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Diffstat (limited to 'eigen/unsupported/Eigen/src/EulerAngles/EulerAngles.h')
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diff --git a/eigen/unsupported/Eigen/src/EulerAngles/EulerAngles.h b/eigen/unsupported/Eigen/src/EulerAngles/EulerAngles.h new file mode 100644 index 0000000..a5d034d --- /dev/null +++ b/eigen/unsupported/Eigen/src/EulerAngles/EulerAngles.h @@ -0,0 +1,355 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2015 Tal Hadad <tal_hd@hotmail.com> +// +// 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/. + +#ifndef EIGEN_EULERANGLESCLASS_H// TODO: Fix previous "EIGEN_EULERANGLES_H" definition? +#define EIGEN_EULERANGLESCLASS_H + +namespace Eigen +{ + /** \class EulerAngles + * + * \ingroup EulerAngles_Module + * + * \brief Represents a rotation in a 3 dimensional space as three Euler angles. + * + * Euler rotation is a set of three rotation of three angles over three fixed axes, defined by the EulerSystem given as a template parameter. + * + * Here is how intrinsic Euler angles works: + * - first, rotate the axes system over the alpha axis in angle alpha + * - then, rotate the axes system over the beta axis(which was rotated in the first stage) in angle beta + * - then, rotate the axes system over the gamma axis(which was rotated in the two stages above) in angle gamma + * + * \note This class support only intrinsic Euler angles for simplicity, + * see EulerSystem how to easily overcome this for extrinsic systems. + * + * ### Rotation representation and conversions ### + * + * It has been proved(see Wikipedia link below) that every rotation can be represented + * by Euler angles, but there is no single representation (e.g. unlike rotation matrices). + * Therefore, you can convert from Eigen rotation and to them + * (including rotation matrices, which is not called "rotations" by Eigen design). + * + * Euler angles usually used for: + * - convenient human representation of rotation, especially in interactive GUI. + * - gimbal systems and robotics + * - efficient encoding(i.e. 3 floats only) of rotation for network protocols. + * + * However, Euler angles are slow comparing to quaternion or matrices, + * because their unnatural math definition, although it's simple for human. + * To overcome this, this class provide easy movement from the math friendly representation + * to the human friendly representation, and vise-versa. + * + * All the user need to do is a safe simple C++ type conversion, + * and this class take care for the math. + * Additionally, some axes related computation is done in compile time. + * + * #### Euler angles ranges in conversions #### + * Rotations representation as EulerAngles are not single (unlike matrices), + * and even have infinite EulerAngles representations.<BR> + * For example, add or subtract 2*PI from either angle of EulerAngles + * and you'll get the same rotation. + * This is the general reason for infinite representation, + * but it's not the only general reason for not having a single representation. + * + * When converting rotation to EulerAngles, this class convert it to specific ranges + * When converting some rotation to EulerAngles, the rules for ranges are as follow: + * - If the rotation we converting from is an EulerAngles + * (even when it represented as RotationBase explicitly), angles ranges are __undefined__. + * - otherwise, alpha and gamma angles will be in the range [-PI, PI].