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 <gael.guennebaud@inria.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 | #ifndef EIGEN_ANGLEAXIS_H
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11 | #define EIGEN_ANGLEAXIS_H
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12 |
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13 | namespace Eigen {
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14 |
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15 | /** \geometry_module \ingroup Geometry_Module
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16 | *
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17 | * \class AngleAxis
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18 | *
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19 | * \brief Represents a 3D rotation as a rotation angle around an arbitrary 3D axis
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20 | *
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21 | * \param _Scalar the scalar type, i.e., the type of the coefficients.
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22 | *
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23 | * \warning When setting up an AngleAxis object, the axis vector \b must \b be \b normalized.
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24 | *
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25 | * The following two typedefs are provided for convenience:
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26 | * \li \c AngleAxisf for \c float
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27 | * \li \c AngleAxisd for \c double
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28 | *
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29 | * Combined with MatrixBase::Unit{X,Y,Z}, AngleAxis can be used to easily
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30 | * mimic Euler-angles. Here is an example:
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31 | * \include AngleAxis_mimic_euler.cpp
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32 | * Output: \verbinclude AngleAxis_mimic_euler.out
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33 | *
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34 | * \note This class is not aimed to be used to store a rotation transformation,
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35 | * but rather to make easier the creation of other rotation (Quaternion, rotation Matrix)
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36 | * and transformation objects.
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37 | *
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38 | * \sa class Quaternion, class Transform, MatrixBase::UnitX()
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39 | */
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40 |
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41 | namespace internal {
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42 | template<typename _Scalar> struct traits<AngleAxis<_Scalar> >
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43 | {
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44 | typedef _Scalar Scalar;
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45 | };
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46 | }
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47 |
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48 | template<typename _Scalar>
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49 | class AngleAxis : public RotationBase<AngleAxis<_Scalar>,3>
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50 | {
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51 | typedef RotationBase<AngleAxis<_Scalar>,3> Base;
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52 |
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53 | public:
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54 |
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55 | using Base::operator*;
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56 |
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57 | enum { Dim = 3 };
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58 | /** the scalar type of the coefficients */
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59 | typedef _Scalar Scalar;
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60 | typedef Matrix<Scalar,3,3> Matrix3;
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61 | typedef Matrix<Scalar,3,1> Vector3;
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62 | typedef Quaternion<Scalar> QuaternionType;
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63 |
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64 | protected:
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65 |
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66 | Vector3 m_axis;
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67 | Scalar m_angle;
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68 |
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69 | public:
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70 |
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71 | /** Default constructor without initialization. */
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72 | AngleAxis() {}
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73 | /** Constructs and initialize the angle-axis rotation from an \a angle in radian
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74 | * and an \a axis which \b must \b be \b normalized.
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75 | *
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76 | * \warning If the \a axis vector is not normalized, then the angle-axis object
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77 | * represents an invalid rotation. */
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78 | template<typename Derived>
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79 | inline AngleAxis(const Scalar& angle, const MatrixBase<Derived>& axis) : m_axis(axis), m_angle(angle) {}
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80 | /** Constructs and initialize the angle-axis rotation from a quaternion \a q. */
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81 | template<typename QuatDerived> inline explicit AngleAxis(const QuaternionBase<QuatDerived>& q) { *this = q; }
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82 | /** Constructs and initialize the angle-axis rotation from a 3x3 rotation matrix. */
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83 | template<typename Derived>
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84 | inline explicit AngleAxis(const MatrixBase<Derived>& m) { *this = m; }
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85 |
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86 | /** \returns the value of the rotation angle in radian */
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87 | Scalar angle() const { return m_angle; }
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88 | /** \returns a read-write reference to the stored angle in radian */
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89 | Scalar& angle() { return m_angle; }
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90 |
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91 | /** \returns the rotation axis */
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92 | const Vector3& axis() const { return m_axis; }
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93 | /** \returns a read-write reference to the stored rotation axis.
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94 | *
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95 | * \warning The rotation axis must remain a \b unit vector.
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96 | */
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97 | Vector3& axis() { return m_axis; }
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98 |
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99 | /** Concatenates two rotations */
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100 | inline QuaternionType operator* (const AngleAxis& other) const
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101 | { return QuaternionType(*this) * QuaternionType(other); }
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102 |
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103 | /** Concatenates two rotations */
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104 | inline QuaternionType operator* (const QuaternionType& other) const
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105 | { return QuaternionType(*this) * other; }
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106 |
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107 | /** Concatenates two rotations */
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108 | friend inline QuaternionType operator* (const QuaternionType& a, const AngleAxis& b)
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109 | { return a * QuaternionType(b); }
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110 |
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111 | /** \returns the inverse rotation, i.e., an angle-axis with opposite rotation angle */
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112 | AngleAxis inverse() const
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113 | { return AngleAxis(-m_angle, m_axis); }
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114 |
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115 | template<class QuatDerived>
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116 | AngleAxis& operator=(const QuaternionBase<QuatDerived>& q);
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117 | template<typename Derived>
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118 | AngleAxis& operator=(const MatrixBase<Derived>& m);
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119 |
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120 | template<typename Derived>
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121 | AngleAxis& fromRotationMatrix(const MatrixBase<Derived>& m);
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122 | Matrix3 toRotationMatrix(void) const;
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123 |
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124 | /** \returns \c *this with scalar type casted to \a NewScalarType
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125 | *
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126 | * Note that if \a NewScalarType is equal to the current scalar type of \c *this
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127 | * then this function smartly returns a const reference to \c *this.
