// This file is part of Eigen, a lightweight C++ template library // for linear algebra. // // Copyright (C) 2008 Gael Guennebaud // // This Source Code Form is subject to the terms of the Mozilla // Public License v. 2.0. If a copy of the MPL was not distributed // with this file, You can obtain one at http://mozilla.org/MPL/2.0/. // no include guard, we'll include this twice from All.h from Eigen2Support, and it's internal anyway namespace Eigen { /** \geometry_module \ingroup Geometry_Module * * \class AngleAxis * * \brief Represents a 3D rotation as a rotation angle around an arbitrary 3D axis * * \param _Scalar the scalar type, i.e., the type of the coefficients. * * The following two typedefs are provided for convenience: * \li \c AngleAxisf for \c float * \li \c AngleAxisd for \c double * * \addexample AngleAxisForEuler \label How to define a rotation from Euler-angles * * Combined with MatrixBase::Unit{X,Y,Z}, AngleAxis can be used to easily * mimic Euler-angles. Here is an example: * \include AngleAxis_mimic_euler.cpp * Output: \verbinclude AngleAxis_mimic_euler.out * * \note This class is not aimed to be used to store a rotation transformation, * but rather to make easier the creation of other rotation (Quaternion, rotation Matrix) * and transformation objects. * * \sa class Quaternion, class Transform, MatrixBase::UnitX() */ template struct ei_traits > { typedef _Scalar Scalar; }; template class AngleAxis : public RotationBase,3> { typedef RotationBase,3> Base; public: using Base::operator*; enum { Dim = 3 }; /** the scalar type of the coefficients */ typedef _Scalar Scalar; typedef Matrix Matrix3; typedef Matrix Vector3; typedef Quaternion QuaternionType; protected: Vector3 m_axis; Scalar m_angle; public: /** Default constructor without initialization. */ AngleAxis() {} /** Constructs and initialize the angle-axis rotation from an \a angle in radian * and an \a axis which must be normalized. */ template inline AngleAxis(Scalar angle, const MatrixBase& axis) : m_axis(axis), m_angle(angle) {} /** Constructs and initialize the angle-axis rotation from a quaternion \a q. */ inline AngleAxis(const QuaternionType& q) { *this = q; } /** Constructs and initialize the angle-axis rotation from a 3x3 rotation matrix. */ template inline explicit AngleAxis(const MatrixBase& m) { *this = m; } Scalar angle() const { return m_angle; } Scalar& angle() { return m_angle; } const Vector3& axis() const { return m_axis; } Vector3& axis() { return m_axis; } /** Concatenates two rotations */ inline QuaternionType operator* (const AngleAxis& other) const { return QuaternionType(*this) * QuaternionType(other); } /** Concatenates two rotations */ inline QuaternionType operator* (const QuaternionType& other) const { return QuaternionType(*this) * other; } /** Concatenates two rotations */ friend inline QuaternionType operator* (const QuaternionType& a, const AngleAxis& b) { return a * QuaternionType(b); } /** Concatenates two rotations */ inline Matrix3 operator* (const Matrix3& other) const { return toRotationMatrix() * other; } /** Concatenates two rotations */ inline friend Matrix3 operator* (const Matrix3& a, const AngleAxis& b) { return a * b.toRotationMatrix(); } /** Applies rotation to vector */ inline Vector3 operator* (const Vector3& other) const { return toRotationMatrix() * other; } /** \returns the inverse rotation, i.e., an angle-axis with opposite rotation angle */ AngleAxis inverse() const { return AngleAxis(-m_angle, m_axis); } AngleAxis& operator=(const QuaternionType& q); template AngleAxis& operator=(const MatrixBase& m); template AngleAxis& fromRotationMatrix(const MatrixBase& m); Matrix3 toRotationMatrix(void) const; /** \returns \c *this with scalar type casted to \a NewScalarType * * Note that if \a NewScalarType is equal to the current scalar type of \c *this * then this function smartly returns a const reference to \c *this. */ template inline typename internal::cast_return_type >::type cast() const { return typename internal::cast_return_type >::type(*this); } /** Copy constructor with scalar type conversion */ template inline explicit AngleAxis(const AngleAxis& other) { m_axis = other.axis().template cast(); m_angle = Scalar(other.angle()); } /** \returns \c true if \c *this is approximately equal to \a other, within the precision * determined by \a prec. * * \sa MatrixBase::isApprox() */ bool isApprox(const AngleAxis& other, typename NumTraits::Real prec = precision()) const { return m_axis.isApprox(other.m_axis, prec) && ei_isApprox(m_angle,other.m_angle, prec); } }; /** \ingroup Geometry_Module * single precision angle-axis type */ typedef AngleAxis AngleAxisf; /** \ingroup Geometry_Module * double precision angle-axis type */ typedef AngleAxis AngleAxisd; /** Set \c *this from a quaternion. * The axis is normalized. */ template AngleAxis& AngleAxis::operator=(const QuaternionType& q) { Scalar n2 = q.vec().squaredNorm(); if (n2 < precision()*precision()) { m_angle = 0; m_axis << 1, 0, 0; } else { m_angle = 2*std::acos(q.w()); m_axis = q.vec() / ei_sqrt(n2); } return *this; } /** Set \c *this from a 3x3 rotation matrix \a mat. */ template template AngleAxis& AngleAxis::operator=(const MatrixBase& mat) { // Since a direct conversion would not be really faster, // let's use the robust Quaternion implementation: return *this = QuaternionType(mat); } /** Constructs and \returns an equivalent 3x3 rotation matrix. */ template typename AngleAxis::Matrix3 AngleAxis::toRotationMatrix(void) const { Matrix3 res; Vector3 sin_axis = ei_sin(m_angle) * m_axis; Scalar c = ei_cos(m_angle); Vector3 cos1_axis = (Scalar(1)-c) * m_axis; Scalar tmp; tmp = cos1_axis.x() * m_axis.y(); res.coeffRef(0,1) = tmp - sin_axis.z(); res.coeffRef(1,0) = tmp + sin_axis.z(); tmp = cos1_axis.x() * m_axis.z(); res.coeffRef(0,2) = tmp + sin_axis.y(); res.coeffRef(2,0) = tmp - sin_axis.y(); tmp = cos1_axis.y() * m_axis.z(); res.coeffRef(1,2) = tmp - sin_axis.x(); res.coeffRef(2,1) = tmp + sin_axis.x(); res.diagonal() = (cos1_axis.cwise() * m_axis).cwise() + c; return res; } } // end namespace Eigen