Public Types | Static Public Attributes | Private Types | Private Member Functions | Static Private Member Functions | Friends | List of all members
Eigen::EulerSystem< _AlphaAxis, _BetaAxis, _GammaAxis > Class Template Reference

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 Types

enum  { I = AlphaAxisAbs - 1, J = (AlphaAxisAbs - 1 + 1 + IsOdd)%3, K = (AlphaAxisAbs - 1 + 2 - IsOdd)%3 }
 

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<bool PositiveRangeAlpha, bool PositiveRangeBeta, bool PositiveRangeGamma, typename Scalar >
static void CalcEulerAngles (EulerAngles< Scalar, EulerSystem > &res, const typename EulerAngles< Scalar, EulerSystem >::Matrix3 &mat)
 
template<typename Scalar >
static void CalcEulerAngles (EulerAngles< Scalar, EulerSystem > &res, const typename EulerAngles< Scalar, EulerSystem >::Matrix3 &mat, bool PositiveRangeAlpha, bool PositiveRangeBeta, bool PositiveRangeGamma)
 
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)
 

Friends

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

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:

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:

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

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:

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
_AlphaAxisthe first fixed EulerAxis
_AlphaAxisthe second fixed EulerAxis
_AlphaAxisthe third fixed EulerAxis

Definition at line 120 of file EulerSystem.h.

Member Enumeration Documentation

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 

weather alpha axis is negative

IsBetaOpposite 

weather beta axis is negative

IsGammaOpposite 

weather gamma axis is negative

IsOdd 

weather the Euler system is odd

IsEven 

weather the Euler system is even

IsTaitBryan 

weather the Euler system is tait bryan

Definition at line 135 of file EulerSystem.h.

template<int _AlphaAxis, int _BetaAxis, int _GammaAxis>
anonymous enum
private
Enumerator

Definition at line 168 of file EulerSystem.h.

Member Function Documentation

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 251 of file EulerSystem.h.

template<int _AlphaAxis, int _BetaAxis, int _GammaAxis>
template<bool PositiveRangeAlpha, bool PositiveRangeBeta, bool PositiveRangeGamma, 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 263 of file EulerSystem.h.

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,
bool  PositiveRangeAlpha,
bool  PositiveRangeBeta,
bool  PositiveRangeGamma 
)
inlinestaticprivate

Definition at line 271 of file EulerSystem.h.

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 180 of file EulerSystem.h.

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 208 of file EulerSystem.h.

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
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
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
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
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

template<int _AlphaAxis, int _BetaAxis, int _GammaAxis>
template<typename _Scalar , class _System >
friend class Eigen::EulerAngles
friend

Definition at line 303 of file EulerSystem.h.

Member Data Documentation

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

The first rotation axis

Definition at line 127 of file EulerSystem.h.

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

The second rotation axis

Definition at line 130 of file EulerSystem.h.

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

The third rotation axis

Definition at line 133 of file EulerSystem.h.


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


gtsam
Author(s):
autogenerated on Sat May 8 2021 02:52:35