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128 | */
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129 | template<typename NewScalarType>
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130 | inline typename internal::cast_return_type<AngleAxis,AngleAxis<NewScalarType> >::type cast() const
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131 | { return typename internal::cast_return_type<AngleAxis,AngleAxis<NewScalarType> >::type(*this); }
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132 |
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133 | /** Copy constructor with scalar type conversion */
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134 | template<typename OtherScalarType>
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135 | inline explicit AngleAxis(const AngleAxis<OtherScalarType>& other)
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136 | {
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137 | m_axis = other.axis().template cast<Scalar>();
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138 | m_angle = Scalar(other.angle());
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139 | }
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140 |
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141 | static inline const AngleAxis Identity() { return AngleAxis(Scalar(0), Vector3::UnitX()); }
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142 |
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143 | /** \returns \c true if \c *this is approximately equal to \a other, within the precision
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144 | * determined by \a prec.
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145 | *
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146 | * \sa MatrixBase::isApprox() */
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147 | bool isApprox(const AngleAxis& other, const typename NumTraits<Scalar>::Real& prec = NumTraits<Scalar>::dummy_precision()) const
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148 | { return m_axis.isApprox(other.m_axis, prec) && internal::isApprox(m_angle,other.m_angle, prec); }
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149 | };
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150 |
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151 | /** \ingroup Geometry_Module
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152 | * single precision angle-axis type */
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153 | typedef AngleAxis<float> AngleAxisf;
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154 | /** \ingroup Geometry_Module
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155 | * double precision angle-axis type */
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156 | typedef AngleAxis<double> AngleAxisd;
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157 |
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158 | /** Set \c *this from a \b unit quaternion.
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159 | * The axis is normalized.
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160 | *
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161 | * \warning As any other method dealing with quaternion, if the input quaternion
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162 | * is not normalized then the result is undefined.
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163 | */
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164 | template<typename Scalar>
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165 | template<typename QuatDerived>
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166 | AngleAxis<Scalar>& AngleAxis<Scalar>::operator=(const QuaternionBase<QuatDerived>& q)
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167 | {
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168 | using std::acos;
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169 | using std::min;
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170 | using std::max;
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171 | using std::sqrt;
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172 | Scalar n2 = q.vec().squaredNorm();
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173 | if (n2 < NumTraits<Scalar>::dummy_precision()*NumTraits<Scalar>::dummy_precision())
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174 | {
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175 | m_angle = Scalar(0);
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176 | m_axis << Scalar(1), Scalar(0), Scalar(0);
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177 | }
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178 | else
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179 | {
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180 | m_angle = Scalar(2)*acos((min)((max)(Scalar(-1),q.w()),Scalar(1)));
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181 | m_axis = q.vec() / sqrt(n2);
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182 | }
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183 | return *this;
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184 | }
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185 |
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186 | /** Set \c *this from a 3x3 rotation matrix \a mat.
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187 | */
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188 | template<typename Scalar>
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189 | template<typename Derived>
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190 | AngleAxis<Scalar>& AngleAxis<Scalar>::operator=(const MatrixBase<Derived>& mat)
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191 | {
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192 | // Since a direct conversion would not be really faster,
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193 | // let's use the robust Quaternion implementation:
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194 | return *this = QuaternionType(mat);
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195 | }
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196 |
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197 | /**
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198 | * \brief Sets \c *this from a 3x3 rotation matrix.
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199 | **/
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200 | template<typename Scalar>
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201 | template<typename Derived>
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202 | AngleAxis<Scalar>& AngleAxis<Scalar>::fromRotationMatrix(const MatrixBase<Derived>& mat)
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203 | {
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204 | return *this = QuaternionType(mat);
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205 | }
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206 |
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207 | /** Constructs and \returns an equivalent 3x3 rotation matrix.
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208 | */
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209 | template<typename Scalar>
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210 | typename AngleAxis<Scalar>::Matrix3
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211 | AngleAxis<Scalar>::toRotationMatrix(void) const
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212 | {
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213 | using std::sin;
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214 | using std::cos;
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215 | Matrix3 res;
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216 | Vector3 sin_axis = sin(m_angle) * m_axis;
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217 | Scalar c = cos(m_angle);
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218 | Vector3 cos1_axis = (Scalar(1)-c) * m_axis;
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219 |
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220 | Scalar tmp;
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221 | tmp = cos1_axis.x() * m_axis.y();
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222 | res.coeffRef(0,1) = tmp - sin_axis.z();
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223 | res.coeffRef(1,0) = tmp + sin_axis.z();
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224 |
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225 | tmp = cos1_axis.x() * m_axis.z();
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226 | res.coeffRef(0,2) = tmp + sin_axis.y();
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227 | res.coeffRef(2,0) = tmp - sin_axis.y();
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228 |
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229 | tmp = cos1_axis.y() * m_axis.z();
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230 | res.coeffRef(1,2) = tmp - sin_axis.x();
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231 | res.coeffRef(2,1) = tmp + sin_axis.x();
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232 |
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233 | res.diagonal() = (cos1_axis.cwiseProduct(m_axis)).array() + c;
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234 |
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235 | return res;
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236 | }
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237 |
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238 | } // end namespace Eigen
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239 |
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240 | #endif // EIGEN_ANGLEAXIS_H
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