Eigen::Rotation2D< Scalar_ > Class Template Reference

Represents a rotation/orientation in a 2 dimensional space. More...

Inheritance diagram for Eigen::Rotation2D< Scalar_ >:

Public Types
enum	{ Dim }
typedef Matrix< Scalar, 2, 2 >	Matrix2
typedef Scalar_	Scalar
typedef Matrix< Scalar, 2, 1 >	Vector2
Public Types inherited from Eigen::RotationBase< Rotation2D< Scalar_ >, 2 >
enum
typedef Matrix< Scalar, Dim, Dim >	RotationMatrixType
typedef internal::traits< Rotation2D< Scalar_ > >::Scalar	Scalar
typedef Matrix< Scalar, Dim, 1 >	VectorType

Public Member Functions
Scalar &	angle ()
Scalar	angle () const
template<typename NewScalarType >
internal::cast_return_type< Rotation2D, Rotation2D< NewScalarType > >::type	cast () const
template<typename Derived >
Rotation2D &	fromRotationMatrix (const MatrixBase< Derived > &m)
template<typename Derived >
Rotation2D< Scalar > &	fromRotationMatrix (const MatrixBase< Derived > &mat)
Rotation2D	inverse () const
bool	isApprox (const Rotation2D &other, const typename NumTraits< Scalar >::Real &prec=NumTraits< Scalar >::dummy_precision()) const
Rotation2D	operator* (const Rotation2D &other) const
Vector2	operator* (const Vector2 &vec) const
Rotation2D &	operator*= (const Rotation2D &other)
template<typename Derived >
Rotation2D &	operator= (const MatrixBase< Derived > &m)
	Rotation2D ()
template<typename Derived >
	Rotation2D (const MatrixBase< Derived > &m)
template<typename OtherScalarType >
	Rotation2D (const Rotation2D< OtherScalarType > &other)
	Rotation2D (const Scalar &a)
Rotation2D	slerp (const Scalar &t, const Rotation2D &other) const
Scalar	smallestAngle () const
Scalar	smallestPositiveAngle () const
Matrix2	toRotationMatrix () const
Public Member Functions inherited from Eigen::RotationBase< Rotation2D< Scalar_ >, 2 >
VectorType	_transformVector (const OtherVectorType &v) const
Rotation2D< Scalar_ > &	derived ()
const Rotation2D< Scalar_ > &	derived () const
Rotation2D< Scalar_ >	inverse () const
RotationMatrixType	matrix () const
internal::rotation_base_generic_product_selector< Rotation2D< Scalar_ >, OtherDerived, OtherDerived::IsVectorAtCompileTime >::ReturnType	operator* (const EigenBase< OtherDerived > &e) const
Transform< Scalar, Dim, Mode >	operator* (const Transform< Scalar, Dim, Mode, Options > &t) const
Transform< Scalar, Dim, Isometry >	operator* (const Translation< Scalar, Dim > &t) const
RotationMatrixType	operator* (const UniformScaling< Scalar > &s) const
RotationMatrixType	toRotationMatrix () const

Static Public Member Functions
static Rotation2D	Identity ()

Protected Attributes
Scalar	m_angle

Private Types
typedef RotationBase< Rotation2D< Scalar_ >, 2 >	Base

Detailed Description

template<typename Scalar_>
class Eigen::Rotation2D< Scalar_ >

Represents a rotation/orientation in a 2 dimensional space.

This is defined in the Geometry module.

#include <Eigen/Geometry> 

Template Parameters

Scalar_

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

This class is equivalent to a single scalar representing a counter clock wise rotation as a single angle in radian. It provides some additional features such as the automatic conversion from/to a 2x2 rotation matrix. Moreover this class aims to provide a similar interface to Quaternion in order to facilitate the writing of generic algorithms dealing with rotations.

See also

class Quaternion, class Transform

Definition at line 43 of file Rotation2D.h.

Member Typedef Documentation

Base

template<typename Scalar_ >

typedef RotationBase<Rotation2D<Scalar_>,2> Eigen::Rotation2D< Scalar_ >::Base

private

Definition at line 45 of file Rotation2D.h.

Matrix2

template<typename Scalar_ >

typedef Matrix<Scalar,2,2> Eigen::Rotation2D< Scalar_ >::Matrix2

Definition at line 55 of file Rotation2D.h.