<BR> + * As for Beta angle: + * - If the system is Tait-Bryan, the beta angle will be in the range [-PI/2, PI/2]. + * - otherwise: + * - If the beta axis is positive, the beta angle will be in the range [0, PI] + * - If the beta axis is negative, the beta angle will be in the range [-PI, 0] + * + * \sa EulerAngles(const MatrixBase<Derived>&) + * \sa EulerAngles(const RotationBase<Derived, 3>&) + * + * ### Convenient user typedefs ### + * + * Convenient typedefs for EulerAngles exist for float and double scalar, + * in a form of EulerAngles{A}{B}{C}{scalar}, + * e.g. \ref EulerAnglesXYZd, \ref EulerAnglesZYZf. + * + * Only for positive axes{+x,+y,+z} Euler systems are have convenient typedef. + * If you need negative axes{-x,-y,-z}, it is recommended to create you own typedef with + * a word that represent what you need. + * + * ### Example ### + * + * \include EulerAngles.cpp + * Output: \verbinclude EulerAngles.out + * + * ### Additional reading ### + * + * If you're want to get more idea about how Euler system work in Eigen see EulerSystem. + * + * More information about Euler angles: https://en.wikipedia.org/wiki/Euler_angles + * + * \tparam _Scalar the scalar type, i.e. the type of the angles. + * + * \tparam _System the EulerSystem to use, which represents the axes of rotation. + */ + template <typename _Scalar, class _System> + class EulerAngles : public RotationBase<EulerAngles<_Scalar, _System>, 3> + { + public: + typedef RotationBase<EulerAngles<_Scalar, _System>, 3> Base; + + /** the scalar type of the angles */ + typedef _Scalar Scalar; + typedef typename NumTraits<Scalar>::Real RealScalar; + + /** the EulerSystem to use, which represents the axes of rotation. */ + typedef _System System; + + typedef Matrix<Scalar,3,3> Matrix3; /*!< the equivalent rotation matrix type */ + typedef Matrix<Scalar,3,1> Vector3; /*!< the equivalent 3 dimension vector type */ + typedef Quaternion<Scalar> QuaternionType; /*!< the equivalent quaternion type */ + typedef AngleAxis<Scalar> AngleAxisType; /*!< the equivalent angle-axis type */ + + /** \returns the axis vector of the first (alpha) rotation */ + static Vector3 AlphaAxisVector() { + const Vector3& u = Vector3::Unit(System::AlphaAxisAbs - 1); + return System::IsAlphaOpposite ? -u : u; + } + + /** \returns the axis vector of the second (beta) rotation */ + static Vector3 BetaAxisVector() { + const Vector3& u = Vector3::Unit(System::BetaAxisAbs - 1); + return System::IsBetaOpposite ? -u : u; + } + + /** \returns the axis vector of the third (gamma) rotation */ + static Vector3 GammaAxisVector() { + const Vector3& u = Vector3::Unit(System::GammaAxisAbs - 1); + return System::IsGammaOpposite ? -u : u; + } + + private: + Vector3 m_angles; + + public: + /** Default constructor without initialization. */ + EulerAngles() {} + /** Constructs and initialize an EulerAngles (\p alpha, \p beta, \p gamma). */ + EulerAngles(const Scalar& alpha, const Scalar& beta, const Scalar& gamma) : + m_angles(alpha, beta, gamma) {} + + // TODO: Test this constructor + /** Constructs and initialize an EulerAngles from the array data {alpha, beta, gamma} */ + explicit EulerAngles(const Scalar* data) : m_angles(data) {} + + /** Constructs and initializes an EulerAngles from either: + * - a 3x3 rotation matrix expression(i.e. pure orthogonal matrix with determinant of +1), + * - a 3D vector expression representing Euler angles. + * + * \note If \p other is a 3x3 rotation matrix, the angles range rules will be as follow:<BR> + * Alpha and gamma angles will be in the range [-PI, PI].