Represents a fixed Euler rotation system. More...

#include <EulerSystem.h>

Public Types
enum	{ AlphaAxisAbs = internal::Abs<AlphaAxis>::value, BetaAxisAbs = internal::Abs<BetaAxis>::value, GammaAxisAbs = internal::Abs<GammaAxis>::value, IsAlphaOpposite = (AlphaAxis < 0) ? 1 : 0, IsBetaOpposite = (BetaAxis < 0) ? 1 : 0, IsGammaOpposite = (GammaAxis < 0) ? 1 : 0, IsOdd = ((AlphaAxisAbs)%3 == (BetaAxisAbs - 1)%3) ? 0 : 1, IsEven = IsOdd ? 0 : 1, IsTaitBryan = ((unsigned)AlphaAxisAbs != (unsigned)GammaAxisAbs) ? 1 : 0 }

Static Public Attributes
static const int	AlphaAxis = _AlphaAxis

static const int	BetaAxis = _BetaAxis

static const int	GammaAxis = _GammaAxis

Private Member Functions
	EIGEN_EULER_ANGLES_CLASS_STATIC_ASSERT (internal::IsValidAxis< AlphaAxis >::value, ALPHA_AXIS_IS_INVALID)

	EIGEN_EULER_ANGLES_CLASS_STATIC_ASSERT (internal::IsValidAxis< BetaAxis >::value, BETA_AXIS_IS_INVALID)

	EIGEN_EULER_ANGLES_CLASS_STATIC_ASSERT (internal::IsValidAxis< GammaAxis >::value, GAMMA_AXIS_IS_INVALID)

	EIGEN_EULER_ANGLES_CLASS_STATIC_ASSERT ((unsigned) AlphaAxisAbs !=(unsigned) BetaAxisAbs, ALPHA_AXIS_CANT_BE_EQUAL_TO_BETA_AXIS)

	EIGEN_EULER_ANGLES_CLASS_STATIC_ASSERT ((unsigned) BetaAxisAbs !=(unsigned) GammaAxisAbs, BETA_AXIS_CANT_BE_EQUAL_TO_GAMMA_AXIS)

Static Private Member Functions
template<typename Scalar >
static void	CalcEulerAngles (EulerAngles< Scalar, EulerSystem > &res, const typename EulerAngles< Scalar, EulerSystem >::Matrix3 &mat)

template<typename Derived >
static void	CalcEulerAngles_imp (Matrix< typename MatrixBase< Derived >::Scalar, 3, 1 > &res, const MatrixBase< Derived > &mat, internal::true_type)

template<typename Derived >
static void	CalcEulerAngles_imp (Matrix< typename MatrixBase< Derived >::Scalar, 3, 1 > &res, const MatrixBase< Derived > &mat, internal::false_type)

Static Private Attributes
static const int	I_ = AlphaAxisAbs - 1

static const int	J_ = (AlphaAxisAbs - 1 + 1 + IsOdd)%3

static const int	K_ = (AlphaAxisAbs - 1 + 2 - IsOdd)%3

Friends
template<typename _Scalar , class _System >
class	Eigen::EulerAngles

template<typename System , typename Other , int OtherRows, int OtherCols>
struct	internal::eulerangles_assign_impl

Detailed Description

template<int _AlphaAxis, int _BetaAxis, int _GammaAxis>
class Eigen::EulerSystem< _AlphaAxis, _BetaAxis, _GammaAxis >

Represents a fixed Euler rotation system.

This meta-class goal is to represent the Euler system in compilation time, for EulerAngles.

You can use this class to get two things:

Build an Euler system, and then pass it as a template parameter to EulerAngles.
Query some compile time data about an Euler system. (e.g. Whether it's Tait-Bryan)

Euler rotation is a set of three rotation on fixed axes. (see EulerAngles) This meta-class store constantly those signed axes. (see EulerAxis)

Types of Euler systems

All and only valid 3 dimension Euler rotation over standard signed axes{+X,+Y,+Z,-X,-Y,-Z} are supported:

all axes X, Y, Z in each valid order (see below what order is valid)
rotation over the axis is supported both over the positive and negative directions.
both Tait-Bryan and proper/classic Euler angles (i.e. the opposite).

Since EulerSystem support both positive and negative directions, you may call this rotation distinction in other names:

right handed or left handed
counterclockwise or clockwise

Notice all axed combination are valid, and would trigger a static assertion. Same unsigned axes can't be neighbors, e.g. {X,X,Y} is invalid. This yield two and only two classes:

Tait-Bryan - all unsigned axes are distinct, e.g. {X,Y,Z}
proper/classic Euler angles - The first and the third unsigned axes is equal, and the second is different, e.g. {X,Y,X}

Intrinsic vs extrinsic Euler systems

Only intrinsic Euler systems are supported for simplicity. If you want to use extrinsic Euler systems, just use the equal intrinsic opposite order for axes and angles. I.e axes (A,B,C) becomes (C,B,A), and angles (a,b,c) becomes (c,b,a).

