Represents a 3D rotation as a rotation angle around an arbitrary 3D axis. More...

#include <AngleAxis.h>

Inheritance diagram for Eigen::AngleAxis< _Scalar >:

Collaboration diagram for Eigen::AngleAxis< _Scalar >:

Public Types
enum	{ Dim = 3 }

enum	{ Dim = 3 }

typedef _Scalar	Scalar

typedef Matrix< Scalar, 3, 3 >	Matrix3

typedef Matrix< Scalar, 3, 1 >	Vector3

typedef Quaternion< Scalar >	QuaternionType

typedef _Scalar	Scalar

typedef Matrix< Scalar, 3, 3 >	Matrix3

typedef Matrix< Scalar, 3, 1 >	Vector3

typedef Quaternion< Scalar >	QuaternionType

Public Types inherited from Eigen::RotationBase< AngleAxis< _Scalar >, 3 >
enum

enum

typedef ei_traits< AngleAxis< _Scalar > >::Scalar	Scalar

typedef internal::traits< AngleAxis< _Scalar > >::Scalar	Scalar

typedef Matrix< Scalar, Dim, Dim >	RotationMatrixType

typedef Matrix< Scalar, Dim, Dim >	RotationMatrixType

typedef Matrix< Scalar, Dim, 1 >	VectorType

Public Member Functions
	AngleAxis ()

template<typename Derived >
	AngleAxis (Scalar angle, const MatrixBase< Derived > &axis)

	AngleAxis (const QuaternionType &q)

template<typename Derived >
	AngleAxis (const MatrixBase< Derived > &m)

Scalar	angle () const

Scalar &	angle ()

const Vector3 &	axis () const

Vector3 &	axis ()

QuaternionType	operator* (const AngleAxis &other) const

QuaternionType	operator* (const QuaternionType &other) const

Matrix3	operator* (const Matrix3 &other) const

Vector3	operator* (const Vector3 &other) const

AngleAxis	inverse () const

AngleAxis &	operator= (const QuaternionType &q)

template<typename Derived >
AngleAxis &	operator= (const MatrixBase< Derived > &m)

template<typename Derived >
AngleAxis &	fromRotationMatrix (const MatrixBase< Derived > &m)

Matrix3	toRotationMatrix (void) const

template<typename NewScalarType >
internal::cast_return_type< AngleAxis, AngleAxis< NewScalarType > >::type	cast () const

template<typename OtherScalarType >
	AngleAxis (const AngleAxis< OtherScalarType > &other)

bool	isApprox (const AngleAxis &other, typename NumTraits< Scalar >::Real prec=precision< Scalar >()) const

	AngleAxis ()

template<typename Derived >
	AngleAxis (const Scalar &angle, const MatrixBase< Derived > &axis)

template<typename QuatDerived >
	AngleAxis (const QuaternionBase< QuatDerived > &q)

template<typename Derived >
	AngleAxis (const MatrixBase< Derived > &m)

Scalar	angle () const

Scalar &	angle ()

const Vector3 &	axis () const

Vector3 &	axis ()

QuaternionType	operator* (const AngleAxis &other) const

QuaternionType	operator* (const QuaternionType &other) const

AngleAxis	inverse () const

template<class QuatDerived >
AngleAxis &	operator= (const QuaternionBase< QuatDerived > &q)

template<typename Derived >
AngleAxis &	operator= (const MatrixBase< Derived > &m)

template<typename Derived >
AngleAxis &	fromRotationMatrix (const MatrixBase< Derived > &m)

Matrix3	toRotationMatrix (void) const

template<typename NewScalarType >
internal::cast_return_type< AngleAxis, AngleAxis< NewScalarType > >::type	cast () const

template<typename OtherScalarType >
	AngleAxis (const AngleAxis< OtherScalarType > &other)

bool	isApprox (const AngleAxis &other, const typename NumTraits< Scalar >::Real &prec=NumTraits< Scalar >::dummy_precision()) const

template<typename Derived >
AngleAxis< Scalar > &	operator= (const MatrixBase< Derived > &mat)

template<typename QuatDerived >
AngleAxis< Scalar > &	operator= (const QuaternionBase< QuatDerived > &q)

template<typename Derived >
AngleAxis< Scalar > &	fromRotationMatrix (const MatrixBase< Derived > &mat)
	Sets `*this` from a 3x3 rotation matrix.

