[136] | 1 | // This file is part of Eigen, a lightweight C++ template library
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| 2 | // for linear algebra.
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| 3 | //
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| 4 | // Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
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| 5 | //
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| 6 | // This Source Code Form is subject to the terms of the Mozilla
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| 7 | // Public License v. 2.0. If a copy of the MPL was not distributed
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| 8 | // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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| 9 |
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| 10 | // no include guard, we'll include this twice from All.h from Eigen2Support, and it's internal anyway
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| 11 |
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| 12 | namespace Eigen {
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| 13 |
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| 14 | /** \geometry_module \ingroup Geometry_Module
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| 15 | *
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| 16 | * \class AngleAxis
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| 17 | *
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| 18 | * \brief Represents a 3D rotation as a rotation angle around an arbitrary 3D axis
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| 19 | *
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| 20 | * \param _Scalar the scalar type, i.e., the type of the coefficients.
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| 21 | *
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| 22 | * The following two typedefs are provided for convenience:
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| 23 | * \li \c AngleAxisf for \c float
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| 24 | * \li \c AngleAxisd for \c double
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| 25 | *
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| 26 | * \addexample AngleAxisForEuler \label How to define a rotation from Euler-angles
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| 27 | *
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| 28 | * Combined with MatrixBase::Unit{X,Y,Z}, AngleAxis can be used to easily
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| 29 | * mimic Euler-angles. Here is an example:
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| 30 | * \include AngleAxis_mimic_euler.cpp
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| 31 | * Output: \verbinclude AngleAxis_mimic_euler.out
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| 32 | *
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| 33 | * \note This class is not aimed to be used to store a rotation transformation,
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| 34 | * but rather to make easier the creation of other rotation (Quaternion, rotation Matrix)
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| 35 | * and transformation objects.
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| 36 | *
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| 37 | * \sa class Quaternion, class Transform, MatrixBase::UnitX()
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| 38 | */
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| 39 |
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| 40 | template<typename _Scalar> struct ei_traits<AngleAxis<_Scalar> >
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| 41 | {
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| 42 | typedef _Scalar Scalar;
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| 43 | };
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| 44 |
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| 45 | template<typename _Scalar>
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| 46 | class AngleAxis : public RotationBase<AngleAxis<_Scalar>,3>
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| 47 | {
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| 48 | typedef RotationBase<AngleAxis<_Scalar>,3> Base;
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| 49 |
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| 50 | public:
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| 51 |
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| 52 | using Base::operator*;
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| 53 |
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| 54 | enum { Dim = 3 };
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| 55 | /** the scalar type of the coefficients */
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| 56 | typedef _Scalar Scalar;
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| 57 | typedef Matrix<Scalar,3,3> Matrix3;
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| 58 | typedef Matrix<Scalar,3,1> Vector3;
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| 59 | typedef Quaternion<Scalar> QuaternionType;
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| 60 |
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| 61 | protected:
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| 62 |
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| 63 | Vector3 m_axis;
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| 64 | Scalar m_angle;
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| 65 |
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| 66 | public:
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| 67 |
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| 68 | /** Default constructor without initialization. */
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| 69 | AngleAxis() {}
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| 70 | /** Constructs and initialize the angle-axis rotation from an \a angle in radian
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| 71 | * and an \a axis which must be normalized. */
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| 72 | template<typename Derived>
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| 73 | inline AngleAxis(Scalar angle, const MatrixBase<Derived>& axis) : m_axis(axis), m_angle(angle) {}
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| 74 | /** Constructs and initialize the angle-axis rotation from a quaternion \a q. */
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| 75 | inline AngleAxis(const QuaternionType& q) { *this = q; }
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| 76 | /** Constructs and initialize the angle-axis rotation from a 3x3 rotation matrix. */
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| 77 | template<typename Derived>
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| 78 | inline explicit AngleAxis(const MatrixBase<Derived>& m) { *this = m; }
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| 79 |
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| 80 | Scalar angle() const { return m_angle; }
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| 81 | Scalar& angle() { return m_angle; }
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| 82 |
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| 83 | const Vector3& axis() const { return m_axis; }
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| 84 | Vector3& axis() { return m_axis; }
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| 85 |
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| 86 | /** Concatenates two rotations */
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| 87 | inline QuaternionType operator* (const AngleAxis& other) const
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| 88 | { return QuaternionType(*this) * QuaternionType(other); }
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| 89 |
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| 90 | /** Concatenates two rotations */
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| 91 | inline QuaternionType operator* (const QuaternionType& other) const
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| 92 | { return QuaternionType(*this) * other; }
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| 93 |
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| 94 | /** Concatenates two rotations */
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| 95 | friend inline QuaternionType operator* (const QuaternionType& a, const AngleAxis& b)
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| 96 | { return a * QuaternionType(b); }
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| 97 |
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| 98 | /** Concatenates two rotations */
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| 99 | inline Matrix3 operator* (const Matrix3& other) const
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| 100 | { return toRotationMatrix() * other; }
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| 101 |
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| 102 | /** Concatenates two rotations */
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| 103 | inline friend Matrix3 operator* (const Matrix3& a, const AngleAxis& b)
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| 104 | { return a * b.toRotationMatrix(); }
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| 105 |
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| 106 | /** Applies rotation to vector */
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| 107 | inline Vector3 operator* (const Vector3& other) const
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| 108 | { return toRotationMatrix() * other; }
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| 109 |
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| 110 | /** \returns the inverse rotation, i.e., an angle-axis with opposite rotation angle */
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| 111 | AngleAxis inverse() const
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| 112 | { return AngleAxis(-m_angle, m_axis); }
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| 113 |
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| 114 | AngleAxis& operator=(const QuaternionType& q);
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| 115 | template<typename Derived>
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| 116 | AngleAxis& operator=(const MatrixBase<Derived>& m);
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| 117 |
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| 118 | template<typename Derived>
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| 119 | AngleAxis& fromRotationMatrix(const MatrixBase<Derived>& m);
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| 120 | Matrix3 toRotationMatrix(void) const;
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| 121 |
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| 122 | /** \returns \c *this with scalar type casted to \a NewScalarType
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| 123 | *
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| 124 | * Note that if \a NewScalarType is equal to the current scalar type of \c *this
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| 125 | * then this function smartly returns a const reference to \c *this.