<BR> + * As for Beta angle: + * - If the system is Tait-Bryan, the beta angle will be in the range [-PI/2, PI/2]. + * - otherwise: + * - If the beta axis is positive, the beta angle will be in the range [0, PI] + * - If the beta axis is negative, the beta angle will be in the range [-PI, 0] + */ + template<typename Derived> + explicit EulerAngles(const MatrixBase<Derived>& other) { *this = other; } + + /** Constructs and initialize Euler angles from a rotation \p rot. + * + * \note If \p rot is an EulerAngles (even when it represented as RotationBase explicitly), + * angles ranges are __undefined__. + * Otherwise, alpha and gamma angles will be in the range [-PI, PI].<BR> + * As for Beta angle: + * - If the system is Tait-Bryan, the beta angle will be in the range [-PI/2, PI/2]. + * - otherwise: + * - If the beta axis is positive, the beta angle will be in the range [0, PI] + * - If the beta axis is negative, the beta angle will be in the range [-PI, 0] + */ + template<typename Derived> + EulerAngles(const RotationBase<Derived, 3>& rot) { System::CalcEulerAngles(*this, rot.toRotationMatrix()); } + + /*EulerAngles(const QuaternionType& q) + { + // TODO: Implement it in a faster way for quaternions + // According to http://www.euclideanspace.com/maths/geometry/rotations/conversions/quaternionToEuler/ + // we can compute only the needed matrix cells and then convert to euler angles. (see ZYX example below) + // Currently we compute all matrix cells from quaternion. + + // Special case only for ZYX + //Scalar y2 = q.y() * q.y(); + //m_angles[0] = std::atan2(2*(q.w()*q.z() + q.x()*q.y()), (1 - 2*(y2 + q.z()*q.z()))); + //m_angles[1] = std::asin( 2*(q.w()*q.y() - q.z()*q.x())); + //m_angles[2] = std::atan2(2*(q.w()*q.x() + q.y()*q.z()), (1 - 2*(q.x()*q.x() + y2))); + }*/ + + /** \returns The angle values stored in a vector (alpha, beta, gamma). */ + const Vector3& angles() const { return m_angles; } + /** \returns A read-write reference to the angle values stored in a vector (alpha, beta, gamma). */ + Vector3& angles() { return m_angles; } + + /** \returns The value of the first angle. */ + Scalar alpha() const { return m_angles[0]; } + /** \returns A read-write reference to the angle of the first angle. */ + Scalar& alpha() { return m_angles[0]; } + + /** \returns The value of the second angle. */ + Scalar beta() const { return m_angles[1]; } + /** \returns A read-write reference to the angle of the second angle. */ + Scalar& beta() { return m_angles[1]; } + + /** \returns The value of the third angle. */ + Scalar gamma() const { return m_angles[2]; } + /** \returns A read-write reference to the angle of the third angle. */ + Scalar& gamma() { return m_angles[2]; } + + /** \returns The Euler angles rotation inverse (which is as same as the negative), + * (-alpha, -beta, -gamma). + */ + EulerAngles inverse() const + { + EulerAngles res; + res.m_angles = -m_angles; + return res; + } + + /** \returns The Euler angles rotation negative (which is as same as the inverse), + * (-alpha, -beta, -gamma). + */ + EulerAngles operator -() const + { + return inverse(); + } + + /** Set \c *this from either: + * - a 3x3 rotation matrix expression(i.e. pure orthogonal matrix with determinant of +1), + * - a 3D vector expression representing Euler angles. + * + * See EulerAngles(const MatrixBase<Derived, 3>&) for more information about + * angles ranges output. + */ + template<class Derived> + EulerAngles& operator=(const MatrixBase<Derived>& other) + { + EIGEN_STATIC_ASSERT((internal::is_same<Scalar, typename Derived::Scalar>::value), + YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY) + + internal::eulerangles_assign_impl<System, Derived>::run(*this, other.derived()); + return *this; + } + + // TODO: Assign and construct from another EulerAngles (with different system) + + /** Set \c *this from a rotation. + * + * See EulerAngles(const RotationBase<Derived, 3>&) for more information about + * angles ranges output. + */ + template<typename Derived> + EulerAngles& operator=(const RotationBase<Derived, 3>& rot) { + System::CalcEulerAngles(*this, rot.toRotationMatrix()); + return *this; + } + + /** \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 EulerAngles& other, + const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const + { return angles().isApprox(other.angles(), prec); } + + /** \returns an equivalent 3x3 rotation matrix. */ + Matrix3 toRotationMatrix() const + { + // TODO: Calc it faster + return static_cast<QuaternionType>(*this).toRotationMatrix(); + } + + /** Convert the Euler angles to quaternion. */ + operator QuaternionType() const + { + return + AngleAxisType(alpha(), AlphaAxisVector()) * + AngleAxisType(beta(), BetaAxisVector()) * + AngleAxisType(gamma(), GammaAxisVector()); + } + + friend std::ostream& operator<<(std::ostream& s, const EulerAngles<Scalar, System>& eulerAngles) + { + s << eulerAngles.angles().transpose(); + return s; + } + + /** \returns \c *this with scalar type casted to \a NewScalarType */ + template <typename NewScalarType> + EulerAngles<NewScalarType, System> cast() const + { + EulerAngles<NewScalarType, System> e; + e.angles() = angles().template cast<NewScalarType>(); + return e; + } + }; + +#define EIGEN_EULER_ANGLES_SINGLE_TYPEDEF(AXES, SCALAR_TYPE, SCALAR_POSTFIX) \ + /** \ingroup EulerAngles_Module */ \ + typedef EulerAngles<SCALAR_TYPE, EulerSystem##AXES> EulerAngles##AXES##SCALAR_POSTFIX; + +#define EIGEN_EULER_ANGLES_TYPEDEFS(SCALAR_TYPE, SCALAR_POSTFIX) \ + EIGEN_EULER_ANGLES_SINGLE_TYPEDEF(XYZ, SCALAR_TYPE, SCALAR_POSTFIX) \ + EIGEN_EULER_ANGLES_SINGLE_TYPEDEF(XYX, SCALAR_TYPE, SCALAR_POSTFIX) \ + EIGEN_EULER_ANGLES_SINGLE_TYPEDEF(XZY, SCALAR_TYPE, SCALAR_POSTFIX) \ + EIGEN_EULER_ANGLES_SINGLE_TYPEDEF(XZX, SCALAR_TYPE, SCALAR_POSTFIX) \ + \ + EIGEN_EULER_ANGLES_SINGLE_TYPEDEF(YZX, SCALAR_TYPE, SCALAR_POSTFIX) \ + EIGEN_EULER_ANGLES_SINGLE_TYPEDEF(YZY, SCALAR_TYPE, SCALAR_POSTFIX) \ + EIGEN_EULER_ANGLES_SINGLE_TYPEDEF(YXZ, SCALAR_TYPE, SCALAR_POSTFIX) \ + EIGEN_EULER_ANGLES_SINGLE_TYPEDEF(YXY, SCALAR_TYPE, SCALAR_POSTFIX) \ + \ + EIGEN_EULER_ANGLES_SINGLE_TYPEDEF(ZXY, SCALAR_TYPE, SCALAR_POSTFIX) \ + EIGEN_EULER_ANGLES_SINGLE_TYPEDEF(ZXZ, SCALAR_TYPE, SCALAR_POSTFIX) \ + EIGEN_EULER_ANGLES_SINGLE_TYPEDEF(ZYX, SCALAR_TYPE, SCALAR_POSTFIX) \ + EIGEN_EULER_ANGLES_SINGLE_TYPEDEF(ZYZ, SCALAR_TYPE, SCALAR_POSTFIX) + +EIGEN_EULER_ANGLES_TYPEDEFS(float, f) +EIGEN_EULER_ANGLES_TYPEDEFS(double, d) + + namespace internal + { + template<typename _Scalar, class _System> + struct traits<EulerAngles<_Scalar, _System> > + { + typedef _Scalar Scalar; + }; + + // set from a rotation matrix + template<class System, class Other> + struct eulerangles_assign_impl<System,Other,3,3> + { + typedef typename Other::Scalar Scalar; + static void run(EulerAngles<Scalar, System>& e, const Other& m) + { + System::CalcEulerAngles(e, m); + } + }; + + // set from a vector of Euler angles + template<class System, class Other> + struct eulerangles_assign_impl<System,Other,4,1> + { + typedef typename Other::Scalar Scalar; + static void run(EulerAngles<Scalar, System>& e, const Other& vec) + { + e.angles() = vec; + } + }; + } +} + +#endif // EIGEN_EULERANGLESCLASS_H |