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vcglib/eigenlib/unsupported/Eigen/src/EulerAngles/EulerAngles.h
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// 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 the mozilla.org home page
#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: xxxps://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 xxxp://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,3,1>
{
typedef typename Other::Scalar Scalar;
static void run(EulerAngles<Scalar, System>& e, const Other& vec)
{
e.angles() = vec;
}
};
}
}
#endif // EIGEN_EULERANGLESCLASS_H