Public Member Functions inherited from Eigen::RotationBase< AngleAxis< _Scalar >, 3 >
const AngleAxis< _Scalar > &	derived () const

AngleAxis< _Scalar > &	derived ()

const AngleAxis< _Scalar > &	derived () const

AngleAxis< _Scalar > &	derived ()

RotationMatrixType	toRotationMatrix () const

RotationMatrixType	toRotationMatrix () const

AngleAxis< _Scalar >	inverse () const

AngleAxis< _Scalar >	inverse () const

Transform< Scalar, Dim >	operator* (const Translation< Scalar, Dim > &t) const

RotationMatrixType	operator* (const Scaling< Scalar, Dim > &s) const

Transform< Scalar, Dim >	operator* (const Transform< Scalar, Dim > &t) const

Transform< Scalar, Dim, Isometry >	operator* (const Translation< Scalar, Dim > &t) const

RotationMatrixType	operator* (const UniformScaling< Scalar > &s) const

EIGEN_STRONG_INLINE internal::rotation_base_generic_product_selector< AngleAxis< _Scalar >, OtherDerived, OtherDerived::IsVectorAtCompileTime >::ReturnType	operator* (const EigenBase< OtherDerived > &e) const

Transform< Scalar, Dim, Mode >	operator* (const Transform< Scalar, Dim, Mode, Options > &t) const

RotationMatrixType	matrix () const

VectorType	_transformVector (const OtherVectorType &v) const

Static Public Member Functions
static const AngleAxis	Identity ()

Protected Attributes
Vector3	m_axis

Scalar	m_angle

Friends
QuaternionType	operator* (const QuaternionType &a, const AngleAxis &b)

Matrix3	operator* (const Matrix3 &a, const AngleAxis &b)

QuaternionType	operator* (const QuaternionType &a, const AngleAxis &b)

Detailed Description

template<typename _Scalar>
class Eigen::AngleAxis< _Scalar >

Represents a 3D rotation as a rotation angle around an arbitrary 3D axis.

Parameters

_Scalar the scalar type, i.e., the type of the coefficients.

The following two typedefs are provided for convenience:

AngleAxisf for float
AngleAxisd for double

AngleAxisForEuler How to define a rotation from Euler-angles

Combined with MatrixBase::Unit{X,Y,Z}, AngleAxis can be used to easily mimic Euler-angles. Here is an example:

Output:

Note: This class is not aimed to be used to store a rotation transformation, but rather to make easier the creation of other rotation (Quaternion, rotation Matrix) and transformation objects.

See also: class Quaternion, class Transform, MatrixBase::UnitX()

Parameters

_Scalar the scalar type, i.e., the type of the coefficients.

Warning: When setting up an AngleAxis object, the axis vector must be normalized.

The following two typedefs are provided for convenience:

AngleAxisf for float
AngleAxisd for double

Combined with MatrixBase::Unit{X,Y,Z}, AngleAxis can be used to easily mimic Euler-angles. Here is an example:

Output:

Note: This class is not aimed to be used to store a rotation transformation, but rather to make easier the creation of other rotation (Quaternion, rotation Matrix) and transformation objects.

See also: class Quaternion, class Transform, MatrixBase::UnitX()

Definition at line 235 of file ForwardDeclarations.h.

Member Typedef Documentation

template<typename _Scalar>

typedef _Scalar Eigen::AngleAxis< _Scalar >::Scalar

the scalar type of the coefficients

Definition at line 56 of file AngleAxis.h.

template<typename _Scalar>

typedef _Scalar Eigen::AngleAxis< _Scalar >::Scalar

the scalar type of the coefficients

Definition at line 59 of file AngleAxis.h.

Constructor & Destructor Documentation

template<typename _Scalar>

Eigen::AngleAxis< _Scalar >::AngleAxis ( )

inline

Default constructor without initialization.

Definition at line 69 of file AngleAxis.h.

69 {}

template<typename _Scalar>

template<typename Derived >

Eigen::AngleAxis< _Scalar >::AngleAxis	(	Scalar	angle,
		const MatrixBase< Derived > &	axis
	)

inline

Constructs and initialize the angle-axis rotation from an angle in radian and an axis which must be normalized.