Scalar

template<typename Scalar_ >

typedef Scalar_ Eigen::Rotation2D< Scalar_ >::Scalar

the scalar type of the coefficients

Definition at line 53 of file Rotation2D.h.

Vector2

template<typename Scalar_ >

typedef Matrix<Scalar,2,1> Eigen::Rotation2D< Scalar_ >::Vector2

Definition at line 54 of file Rotation2D.h.

Member Enumeration Documentation

anonymous enum

template<typename Scalar_ >

anonymous enum

Enumerator
Dim

Definition at line 51 of file Rotation2D.h.

{ Dim = 2 };

Constructor & Destructor Documentation

Rotation2D() [1/4]

template<typename Scalar_ >

Eigen::Rotation2D< Scalar_ >::Rotation2D ( const Scalar &  a )

inlineexplicit

Construct a 2D counter clock wise rotation from the angle a in radian.

Definition at line 64 of file Rotation2D.h.

: m_angle(a) {}

Rotation2D() [2/4]

template<typename Scalar_ >

Eigen::Rotation2D< Scalar_ >::Rotation2D ( )

inline

Default constructor wihtout initialization. The represented rotation is undefined.

Definition at line 67 of file Rotation2D.h.

{}

Rotation2D() [3/4]

template<typename Scalar_ >

template<typename Derived >

Eigen::Rotation2D< Scalar_ >::Rotation2D ( const MatrixBase< Derived > &  m )

inlineexplicit

Construct a 2D rotation from a 2x2 rotation matrix mat.

See also

fromRotationMatrix()

Definition at line 74 of file Rotation2D.h.

  {
    fromRotationMatrix(m.derived());
  }

Rotation2D() [4/4]

template<typename Scalar_ >

template<typename OtherScalarType >

Eigen::Rotation2D< Scalar_ >::Rotation2D ( const Rotation2D< OtherScalarType > &  other )

inlineexplicit

Copy constructor with scalar type conversion

Definition at line 149 of file Rotation2D.h.

  {
    m_angle = Scalar(other.angle());
  }

Member Function Documentation

angle() [1/2]

template<typename Scalar_ >

Scalar& Eigen::Rotation2D< Scalar_ >::angle ( )

inline

Returns

a read-write reference to the rotation angle

Definition at line 83 of file Rotation2D.h.

{ return m_angle; }

angle() [2/2]

template<typename Scalar_ >

Scalar Eigen::Rotation2D< Scalar_ >::angle ( ) const

inline

Returns

the rotation angle

Definition at line 80 of file Rotation2D.h.

{ return m_angle; }

cast()

template<typename Scalar_ >

template<typename NewScalarType >

internal::cast_return_type<Rotation2D,Rotation2D<NewScalarType> >::type Eigen::Rotation2D< 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 144 of file Rotation2D.h.

  { return typename internal::cast_return_type<Rotation2D,Rotation2D<NewScalarType> >::type(*this); }

fromRotationMatrix() [1/2]

template<typename Scalar_ >

template<typename Derived >

Rotation2D& Eigen::Rotation2D< Scalar_ >::fromRotationMatrix

(

const MatrixBase< Derived > &

m

)

fromRotationMatrix() [2/2]

template<typename Scalar_ >

template<typename Derived >

Rotation2D<Scalar>& Eigen::Rotation2D< Scalar_ >::fromRotationMatrix

(

const MatrixBase< Derived > &

mat

)

Set *this from a 2x2 rotation matrix mat. In other words, this function extract the rotation angle from the rotation matrix.

Definition at line 178 of file Rotation2D.h.

{
  EIGEN_USING_STD(atan2)
  EIGEN_STATIC_ASSERT(Derived::RowsAtCompileTime==2 && Derived::ColsAtCompileTime==2,YOU_MADE_A_PROGRAMMING_MISTAKE)
  m_angle = atan2(mat.coeff(1,0), mat.coeff(0,0));
  return *this;
}

Identity()

template<typename Scalar_ >

static Rotation2D Eigen::Rotation2D< Scalar_ >::Identity ( )

inlinestatic

Definition at line 154 of file Rotation2D.h.

