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 >:

Collaboration diagram for Eigen::Rotation2D< _Scalar >:

List of all members.

Public Types
enum	{ Dim = 2 }
typedef _Scalar	Scalar
typedef Matrix< Scalar, 2, 1 >	Vector2
typedef Matrix< Scalar, 2, 2 >	Matrix2
Public Member Functions
	Rotation2D (const Scalar &a)
	Rotation2D ()
template<typename Derived >
	Rotation2D (const MatrixBase< Derived > &m)
Scalar	angle () const
Scalar &	angle ()
Scalar	smallestPositiveAngle () const
Scalar	smallestAngle () const
Rotation2D	inverse () const
Rotation2D	operator* (const Rotation2D &other) const
Rotation2D &	operator*= (const Rotation2D &other)
Vector2	operator* (const Vector2 &vec) const
template<typename Derived >
Rotation2D &	fromRotationMatrix (const MatrixBase< Derived > &m)
Matrix2	toRotationMatrix () const
template<typename Derived >
Rotation2D &	operator= (const MatrixBase< Derived > &m)
Rotation2D	slerp (const Scalar &t, const Rotation2D &other) const
template<typename NewScalarType >
internal::cast_return_type < Rotation2D, Rotation2D < NewScalarType > >::type	cast () const
template<typename OtherScalarType >
	Rotation2D (const Rotation2D< OtherScalarType > &other)
bool	isApprox (const Rotation2D &other, const typename NumTraits< Scalar >::Real &prec=NumTraits< Scalar >::dummy_precision()) 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.

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 41 of file Rotation2D.h.

---

Member Typedef Documentation

template<typename _Scalar>

typedef RotationBase<Rotation2D<_Scalar>,2> Eigen::Rotation2D< _Scalar >::Base [private]

Definition at line 43 of file Rotation2D.h.

template<typename _Scalar>

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

Definition at line 53 of file Rotation2D.h.

template<typename _Scalar>

typedef _Scalar Eigen::Rotation2D< _Scalar >::Scalar

the scalar type of the coefficients

Reimplemented from Eigen::RotationBase< Rotation2D< _Scalar >, 2 >.

Definition at line 51 of file Rotation2D.h.

template<typename _Scalar>

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

Definition at line 52 of file Rotation2D.h.

---

Member Enumeration Documentation

template<typename _Scalar>

anonymous enum

Enumerator:

Dim

Definition at line 49 of file Rotation2D.h.

{ Dim = 2 };

---

Constructor & Destructor Documentation

template<typename _Scalar>

Eigen::Rotation2D< _Scalar >::Rotation2D

(

const Scalar &

a

)

[inline, explicit]

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

Definition at line 62 of file Rotation2D.h.

: m_angle(a) {}

template<typename _Scalar>

Eigen::Rotation2D< _Scalar >::Rotation2D

(

)

[inline]

Default constructor wihtout initialization. The represented rotation is undefined.

Definition at line 65 of file Rotation2D.h.

{}

template<typename _Scalar>

template<typename Derived >

Eigen::Rotation2D< _Scalar >::Rotation2D

(

const MatrixBase< Derived > &

m

)

[inline, explicit]

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

See also:

fromRotationMatrix()

Definition at line 72 of file Rotation2D.h.

  {
    fromRotationMatrix(m.derived());
  }

template<typename _Scalar>

template<typename OtherScalarType >

Eigen::Rotation2D< _Scalar >::Rotation2D

(

const Rotation2D< OtherScalarType > &

other

)

[inline, explicit]

Copy constructor with scalar type conversion

Definition at line 147 of file Rotation2D.h.

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

---

Member Function Documentation

template<typename _Scalar>

Scalar Eigen::Rotation2D< _Scalar >::angle

(

)

const [inline]

Returns:

the rotation angle

Definition at line 78 of file Rotation2D.h.

{ return m_angle; }

template<typename _Scalar>

Scalar& Eigen::Rotation2D< _Scalar >::angle

(

)

[inline]

Returns:

a read-write reference to the rotation angle

Definition at line 81 of file Rotation2D.h.

{ return m_angle; }

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 142 of file Rotation2D.h.

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

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 176 of file Rotation2D.h.

{
  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;
}

template<typename _Scalar>

static Rotation2D Eigen::Rotation2D< _Scalar >::Identity

(

)

[inline, static]

Definition at line 152 of file Rotation2D.h.

{ return Rotation2D(0); }

template<typename _Scalar>

Rotation2D Eigen::Rotation2D< _Scalar >::inverse

(

)

const [inline]

Returns:

the inverse rotation

Reimplemented from Eigen::RotationBase< Rotation2D< _Scalar >, 2 >.

Definition at line 98 of file Rotation2D.h.

{ return Rotation2D(-m_angle); }

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 158 of file Rotation2D.h.

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

template<typename _Scalar>

Rotation2D Eigen::Rotation2D< _Scalar >::operator*

(

const Rotation2D< _Scalar > &

other

)

const [inline]

Concatenates two rotations

Definition at line 101 of file Rotation2D.h.

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

template<typename _Scalar>

Vector2 Eigen::Rotation2D< _Scalar >::operator*

(

const Vector2 &

vec

)

const [inline]

Applies the rotation to a 2D vector

Definition at line 109 of file Rotation2D.h.

  { return toRotationMatrix() * vec; }

template<typename _Scalar>

Rotation2D& Eigen::Rotation2D< _Scalar >::operator*=

(

const Rotation2D< _Scalar > &

other

)

[inline]

Concatenates two rotations

Definition at line 105 of file Rotation2D.h.

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

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 124 of file Rotation2D.h.

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

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 130 of file Rotation2D.h.

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

template<typename _Scalar>

Scalar Eigen::Rotation2D< _Scalar >::smallestAngle

(

)

const [inline]

Returns:

the rotation angle in [-pi,pi]

Definition at line 90 of file Rotation2D.h.

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

template<typename _Scalar>

Scalar Eigen::Rotation2D< _Scalar >::smallestPositiveAngle

(

)

const [inline]

Returns:

the rotation angle in [0,2pi]

Definition at line 84 of file Rotation2D.h.

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

template<typename Scalar >

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

(

void

)

const

Constructs and

Returns:

an equivalent 2x2 rotation matrix.

Reimplemented from Eigen::RotationBase< Rotation2D< _Scalar >, 2 >.

Definition at line 188 of file Rotation2D.h.

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

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Member Data Documentation

template<typename _Scalar>

Scalar Eigen::Rotation2D< _Scalar >::m_angle [protected]

Definition at line 57 of file Rotation2D.h.

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

• Rotation2D.h