Definition at line 73 of file AngleAxis.h.

73 : m_axis(axis), m_angle(angle) {}

template<typename _Scalar>

Eigen::AngleAxis< _Scalar >::AngleAxis ( const QuaternionType & q )

inline

Constructs and initialize the angle-axis rotation from a quaternion q.

Definition at line 75 of file AngleAxis.h.

75 { *this = q; }

template<typename _Scalar>

template<typename Derived >

Eigen::AngleAxis< _Scalar >::AngleAxis ( const MatrixBase< Derived > & m )

inlineexplicit

Constructs and initialize the angle-axis rotation from a 3x3 rotation matrix.

Definition at line 78 of file AngleAxis.h.

78 { *this = m; }

template<typename _Scalar>

template<typename OtherScalarType >

Eigen::AngleAxis< _Scalar >::AngleAxis ( const AngleAxis< OtherScalarType > & other )

inlineexplicit

Copy constructor with scalar type conversion

Definition at line 133 of file AngleAxis.h.

   {
     m_axis = other.axis().template cast<Scalar>();
     m_angle = Scalar(other.angle());
   }

template<typename _Scalar>

Eigen::AngleAxis< _Scalar >::AngleAxis ( )

inline

Default constructor without initialization.

Definition at line 72 of file AngleAxis.h.

72 {}

template<typename _Scalar>

template<typename Derived >

Eigen::AngleAxis< _Scalar >::AngleAxis	(	const Scalar &	angle,
		const MatrixBase< Derived > &	axis
	)

inline

Constructs and initialize the angle-axis rotation from an angle in radian and an axis which must be normalized.

Warning: If the axis vector is not normalized, then the angle-axis object represents an invalid rotation.

Definition at line 79 of file AngleAxis.h.

79 : m_axis(axis), m_angle(angle) {}

template<typename _Scalar>

template<typename QuatDerived >

Eigen::AngleAxis< _Scalar >::AngleAxis ( const QuaternionBase< QuatDerived > & q )

inlineexplicit

Constructs and initialize the angle-axis rotation from a quaternion q.

Definition at line 81 of file AngleAxis.h.

81 { *this = q; }

template<typename _Scalar>

template<typename Derived >

Eigen::AngleAxis< _Scalar >::AngleAxis ( const MatrixBase< Derived > & m )

inlineexplicit

Constructs and initialize the angle-axis rotation from a 3x3 rotation matrix.

Definition at line 84 of file AngleAxis.h.

84 { *this = m; }

template<typename _Scalar>

template<typename OtherScalarType >

Eigen::AngleAxis< _Scalar >::AngleAxis ( const AngleAxis< OtherScalarType > & other )

inlineexplicit

Copy constructor with scalar type conversion

Definition at line 128 of file AngleAxis.h.

   {
     m_axis = other.axis().template cast<Scalar>();
     m_angle = Scalar(other.angle());
   }

Member Function Documentation

template<typename _Scalar>

template<typename NewScalarType >

internal::cast_return_type<AngleAxis,AngleAxis<NewScalarType> >::type Eigen::AngleAxis< _Scalar >::cast ( ) const

inline

Returns: *this with scalar type casted to NewScalarType

Note that if NewScalarType is equal to the current scalar type of *this then this function smartly returns a const reference to *this.

Definition at line 123 of file AngleAxis.h.

124 { return typename internal::cast_return_type<AngleAxis,AngleAxis<NewScalarType> >::type(*this); }

template<typename _Scalar>

template<typename NewScalarType >

internal::cast_return_type<AngleAxis,AngleAxis<NewScalarType> >::type Eigen::AngleAxis< _Scalar >::cast ( ) const

inline

Returns: *this with scalar type casted to NewScalarType

Note that if NewScalarType is equal to the current scalar type of *this then this function smartly returns a const reference to *this.

Definition at line 128 of file AngleAxis.h.

129 { return typename internal::cast_return_type<AngleAxis,AngleAxis<NewScalarType> >::type(*this); }

template<typename _Scalar>

AngleAxis Eigen::AngleAxis< _Scalar >::inverse ( void ) const

inline

Returns: the inverse rotation, i.e., an angle-axis with opposite rotation angle

Definition at line 105 of file AngleAxis.h.

