), Radian(fRAngle) );
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| 255 | }
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| 256 | inline void FromEulerAnglesYXZ (float fYAngle, float fPAngle, float fRAngle) {
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| 257 | FromEulerAnglesYXZ ( Radian(fYAngle), Radian(fPAngle), Radian(fRAngle) );
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| 258 | }
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| 259 | inline void FromEulerAnglesYZX (float fYAngle, float fPAngle, float fRAngle) {
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| 260 | FromEulerAnglesYZX ( Radian(fYAngle), Radian(fPAngle), Radian(fRAngle) );
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| 261 | }
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| 262 | inline void FromEulerAnglesZXY (float fYAngle, float fPAngle, float fRAngle) {
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| 263 | FromEulerAnglesZXY ( Radian(fYAngle), Radian(fPAngle), Radian(fRAngle) );
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| 264 | }
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| 265 | inline void FromEulerAnglesZYX (float fYAngle, float fPAngle, float fRAngle) {
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| 266 | FromEulerAnglesZYX ( Radian(fYAngle), Radian(fPAngle), Radian(fRAngle) );
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| 267 | }
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| 268 | #endif//OGRE_FORCE_ANGLE_TYPES
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| 269 | // eigensolver, matrix must be symmetric
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| 270 | void EigenSolveSymmetric (Real afEigenvalue[3],
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| 271 | Vector3 akEigenvector[3]) const;
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| 272 |
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| 273 | static void TensorProduct (const Vector3& rkU, const Vector3& rkV,
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| 274 | Matrix3& rkProduct);
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| 275 |
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| 276 | static const Real EPSILON;
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| 277 | static const Matrix3 ZERO;
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| 278 | static const Matrix3 IDENTITY;
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| 279 |
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| 280 | protected:
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| 281 | // support for eigensolver
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| 282 | void Tridiagonal (Real afDiag[3], Real afSubDiag[3]);
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| 283 | bool QLAlgorithm (Real afDiag[3], Real afSubDiag[3]);
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| 284 |
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| 285 | // support for singular value decomposition
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| 286 | static const Real ms_fSvdEpsilon;
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| 287 | static const unsigned int ms_iSvdMaxIterations;
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| 288 | static void Bidiagonalize (Matrix3& kA, Matrix3& kL,
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| 289 | Matrix3& kR);
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| 290 | static void GolubKahanStep (Matrix3& kA, Matrix3& kL,
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| 291 | Matrix3& kR);
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| 292 |
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| 293 | // support for spectral norm
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| 294 | static Real MaxCubicRoot (Real afCoeff[3]);
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| 295 |
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| 296 | Real m[3][3];
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| 297 |
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| 298 | // for faster access
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| 299 | friend class Matrix4;
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| 300 | };
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| 301 | }
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| 302 | #endif
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