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| 126 | */
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| 127 | template<typename NewScalarType>
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| 128 | inline typename internal::cast_return_type<AngleAxis,AngleAxis<NewScalarType> >::type cast() const
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| 129 | { return typename internal::cast_return_type<AngleAxis,AngleAxis<NewScalarType> >::type(*this); }
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| 130 |
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| 131 | /** Copy constructor with scalar type conversion */
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| 132 | template<typename OtherScalarType>
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| 133 | inline explicit AngleAxis(const AngleAxis<OtherScalarType>& other)
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| 134 | {
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| 135 | m_axis = other.axis().template cast<Scalar>();
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| 136 | m_angle = Scalar(other.angle());
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| 137 | }
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| 138 |
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| 139 | /** \returns \c true if \c *this is approximately equal to \a other, within the precision
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| 140 | * determined by \a prec.
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| 141 | *
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| 142 | * \sa MatrixBase::isApprox() */
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| 143 | bool isApprox(const AngleAxis& other, typename NumTraits<Scalar>::Real prec = precision<Scalar>()) const
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| 144 | { return m_axis.isApprox(other.m_axis, prec) && ei_isApprox(m_angle,other.m_angle, prec); }
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| 145 | };
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| 146 |
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| 147 | /** \ingroup Geometry_Module
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| 148 | * single precision angle-axis type */
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| 149 | typedef AngleAxis<float> AngleAxisf;
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| 150 | /** \ingroup Geometry_Module
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| 151 | * double precision angle-axis type */
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| 152 | typedef AngleAxis<double> AngleAxisd;
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| 153 |
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| 154 | /** Set \c *this from a quaternion.
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| 155 | * The axis is normalized.
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| 156 | */
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| 157 | template<typename Scalar>
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| 158 | AngleAxis<Scalar>& AngleAxis<Scalar>::operator=(const QuaternionType& q)
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| 159 | {
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| 160 | Scalar n2 = q.vec().squaredNorm();
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| 161 | if (n2 < precision<Scalar>()*precision<Scalar>())
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| 162 | {
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| 163 | m_angle = 0;
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| 164 | m_axis << 1, 0, 0;
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| 165 | }
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| 166 | else
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| 167 | {
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| 168 | m_angle = 2*std::acos(q.w());
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| 169 | m_axis = q.vec() / ei_sqrt(n2);
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| 170 | }
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| 171 | return *this;
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| 172 | }
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| 173 |
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| 174 | /** Set \c *this from a 3x3 rotation matrix \a mat.
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| 175 | */
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| 176 | template<typename Scalar>
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| 177 | template<typename Derived>
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| 178 | AngleAxis<Scalar>& AngleAxis<Scalar>::operator=(const MatrixBase<Derived>& mat)
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| 179 | {
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| 180 | // Since a direct conversion would not be really faster,
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| 181 | // let's use the robust Quaternion implementation:
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| 182 | return *this = QuaternionType(mat);
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| 183 | }
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| 184 |
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| 185 | /** Constructs and \returns an equivalent 3x3 rotation matrix.
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| 186 | */
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| 187 | template<typename Scalar>
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| 188 | typename AngleAxis<Scalar>::Matrix3
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| 189 | AngleAxis<Scalar>::toRotationMatrix(void) const
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| 190 | {
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| 191 | Matrix3 res;
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| 192 | Vector3 sin_axis = ei_sin(m_angle) * m_axis;
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| 193 | Scalar c = ei_cos(m_angle);
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| 194 | Vector3 cos1_axis = (Scalar(1)-c) * m_axis;
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| 195 |
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| 196 | Scalar tmp;
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| 197 | tmp = cos1_axis.x() * m_axis.y();
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| 198 | res.coeffRef(0,1) = tmp - sin_axis.z();
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| 199 | res.coeffRef(1,0) = tmp + sin_axis.z();
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| 200 |
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| 201 | tmp = cos1_axis.x() * m_axis.z();
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| 202 | res.coeffRef(0,2) = tmp + sin_axis.y();
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| 203 | res.coeffRef(2,0) = tmp - sin_axis.y();
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| 204 |
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| 205 | tmp = cos1_axis.y() * m_axis.z();
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| 206 | res.coeffRef(1,2) = tmp - sin_axis.x();
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| 207 | res.coeffRef(2,1) = tmp + sin_axis.x();
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| 208 |
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| 209 | res.diagonal() = (cos1_axis.cwise() * m_axis).cwise() + c;
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| 210 |
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| 211 | return res;
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| 212 | }
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| 213 |
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| 214 | } // end namespace Eigen
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