Eigen::Rotation2D< Scalar_ > Class Template Reference

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

#include <Rotation2D.h>

Inheritance diagram for Eigen::Rotation2D< Scalar_ >:

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

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

Static Public Member Functions
static EIGEN_DEVICE_FUNC 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.

\geometry_module

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

Member Typedef Documentation

Base

template<typename Scalar_ >

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

private

Matrix2

template<typename Scalar_ >

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

Scalar

template<typename Scalar_ >

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

the scalar type of the coefficients

Vector2

template<typename Scalar_ >

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

Member Enumeration Documentation

anonymous enum

template<typename Scalar_ >

anonymous enum

Enumerator
Dim

{ Dim = 2 };

Constructor & Destructor Documentation

Rotation2D() [1/4]

template<typename Scalar_ >

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

inlineexplicit

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

: m_angle(a) {}

Rotation2D() [2/4]

template<typename Scalar_ >

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

inline

Default constructor without initialization. The represented rotation is undefined.

{}

Referenced by Eigen::Rotation2D< Scalar_ >::Identity(), Eigen::Rotation2D< Scalar_ >::inverse(), Eigen::Rotation2D< Scalar_ >::operator*(), and Eigen::Rotation2D< Scalar_ >::slerp().

Rotation2D() [3/4]

template<typename Scalar_ >

template<typename Derived >

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

inlineexplicit

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

See also

fromRotationMatrix()

                                                                      {
    fromRotationMatrix(m.derived());
  }

References Eigen::Rotation2D< Scalar_ >::fromRotationMatrix(), and m.

Rotation2D() [4/4]

template<typename Scalar_ >

template<typename OtherScalarType >

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

inlineexplicit

Copy constructor with scalar type conversion

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

References Eigen::Rotation2D< Scalar_ >::angle(), and Eigen::Rotation2D< Scalar_ >::m_angle.

Member Function Documentation

angle() [1/2]

template<typename Scalar_ >

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

inline

Returns

a read-write reference to the rotation angle

{ return m_angle; }

References Eigen::Rotation2D< Scalar_ >::m_angle.

angle() [2/2]

template<typename Scalar_ >

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

inline

Returns

the rotation angle

{ return m_angle; }

References Eigen::Rotation2D< Scalar_ >::m_angle.

Referenced by Eigen::Rotation2D< Scalar_ >::Rotation2D(), and transformations().

cast()

template<typename Scalar_ >

template<typename NewScalarType >

EIGEN_DEVICE_FUNC 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.

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

References compute_granudrum_aor::type.

fromRotationMatrix() [1/2]

template<typename Scalar_ >

template<typename Derived >

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

(

const MatrixBase< Derived > &

m

)

Referenced by Eigen::Rotation2D< Scalar_ >::operator=(), and Eigen::Rotation2D< Scalar_ >::Rotation2D().

fromRotationMatrix() [2/2]

template<typename Scalar_ >

template<typename Derived >

EIGEN_DEVICE_FUNC 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.

                                                                                                           {
  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;
}

References Eigen::atan2(), Eigen::SparseMatrix< Scalar_, Options_, StorageIndex_ >::coeff(), EIGEN_STATIC_ASSERT, and EIGEN_USING_STD.

Identity()

template<typename Scalar_ >

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

inlinestatic

{ return Rotation2D(0); }

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

inverse()

template<typename Scalar_ >

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

inline

Returns

the inverse rotation

{ return Rotation2D(-m_angle); }

References Eigen::Rotation2D< Scalar_ >::m_angle, and Eigen::Rotation2D< Scalar_ >::Rotation2D().

isApprox()

template<typename Scalar_ >

EIGEN_DEVICE_FUNC 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()

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

References Eigen::internal::isApprox(), and Eigen::Rotation2D< Scalar_ >::m_angle.

operator*() [1/2]

template<typename Scalar_ >

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

inline

Concatenates two rotations

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

References Eigen::Rotation2D< Scalar_ >::m_angle, and Eigen::Rotation2D< Scalar_ >::Rotation2D().

operator*() [2/2]

template<typename Scalar_ >

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

inline

Applies the rotation to a 2D vector

{ return toRotationMatrix() * vec; }

References Eigen::Rotation2D< Scalar_ >::toRotationMatrix().

operator*=()

template<typename Scalar_ >

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

inline

Concatenates two rotations

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

References Eigen::Rotation2D< Scalar_ >::m_angle.

operator=()

template<typename Scalar_ >

template<typename Derived >

EIGEN_DEVICE_FUNC 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()

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

References Eigen::Rotation2D< Scalar_ >::fromRotationMatrix(), and m.

slerp()

template<typename Scalar_ >

EIGEN_DEVICE_FUNC 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.

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

References Eigen::Rotation2D< Scalar_ >::m_angle, Eigen::Rotation2D< Scalar_ >::Rotation2D(), and plotPSD::t.

smallestAngle()

template<typename Scalar_ >

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

inline

Returns

the rotation angle in [-pi,pi]

                                                        {
    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;
  }

References EIGEN_PI, Eigen::numext::fmod(), Eigen::Rotation2D< Scalar_ >::m_angle, and tmp.

Referenced by transformations().

smallestPositiveAngle()

template<typename Scalar_ >

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

inline

Returns

the rotation angle in [0,2pi]

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

References EIGEN_PI, Eigen::numext::fmod(), Eigen::Rotation2D< Scalar_ >::m_angle, and tmp.

Referenced by transformations().

toRotationMatrix()

template<typename Scalar >

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

(

void

)

const

Constructs and

Returns

an equivalent 2x2 rotation matrix.

                                                                                                    {
  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();
}

References cos(), EIGEN_USING_STD, and sin().

Referenced by Eigen::Rotation2D< Scalar_ >::operator*(), rotate2DIntegral(), Eigen::internal::toRotationMatrix(), and transformations().

Member Data Documentation

m_angle

template<typename Scalar_ >

Scalar Eigen::Rotation2D< Scalar_ >::m_angle

protected

Referenced by Eigen::Rotation2D< Scalar_ >::angle(), Eigen::Rotation2D< Scalar_ >::inverse(), Eigen::Rotation2D< Scalar_ >::isApprox(), Eigen::Rotation2D< Scalar_ >::operator*(), Eigen::Rotation2D< Scalar_ >::operator*=(), Eigen::Rotation2D< Scalar_ >::Rotation2D(), Eigen::Rotation2D< Scalar_ >::slerp(), Eigen::Rotation2D< Scalar_ >::smallestAngle(), and Eigen::Rotation2D< Scalar_ >::smallestPositiveAngle().

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

• ForwardDeclarations.h
• Rotation2D.h