106 { return AngleAxis(-m_angle, m_axis); }

Eigen::AngleAxis::AngleAxis

AngleAxis()

Definition: AngleAxis.h:69

template<typename _Scalar>

AngleAxis Eigen::AngleAxis< _Scalar >::inverse ( ) const

inline

Returns: the inverse rotation, i.e., an angle-axis with opposite rotation angle

Definition at line 111 of file AngleAxis.h.

112 { return AngleAxis(-m_angle, m_axis); }

Eigen::AngleAxis::AngleAxis

AngleAxis()

Definition: AngleAxis.h:69

template<typename _Scalar>

bool Eigen::AngleAxis< _Scalar >::isApprox	(	const AngleAxis< _Scalar > &	other,
		const typename NumTraits< Scalar >::Real &	prec = `NumTraits<Scalar>::dummy_precision()`
	)		const

inline

Returns: true if *this is approximately equal to other, within the precision determined by prec.

See also: MatrixBase::isApprox()

Definition at line 140 of file AngleAxis.h.

141 { return m_axis.isApprox(other.m_axis, prec) && internal::isApprox(m_angle,other.m_angle, prec); }

template<typename _Scalar>

bool Eigen::AngleAxis< _Scalar >::isApprox	(	const AngleAxis< _Scalar > &	other,
		typename NumTraits< Scalar >::Real	prec = `precision<Scalar>()`
	)		const

inline

Returns: true if *this is approximately equal to other, within the precision determined by prec.

See also: MatrixBase::isApprox()

Definition at line 143 of file AngleAxis.h.

144 { return m_axis.isApprox(other.m_axis, prec) && ei_isApprox(m_angle,other.m_angle, prec); }

template<typename _Scalar>

QuaternionType Eigen::AngleAxis< _Scalar >::operator* ( const AngleAxis< _Scalar > & other ) const

inline

Concatenates two rotations

Definition at line 87 of file AngleAxis.h.

88 { return QuaternionType(*this) * QuaternionType(other); }

template<typename _Scalar>

QuaternionType Eigen::AngleAxis< _Scalar >::operator* ( const QuaternionType & other ) const

inline

Concatenates two rotations

Definition at line 91 of file AngleAxis.h.

92 { return QuaternionType(*this) * other; }

template<typename _Scalar>

QuaternionType Eigen::AngleAxis< _Scalar >::operator* ( const AngleAxis< _Scalar > & other ) const

inline

Concatenates two rotations

Definition at line 93 of file AngleAxis.h.

94 { return QuaternionType(*this) * QuaternionType(other); }

template<typename _Scalar>

QuaternionType Eigen::AngleAxis< _Scalar >::operator* ( const QuaternionType & other ) const

inline

Concatenates two rotations

Definition at line 97 of file AngleAxis.h.

98 { return QuaternionType(*this) * other; }

template<typename _Scalar>

Matrix3 Eigen::AngleAxis< _Scalar >::operator* ( const Matrix3 & other ) const

inline

Concatenates two rotations

Definition at line 99 of file AngleAxis.h.

100 { return toRotationMatrix() * other; }

Eigen::AngleAxis::toRotationMatrix

Matrix3 toRotationMatrix(void) const

Definition: AngleAxis.h:189

template<typename _Scalar>

Vector3 Eigen::AngleAxis< _Scalar >::operator* ( const Vector3 & other ) const

inline

Applies rotation to vector

Definition at line 107 of file AngleAxis.h.

108 { return toRotationMatrix() * other; }

Eigen::AngleAxis::toRotationMatrix

Matrix3 toRotationMatrix(void) const

Definition: AngleAxis.h:189

template<typename Scalar >

AngleAxis< Scalar > & Eigen::AngleAxis< Scalar >::operator= ( const QuaternionType & q )

Set *this from a quaternion. The axis is normalized.

Definition at line 158 of file AngleAxis.h.