Convenient user typedefs

Convenient typedefs for EulerSystem exist (only for positive axes Euler systems), in a form of EulerSystem{A}{B}{C}, e.g. EulerSystemXYZ.

Additional reading

More information about Euler angles: https://en.wikipedia.org/wiki/Euler_angles

Template Parameters

_AlphaAxis	the first fixed EulerAxis
_BetaAxis	the second fixed EulerAxis
_GammaAxis	the third fixed EulerAxis

Definition at line 126 of file EulerSystem.h.

Member Enumeration Documentation

◆ anonymous enum

template<int _AlphaAxis, int _BetaAxis, int _GammaAxis>

anonymous enum

Enumerator
AlphaAxisAbs	the first rotation axis unsigned
BetaAxisAbs	the second rotation axis unsigned
GammaAxisAbs	the third rotation axis unsigned
IsAlphaOpposite	whether alpha axis is negative
IsBetaOpposite	whether beta axis is negative
IsGammaOpposite	whether gamma axis is negative
IsOdd	whether the Euler system is odd
IsEven	whether the Euler system is even
IsTaitBryan	whether the Euler system is Tait-Bryan

Definition at line 141 of file EulerSystem.h.

Member Function Documentation

◆ CalcEulerAngles()

template<int _AlphaAxis, int _BetaAxis, int _GammaAxis>

template<typename Scalar >

static void Eigen::EulerSystem< _AlphaAxis, _BetaAxis, _GammaAxis >::CalcEulerAngles	(	EulerAngles< Scalar, EulerSystem< _AlphaAxis, _BetaAxis, _GammaAxis > > &	res,
		const typename EulerAngles< Scalar, EulerSystem< _AlphaAxis, _BetaAxis, _GammaAxis > >::Matrix3 &	mat
	)

inlinestaticprivate

Definition at line 257 of file EulerSystem.h.

◆ CalcEulerAngles_imp() [1/2]

template<int _AlphaAxis, int _BetaAxis, int _GammaAxis>

template<typename Derived >

static void Eigen::EulerSystem< _AlphaAxis, _BetaAxis, _GammaAxis >::CalcEulerAngles_imp	(	Matrix< typename MatrixBase< Derived >::Scalar, 3, 1 > &	res,
		const MatrixBase< Derived > &	mat,
		internal::true_type
	)

inlinestaticprivate

Definition at line 187 of file EulerSystem.h.

◆ CalcEulerAngles_imp() [2/2]

template<int _AlphaAxis, int _BetaAxis, int _GammaAxis>

template<typename Derived >

static void Eigen::EulerSystem< _AlphaAxis, _BetaAxis, _GammaAxis >::CalcEulerAngles_imp	(	Matrix< typename MatrixBase< Derived >::Scalar, 3, 1 > &	res,
		const MatrixBase< Derived > &	mat,
		internal::false_type
	)

inlinestaticprivate

Definition at line 222 of file EulerSystem.h.

◆ EIGEN_EULER_ANGLES_CLASS_STATIC_ASSERT() [1/5]

template<int _AlphaAxis, int _BetaAxis, int _GammaAxis>

Eigen::EulerSystem< _AlphaAxis, _BetaAxis, _GammaAxis >::EIGEN_EULER_ANGLES_CLASS_STATIC_ASSERT	(	internal::IsValidAxis< AlphaAxis >::value	,
		ALPHA_AXIS_IS_INVALID
	)

private

◆ EIGEN_EULER_ANGLES_CLASS_STATIC_ASSERT() [2/5]

template<int _AlphaAxis, int _BetaAxis, int _GammaAxis>

Eigen::EulerSystem< _AlphaAxis, _BetaAxis, _GammaAxis >::EIGEN_EULER_ANGLES_CLASS_STATIC_ASSERT	(	internal::IsValidAxis< BetaAxis >::value	,
		BETA_AXIS_IS_INVALID
	)

private

◆ EIGEN_EULER_ANGLES_CLASS_STATIC_ASSERT() [3/5]

template<int _AlphaAxis, int _BetaAxis, int _GammaAxis>

Eigen::EulerSystem< _AlphaAxis, _BetaAxis, _GammaAxis >::EIGEN_EULER_ANGLES_CLASS_STATIC_ASSERT	(	internal::IsValidAxis< GammaAxis >::value	,
		GAMMA_AXIS_IS_INVALID
	)

private

◆ EIGEN_EULER_ANGLES_CLASS_STATIC_ASSERT() [4/5]

template<int _AlphaAxis, int _BetaAxis, int _GammaAxis>

Eigen::EulerSystem< _AlphaAxis, _BetaAxis, _GammaAxis >::EIGEN_EULER_ANGLES_CLASS_STATIC_ASSERT	(	(unsigned) AlphaAxisAbs !	= `(unsigned) BetaAxisAbs`,
		ALPHA_AXIS_CANT_BE_EQUAL_TO_BETA_AXIS
	)

