Rotation2D< _Scalar > Class Template Reference [Geometry_Module]

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Detailed Description

template<typename _Scalar>
class Rotation2D< _Scalar >

Represents a rotation/orientation in a 2 dimensional space.

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 54 of file Rotation2D.h.

#include <src/Geometry/Rotation2D.h>

Inheritance diagram for Rotation2D< _Scalar >:

List of all members.

Public Types
enum	{ Dim = 2 }
typedef _Scalar	Scalar
	the scalar type of the coefficients
typedef Matrix< Scalar, 2, 1 >	Vector2
typedef Matrix< Scalar, 2, 2 >	Matrix2
Public Member Functions
	Rotation2D (Scalar a)
	Construct a 2D counter clock wise rotation from the angle a in radian.
Scalar	angle () const
Scalar &	angle ()
Rotation2D	inverse () const
Rotation2D	operator* (const Rotation2D &other) const
	Concatenates two rotations.
Rotation2D &	operator*= (const Rotation2D &other)
	Concatenates two rotations.
Vector2	operator* (const Vector2 &vec) const
	Applies the rotation to a 2D vector.
template<typename Derived >
Rotation2D &	fromRotationMatrix (const MatrixBase< Derived > &m)
	Set *this from a 2x2 rotation matrix mat.
Matrix2	toRotationMatrix (void) const
	Constructs and.
Rotation2D	slerp (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)
	Copy constructor with scalar type conversion.
bool	isApprox (const Rotation2D &other, 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

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Member Typedef Documentation

template<typename _Scalar>

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

Definition at line 56 of file Rotation2D.h.

template<typename _Scalar>

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

Definition at line 66 of file Rotation2D.h.

template<typename _Scalar>

typedef _Scalar Rotation2D< _Scalar >::Scalar

the scalar type of the coefficients

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

Definition at line 64 of file Rotation2D.h.

template<typename _Scalar>

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

Definition at line 65 of file Rotation2D.h.

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Member Enumeration Documentation

template<typename _Scalar>

anonymous enum

Enumerator:

Dim

Definition at line 62 of file Rotation2D.h.

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Constructor & Destructor Documentation

template<typename _Scalar>

Rotation2D< _Scalar >::Rotation2D

(

Scalar

a )

[inline]

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

Definition at line 75 of file Rotation2D.h.

Referenced by Rotation2D< _Scalar >::Identity().

template<typename _Scalar>

template<typename OtherScalarType >

Rotation2D< _Scalar >::Rotation2D

(

const Rotation2D< OtherScalarType > &

other )

[inline, explicit]

Copy constructor with scalar type conversion.

Definition at line 119 of file Rotation2D.h.

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

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Member Function Documentation

template<typename _Scalar>

Scalar Rotation2D< _Scalar >::angle

(

)

const [inline]

Returns:

the rotation angle

Definition at line 78 of file Rotation2D.h.

References Rotation2D< _Scalar >::m_angle.

Referenced by Rotation2D< _Scalar >::Rotation2D(), and Rotation2D< _Scalar >::slerp().

template<typename _Scalar>

Scalar& Rotation2D< _Scalar >::angle

(

)

[inline]

Returns:

a read-write reference to the rotation angle

Definition at line 81 of file Rotation2D.h.

References Rotation2D< _Scalar >::m_angle.

template<typename _Scalar>

template<typename NewScalarType >

internal::cast_return_type<Rotation2D,Rotation2D<NewScalarType> >::type 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 114 of file Rotation2D.h.

template<typename Scalar >

template<typename Derived >

Rotation2D< Scalar > & 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 147 of file Rotation2D.h.

References EIGEN_STATIC_ASSERT.

template<typename _Scalar>

static Rotation2D Rotation2D< _Scalar >::Identity

(

)

[inline, static]

Definition at line 124 of file Rotation2D.h.

References Rotation2D< _Scalar >::Rotation2D().

template<typename _Scalar>

Rotation2D Rotation2D< _Scalar >::inverse

(

)

const [inline]

Returns:

the inverse rotation

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

Definition at line 84 of file Rotation2D.h.

References Rotation2D< _Scalar >::m_angle.

template<typename _Scalar>

bool Rotation2D< _Scalar >::isApprox	(	const Rotation2D< _Scalar > &	other,
		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 130 of file Rotation2D.h.

References Rotation2D< _Scalar >::m_angle.

template<typename _Scalar>

Rotation2D Rotation2D< _Scalar >::operator*

(

const Rotation2D< _Scalar > &

other )

const [inline]

Concatenates two rotations.

Definition at line 87 of file Rotation2D.h.

References Rotation2D< _Scalar >::m_angle.

template<typename _Scalar>

Vector2 Rotation2D< _Scalar >::operator*

(

const Vector2 &

vec )

const [inline]

Applies the rotation to a 2D vector.

Definition at line 95 of file Rotation2D.h.

References Rotation2D< _Scalar >::toRotationMatrix().

template<typename _Scalar>

Rotation2D& Rotation2D< _Scalar >::operator*=

(

const Rotation2D< _Scalar > &

other )

[inline]

Concatenates two rotations.

Definition at line 91 of file Rotation2D.h.

References Rotation2D< _Scalar >::m_angle.

template<typename _Scalar>

Rotation2D Rotation2D< _Scalar >::slerp	(	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 105 of file Rotation2D.h.

References Rotation2D< _Scalar >::angle(), Rotation2D< _Scalar >::m_angle, and t().

template<typename Scalar >

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

(

void

)

const

Constructs and.

Returns:

an equivalent 2x2 rotation matrix.

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

Definition at line 158 of file Rotation2D.h.

References cos(), and sin().

Referenced by Rotation2D< _Scalar >::operator*().

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Member Data Documentation

template<typename _Scalar>

Scalar Rotation2D< _Scalar >::m_angle [protected]

Definition at line 70 of file Rotation2D.h.

Referenced by Rotation2D< _Scalar >::angle(), Rotation2D< _Scalar >::inverse(), Rotation2D< _Scalar >::isApprox(), Rotation2D< _Scalar >::operator*(), Rotation2D< _Scalar >::operator*=(), Rotation2D< _Scalar >::Rotation2D(), and Rotation2D< _Scalar >::slerp().