{ return Rotation2D(0); }

inverse()

template<typename Scalar_ >

Rotation2D Eigen::Rotation2D< Scalar_ >::inverse ( ) const

inline

Returns

the inverse rotation

Definition at line 100 of file Rotation2D.h.

{ return Rotation2D(-m_angle); }

isApprox()

template<typename Scalar_ >

bool Eigen::Rotation2D< Scalar_ >::isApprox ( const Rotation2D< 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 160 of file Rotation2D.h.

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

operator*() [1/2]

template<typename Scalar_ >

Rotation2D Eigen::Rotation2D< Scalar_ >::operator* ( const Rotation2D< Scalar_ > &  other ) const

inline

Concatenates two rotations

Definition at line 103 of file Rotation2D.h.

  { return Rotation2D(m_angle + other.m_angle); }

operator*() [2/2]

template<typename Scalar_ >

Vector2 Eigen::Rotation2D< Scalar_ >::operator* ( const Vector2 &  vec ) const

inline

Applies the rotation to a 2D vector

Definition at line 111 of file Rotation2D.h.

  { return toRotationMatrix() * vec; }

operator*=()

template<typename Scalar_ >

Rotation2D& Eigen::Rotation2D< Scalar_ >::operator*= ( const Rotation2D< Scalar_ > &  other )

inline

Concatenates two rotations

Definition at line 107 of file Rotation2D.h.

  { m_angle += other.m_angle; return *this; }

operator=()

template<typename Scalar_ >

template<typename Derived >

Rotation2D& Eigen::Rotation2D< Scalar_ >::operator= ( const MatrixBase< Derived > &  m )

inline

Set *this from a 2x2 rotation matrix mat. In other words, this function extract the rotation angle from the rotation matrix.

This method is an alias for fromRotationMatrix()

See also

fromRotationMatrix()

Definition at line 126 of file Rotation2D.h.

  { return fromRotationMatrix(m.derived()); }

slerp()

template<typename Scalar_ >

Rotation2D Eigen::Rotation2D< Scalar_ >::slerp ( const Scalar &  t, const Rotation2D< Scalar_ > &  other  ) const

inline

Returns

the spherical interpolation between *this and other using parameter t. It is in fact equivalent to a linear interpolation.

Definition at line 132 of file Rotation2D.h.

  {
    Scalar dist = Rotation2D(other.m_angle-m_angle).smallestAngle();
    return Rotation2D(m_angle + dist*t);
  }

smallestAngle()

template<typename Scalar_ >

Scalar Eigen::Rotation2D< Scalar_ >::smallestAngle ( ) const

inline

Returns

the rotation angle in [-pi,pi]

Definition at line 92 of file Rotation2D.h.

                                                        {
    Scalar tmp = numext::fmod(m_angle,Scalar(2*EIGEN_PI));
    if(tmp>Scalar(EIGEN_PI))       tmp -= Scalar(2*EIGEN_PI);
    else if(tmp<-Scalar(EIGEN_PI)) tmp += Scalar(2*EIGEN_PI);
    return tmp;
  }

smallestPositiveAngle()

template<typename Scalar_ >

Scalar Eigen::Rotation2D< Scalar_ >::smallestPositiveAngle ( ) const

inline

Returns

the rotation angle in [0,2pi]

Definition at line 86 of file Rotation2D.h.

                                                                {
    Scalar tmp = numext::fmod(m_angle,Scalar(2*EIGEN_PI));
    return tmp<Scalar(0) ? tmp + Scalar(2*EIGEN_PI) : tmp;
  }

toRotationMatrix()

template<typename Scalar >

Rotation2D< Scalar >::Matrix2 Eigen::Rotation2D< Scalar >::toRotationMatrix

(

void

)

const

Constructs and

Returns

an equivalent 2x2 rotation matrix.

Definition at line 190 of file Rotation2D.h.

{
  EIGEN_USING_STD(sin)
  EIGEN_USING_STD(cos)
  Scalar sinA = sin(m_angle);
  Scalar cosA = cos(m_angle);
  return (Matrix2() << cosA, -sinA, sinA, cosA).finished();
}

Member Data Documentation

m_angle

template<typename Scalar_ >

Scalar Eigen::Rotation2D< Scalar_ >::m_angle

protected

Definition at line 59 of file Rotation2D.h.

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

• ForwardDeclarations.h
• Rotation2D.h