private

◆ EIGEN_EULER_ANGLES_CLASS_STATIC_ASSERT() [5/5]

template<int _AlphaAxis, int _BetaAxis, int _GammaAxis>

Eigen::EulerSystem< _AlphaAxis, _BetaAxis, _GammaAxis >::EIGEN_EULER_ANGLES_CLASS_STATIC_ASSERT	(	(unsigned) BetaAxisAbs !	= `(unsigned) GammaAxisAbs`,
		BETA_AXIS_CANT_BE_EQUAL_TO_GAMMA_AXIS
	)

private

Friends And Related Function Documentation

◆ Eigen::EulerAngles

template<int _AlphaAxis, int _BetaAxis, int _GammaAxis>

template<typename _Scalar , class _System >

friend class Eigen::EulerAngles

friend

Definition at line 276 of file EulerSystem.h.

◆ internal::eulerangles_assign_impl

template<int _AlphaAxis, int _BetaAxis, int _GammaAxis>

template<typename System , typename Other , int OtherRows, int OtherCols>

friend struct internal::eulerangles_assign_impl

friend

Definition at line 282 of file EulerSystem.h.

Member Data Documentation

◆ AlphaAxis

template<int _AlphaAxis, int _BetaAxis, int _GammaAxis>

const int Eigen::EulerSystem< _AlphaAxis, _BetaAxis, _GammaAxis >::AlphaAxis = _AlphaAxis

static

The first rotation axis

Definition at line 133 of file EulerSystem.h.

◆ BetaAxis

template<int _AlphaAxis, int _BetaAxis, int _GammaAxis>

const int Eigen::EulerSystem< _AlphaAxis, _BetaAxis, _GammaAxis >::BetaAxis = _BetaAxis

static

The second rotation axis

Definition at line 136 of file EulerSystem.h.

◆ GammaAxis

template<int _AlphaAxis, int _BetaAxis, int _GammaAxis>

const int Eigen::EulerSystem< _AlphaAxis, _BetaAxis, _GammaAxis >::GammaAxis = _GammaAxis

static

The third rotation axis

Definition at line 139 of file EulerSystem.h.

◆ I_

template<int _AlphaAxis, int _BetaAxis, int _GammaAxis>

const int Eigen::EulerSystem< _AlphaAxis, _BetaAxis, _GammaAxis >::I_ = AlphaAxisAbs - 1

staticprivate

Definition at line 180 of file EulerSystem.h.

◆ J_

template<int _AlphaAxis, int _BetaAxis, int _GammaAxis>

const int Eigen::EulerSystem< _AlphaAxis, _BetaAxis, _GammaAxis >::J_ = (AlphaAxisAbs - 1 + 1 + IsOdd)%3

staticprivate

Definition at line 181 of file EulerSystem.h.

◆ K_

template<int _AlphaAxis, int _BetaAxis, int _GammaAxis>

const int Eigen::EulerSystem< _AlphaAxis, _BetaAxis, _GammaAxis >::K_ = (AlphaAxisAbs - 1 + 2 - IsOdd)%3

staticprivate

Definition at line 182 of file EulerSystem.h.

The documentation for this class was generated from the following file:

EulerSystem.h

Public Types

Static Public Attributes

Private Member Functions

Static Private Member Functions

Static Private Attributes

Friends

Detailed Description

template<int _AlphaAxis, int _BetaAxis, int _GammaAxis> class Eigen::EulerSystem< _AlphaAxis, _BetaAxis, _GammaAxis >

Types of Euler systems

Intrinsic vs extrinsic Euler systems

Convenient user typedefs

Additional reading

Member Enumeration Documentation

◆ anonymous enum

Member Function Documentation

◆ CalcEulerAngles()

◆ CalcEulerAngles_imp() [1/2]

◆ CalcEulerAngles_imp() [2/2]

◆ EIGEN_EULER_ANGLES_CLASS_STATIC_ASSERT() [1/5]

◆ EIGEN_EULER_ANGLES_CLASS_STATIC_ASSERT() [2/5]

◆ EIGEN_EULER_ANGLES_CLASS_STATIC_ASSERT() [3/5]

◆ EIGEN_EULER_ANGLES_CLASS_STATIC_ASSERT() [4/5]

◆ EIGEN_EULER_ANGLES_CLASS_STATIC_ASSERT() [5/5]

Friends And Related Function Documentation

◆ Eigen::EulerAngles

◆ internal::eulerangles_assign_impl

Member Data Documentation

◆ AlphaAxis

◆ BetaAxis

◆ GammaAxis

◆ I_

◆ J_

◆ K_

template<int _AlphaAxis, int _BetaAxis, int _GammaAxis>
class Eigen::EulerSystem< _AlphaAxis, _BetaAxis, _GammaAxis >