 {
   Scalar n2 = q.vec().squaredNorm();
   if (n2 < precision<Scalar>()*precision<Scalar>())
   {
     m_angle = 0;
     m_axis << 1, 0, 0;
   }
   else
   {
     m_angle = 2*std::acos(q.w());
     m_axis = q.vec() / ei_sqrt(n2);
   }
   return *this;
 }

template<typename _Scalar>

template<typename QuatDerived >

AngleAxis<Scalar>& Eigen::AngleAxis< _Scalar >::operator= ( const QuaternionBase< QuatDerived > & q )

Set *this from a unit quaternion. The axis is normalized.

Warning: As any other method dealing with quaternion, if the input quaternion is not normalized then the result is undefined.

Definition at line 159 of file AngleAxis.h.

 {
   using std::acos;
   using std::min;
   using std::max;
   using std::sqrt;
   Scalar n2 = q.vec().squaredNorm();
   if (n2 < NumTraits<Scalar>::dummy_precision()*NumTraits<Scalar>::dummy_precision())
   {
     m_angle = 0;
     m_axis << 1, 0, 0;
   }
   else
   {
     m_angle = Scalar(2)*acos((min)((max)(Scalar(-1),q.w()),Scalar(1)));
     m_axis = q.vec() / sqrt(n2);
   }
   return *this;
 }

template<typename Scalar >

template<typename Derived >

AngleAxis< Scalar > & Eigen::AngleAxis< Scalar >::operator= ( const MatrixBase< Derived > & mat )

Set *this from a 3x3 rotation matrix mat.

Definition at line 178 of file AngleAxis.h.

 {
   // Since a direct conversion would not be really faster,
   // let's use the robust Quaternion implementation:
   return *this = QuaternionType(mat);
 }

template<typename Scalar >

AngleAxis< Scalar >::Matrix3 Eigen::AngleAxis< Scalar >::toRotationMatrix ( void ) const

Constructs and

Returns: an equivalent 3x3 rotation matrix.

Definition at line 189 of file AngleAxis.h.

 {
   Matrix3 res;
   Vector3 sin_axis  = ei_sin(m_angle) * m_axis;
   Scalar c = ei_cos(m_angle);
   Vector3 cos1_axis = (Scalar(1)-c) * m_axis;
 
   Scalar tmp;
   tmp = cos1_axis.x() * m_axis.y();
   res.coeffRef(0,1) = tmp - sin_axis.z();
   res.coeffRef(1,0) = tmp + sin_axis.z();
 
   tmp = cos1_axis.x() * m_axis.z();
   res.coeffRef(0,2) = tmp + sin_axis.y();
   res.coeffRef(2,0) = tmp - sin_axis.y();
 
   tmp = cos1_axis.y() * m_axis.z();
   res.coeffRef(1,2) = tmp - sin_axis.x();
   res.coeffRef(2,1) = tmp + sin_axis.x();
 
   res.diagonal() = (cos1_axis.cwise() * m_axis).cwise() + c;
 
   return res;
 }

Friends And Related Function Documentation

template<typename _Scalar>

QuaternionType operator*	(	const QuaternionType &	a,
		const AngleAxis< _Scalar > &	b
	)

friend

Concatenates two rotations

Definition at line 95 of file AngleAxis.h.

96 { return a * QuaternionType(b); }

template<typename _Scalar>

QuaternionType operator*	(	const QuaternionType &	a,
		const AngleAxis< _Scalar > &	b
	)

friend

Concatenates two rotations

Definition at line 101 of file AngleAxis.h.

102 { return a * QuaternionType(b); }

template<typename _Scalar>

Matrix3 operator*	(	const Matrix3 &	a,
		const AngleAxis< _Scalar > &	b
	)

friend

Concatenates two rotations

Definition at line 103 of file AngleAxis.h.

104 { return a * b.toRotationMatrix(); }

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

C:/Users/Brig/Documents/ShapeWorksStudio/src/Surfworks/Eigen/src/Core/util/ForwardDeclarations.h
C:/Users/Brig/Documents/ShapeWorksStudio/src/Surfworks/Eigen/src/Eigen2Support/Geometry/AngleAxis.h

Public Types

Public Member Functions

Static Public Member Functions

Protected Attributes

Friends

Detailed Description

template<typename _Scalar> class Eigen::AngleAxis< _Scalar >

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation

template<typename _Scalar>
class Eigen::AngleAxis< _Scalar >