// 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
{
/*template<typename Other,
int OtherRows=Other::RowsAtCompileTime,
int OtherCols=Other::ColsAtCompileTime>
struct ei_eulerangles_assign_impl;*/
/** \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 singular 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 ####
*
* When converting some rotation to Euler angles, there are some ways you can guarantee
* the Euler angles ranges.
*
* #### implicit ranges ####
* When using implicit ranges, all angles are guarantee to be in the range [-PI, +PI],
* unless you convert from some other Euler angles.
* In this case, the range is __undefined__ (might be even less than -PI or greater than +2*PI).
* \sa EulerAngles(const MatrixBase<Derived>&)
* \sa EulerAngles(const RotationBase<Derived, 3>&)
*
* #### explicit ranges ####
* When using explicit ranges, all angles are guarantee to be in the range you choose.
* In the range Boolean parameter, you're been ask whether you prefer the positive range or not:
* - _true_ - force the range between [0, +2*PI]
* - _false_ - force the range between [-PI, +PI]
*
* ##### compile time ranges #####
* This is when you have compile time ranges and you prefer to
* use template parameter. (e.g. for performance)
* \sa FromRotation()
*
* ##### run-time time ranges #####
* Run-time ranges are also supported.
* \sa EulerAngles(const MatrixBase<Derived>&, bool, bool, bool)
* \sa EulerAngles(const RotationBase<Derived, 3>&, bool, bool, bool)
*
* ### 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:
/** the scalar type of the angles */
typedef _Scalar Scalar;
/** 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 Euler angles(\p alpha, \p beta, \p gamma). */
EulerAngles(const Scalar& alpha, const Scalar& beta, const Scalar& gamma) :
m_angles(alpha, beta, gamma) {}
/** Constructs and initialize Euler angles from a 3x3 rotation matrix \p m.
*
* \note All angles will be in the range [-PI, PI].
*/
template<typename Derived>
EulerAngles(const MatrixBase<Derived>& m) { *this = m; }
/** Constructs and initialize Euler angles from a 3x3 rotation matrix \p m,
* with options to choose for each angle the requested range.
*
* If positive range is true, then the specified angle will be in the range [0, +2*PI].
* Otherwise, the specified angle will be in the range [-PI, +PI].
*
* \param m The 3x3 rotation matrix to convert
* \param positiveRangeAlpha If true, alpha will be in [0, 2*PI]. Otherwise, in [-PI, +PI].
* \param positiveRangeBeta If true, beta will be in [0, 2*PI]. Otherwise, in [-PI, +PI].
* \param positiveRangeGamma If true, gamma will be in [0, 2*PI]. Otherwise, in [-PI, +PI].
*/
template<typename Derived>
EulerAngles(
const MatrixBase<Derived>& m,
bool positiveRangeAlpha,
bool positiveRangeBeta,
bool positiveRangeGamma) {
System::CalcEulerAngles(*this, m, positiveRangeAlpha, positiveRangeBeta, positiveRangeGamma);
}
/** Constructs and initialize Euler angles from a rotation \p rot.
*
* \note All angles will be in the range [-PI, PI], unless \p rot is an EulerAngles.
* If rot is an EulerAngles, expected EulerAngles range is __undefined__.
* (Use other functions here for enforcing range if this effect is desired)
*/
template<typename Derived>
EulerAngles(const RotationBase<Derived, 3>& rot) { *this = rot; }
/** Constructs and initialize Euler angles from a rotation \p rot,
* with options to choose for each angle the requested range.
*
* If positive range is true, then the specified angle will be in the range [0, +2*PI].
* Otherwise, the specified angle will be in the range [-PI, +PI].
*
* \param rot The 3x3 rotation matrix to convert
* \param positiveRangeAlpha If true, alpha will be in [0, 2*PI]. Otherwise, in [-PI, +PI].
* \param positiveRangeBeta If true, beta will be in [0, 2*PI]. Otherwise, in [-PI, +PI].
* \param positiveRangeGamma If true, gamma will be in [0, 2*PI]. Otherwise, in [-PI, +PI].
*/
template<typename Derived>
EulerAngles(
const RotationBase<Derived, 3>& rot,
bool positiveRangeAlpha,
bool positiveRangeBeta,
bool positiveRangeGamma) {
System::CalcEulerAngles(*this, rot.toRotationMatrix(), positiveRangeAlpha, positiveRangeBeta, positiveRangeGamma);
}
/** \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();
}
/** Constructs and initialize Euler angles from a 3x3 rotation matrix \p m,
* with options to choose for each angle the requested range (__only in compile time__).
*
* If positive range is true, then the specified angle will be in the range [0, +2*PI].
* Otherwise, the specified angle will be in the range [-PI, +PI].
*
* \param m The 3x3 rotation matrix to convert
* \tparam positiveRangeAlpha If true, alpha will be in [0, 2*PI]. Otherwise, in [-PI, +PI].
* \tparam positiveRangeBeta If true, beta will be in [0, 2*PI]. Otherwise, in [-PI, +PI].
* \tparam positiveRangeGamma If true, gamma will be in [0, 2*PI]. Otherwise, in [-PI, +PI].
*/
template<
bool PositiveRangeAlpha,
bool PositiveRangeBeta,
bool PositiveRangeGamma,
typename Derived>
static EulerAngles FromRotation(const MatrixBase<Derived>& m)
{
EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(Derived, 3, 3)
EulerAngles e;
System::template CalcEulerAngles<
PositiveRangeAlpha, PositiveRangeBeta, PositiveRangeGamma, _Scalar>(e, m);
return e;
}
/** Constructs and initialize Euler angles from a rotation \p rot,
* with options to choose for each angle the requested range (__only in compile time__).
*
* If positive range is true, then the specified angle will be in the range [0, +2*PI].
* Otherwise, the specified angle will be in the range [-PI, +PI].
*
* \param rot The 3x3 rotation matrix to convert
* \tparam positiveRangeAlpha If true, alpha will be in [0, 2*PI]. Otherwise, in [-PI, +PI].
* \tparam positiveRangeBeta If true, beta will be in [0, 2*PI]. Otherwise, in [-PI, +PI].
* \tparam positiveRangeGamma If true, gamma will be in [0, 2*PI]. Otherwise, in [-PI, +PI].
*/
template<
bool PositiveRangeAlpha,
bool PositiveRangeBeta,
bool PositiveRangeGamma,
typename Derived>
static EulerAngles FromRotation(const RotationBase<Derived, 3>& rot)
{
return FromRotation<PositiveRangeAlpha, PositiveRangeBeta, PositiveRangeGamma>(rot.toRotationMatrix());
}
/*EulerAngles& fromQuaternion(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)));
}*/
/** Set \c *this from a rotation matrix(i.e. pure orthogonal matrix with determinant of +1). */
template<typename Derived>
EulerAngles& operator=(const MatrixBase<Derived>& m) {
EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(Derived, 3, 3)
System::CalcEulerAngles(*this, m);
return *this;
}
// TODO: Assign and construct from another EulerAngles (with different system)
/** Set \c *this from a rotation. */
template<typename Derived>
EulerAngles& operator=(const RotationBase<Derived, 3>& rot) {
System::CalcEulerAngles(*this, rot.toRotationMatrix());
return *this;
}
// TODO: Support isApprox function
/** \returns an equivalent 3x3 rotation matrix. */
Matrix3 toRotationMatrix() const
{
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;
}
};
#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;
};
}
}
#endif // EIGEN_EULERANGLESCLASS_H