Ocean::RotationT< T > Class Template Reference

This class implements a axis-angle rotation using floating point values. More...

#include <Rotation.h>

Public Types
typedef T	Type
	Definition of the used data type.

Public Member Functions
	RotationT ()=default
	Creates a rotation object with default values so that the rotation represents the identity rotation.
	RotationT (const T x, const T y, const T z, const T angle)
	Creates a rotation object by four given values.
	RotationT (const VectorT3< T > &axis, const T angle)
	Creates a rotation object by an axis and the angle.
	RotationT (const VectorT3< T > &reference, const VectorT3< T > &offset)
	Creates a rotation object based on two given unit vectors.
	RotationT (const QuaternionT< T > &quaternion)
	Creates a rotation object by a given quaternion rotation.
	RotationT (const EulerT< T > &euler)
	Creates an angle-axis rotation by a given euler rotation.
	RotationT (const SquareMatrixT3< T > &matrix)
	Creates a rotation object by a given 3x3 rotation matrix.
	RotationT (const HomogenousMatrixT4< T > &transformation)
	Creates a rotation object by a given 4x4 transformation matrix.
	RotationT (const T *valueArray)
	Creates a rotation object by an array with four elements.
void	setAxis (const VectorT3< T > &axis)
	Sets the axis of the rotation.
void	setAngle (const T angle)
	Sets the angle of the rotation.
const T *	data () const
	Returns a pointer to the internal values.
T *	data ()
	Returns a pointer to the internal values.
VectorT3< T >	axis () const
	Returns the axis of the rotation.
T	angle () const
	Returns the angle of the rotation.
RotationT	inverted () const
	Returns the inverted rotation, this rotation must be valid.
void	invert ()
	Inverts this rotation, this rotation must be valid.
bool	isValid () const
	Returns whether this rotation has valid parameters.
bool	operator== (const RotationT< T > &right) const
	Returns whether two rotations are identical up to a small epsilon.
bool	operator!= (const RotationT< T > &right) const
	Returns whether two rotations are not identical up to a small epsilon.
RotationT	operator- () const
	Returns the inverse rotation, this rotation must be valid.
RotationT	operator* (const QuaternionT< T > &quaternion) const
	Multiplies two rotations, this rotation must be valid.
RotationT &	operator*= (const QuaternionT< T > &quaternion)
	Multiplies and assign two rotations, this rotation must be valid.
RotationT	operator* (const RotationT< T > &right) const
	Multiplies two rotations, this rotation must be valid.
RotationT &	operator*= (const RotationT< T > &right)
	Multiplies and assign two rotations, this rotation must be valid.
VectorT3< T >	operator* (const VectorT3< T > &vector) const
	Rotates a 3D vector with this rotation, this rotation must be valid.
T	operator() (unsigned int index) const
	Element access operator.
T &	operator() (unsigned int index)
	Element access operator.
T	operator[] (unsigned int index) const
	Element access operator.
T &	operator[] (unsigned int index)
	Element access operator.
const T *	operator() () const
	Access operator.
T *	operator() ()
	Access operator.

Protected Attributes
T	values_ [4] = {T(0), T(1), T(0), T(0)}
	The four values of the angle-axis rotation.

Detailed Description

template<typename T>
class Ocean::RotationT< T >

This class implements a axis-angle rotation using floating point values.

The angle is defined in radian [0, 2*PI).
The four elements are stored with order: (x, y, z, angle).

Template Parameters

T	Data type used to represent axis and angle

See also

Rotation, RotationF, RotationD, Quaternion, Euler, SquareMatrix3, ExponentialMap.

Member Typedef Documentation

Type

template<typename T >

typedef T Ocean::RotationT< T >::Type

Definition of the used data type.

Constructor & Destructor Documentation

RotationT() [1/9]

template<typename T >

Ocean::RotationT< T >::RotationT ( )

default

Creates a rotation object with default values so that the rotation represents the identity rotation.

The axis will be set to (0, 1, 0) and the angle to 0.

RotationT() [2/9]

template<typename T >

Ocean::RotationT< T >::RotationT	(	const T	x,
		const T	y,
		const T	z,
		const T	angle
	)

Creates a rotation object by four given values.

The axis must have length 1.

Parameters

x	X value of the rotation axis
y	Y value of the rotation axis
z	Z value of the rotation axis
angle	The angle of the rotation in radian, with range (-infinity, infinity), however will be converted to the range [0.0, 2 * PI)

RotationT() [3/9]

template<typename T >

Ocean::RotationT< T >::RotationT	(	const VectorT3< T > &	axis,
		const T	angle
	)

Creates a rotation object by an axis and the angle.

Parameters

axis	The axis of the rotation with length 1
angle	The angle of the rotation in radian, with range (-infinity, infinity), however will be converted to the range [0.0, 2 * PI)

RotationT() [4/9]

template<typename T >

Ocean::RotationT< T >::RotationT	(	const VectorT3< T > &	reference,
		const VectorT3< T > &	offset
	)

Creates a rotation object based on two given unit vectors.

The resulting rotation defines a transformation that rotates that reference vector into the offset vector: Rotation(reference, offset) = offset_R_reference.
The following equation holds:

offset = Rotation(reference, offset) * reference.

Parameters

reference	The reference vector, with length 1
offset	The offset vector, with length 1

RotationT() [5/9]

template<typename T >

Ocean::RotationT< T >::RotationT ( const QuaternionT< T > &  quaternion )

explicit

Creates a rotation object by a given quaternion rotation.

Parameters

quaternion

the quaternion rotation to create an axis-angle rotation from, must be valid

RotationT() [6/9]

template<typename T >

Ocean::RotationT< T >::RotationT ( const EulerT< T > &  euler )

explicit

Creates an angle-axis rotation by a given euler rotation.

Parameters

euler

Euler rotation to create a angle-axis rotation from, must be valid

RotationT() [7/9]

template<typename T >

Ocean::RotationT< T >::RotationT ( const SquareMatrixT3< T > &  matrix )

explicit

Creates a rotation object by a given 3x3 rotation matrix.

Beware: Ensure that the provided matrix does not contain any scale.

Parameters

matrix

Rotation matrix to create a axis-angle rotation from, with determinant 1

RotationT() [8/9]

template<typename T >

Ocean::RotationT< T >::RotationT ( const HomogenousMatrixT4< T > &  transformation )

explicit

Creates a rotation object by a given 4x4 transformation matrix.

Parameters

transformation

The transformation matrix to create a axis-angle rotation from, must be valid

RotationT() [9/9]

template<typename T >

Ocean::RotationT< T >::RotationT ( const T *  valueArray )

explicit

Creates a rotation object by an array with four elements.

The element order in the array has to be: (x, y, z, angle).
The axis must have length 1, the angle is provided as radian with range (-infinity, infinity), however will be converted to the range [0.0, 2 * PI)

Parameters

valueArray

Array with four elements

Member Function Documentation

angle()

template<typename T >

T Ocean::RotationT< T >::angle ( ) const

inline

Returns the angle of the rotation.

Returns

Rotation angle in radian, with range [0.0, 2 * PI)

axis()

template<typename T >

VectorT3< T > Ocean::RotationT< T >::axis ( ) const

inline

Returns the axis of the rotation.

Returns

Rotation axis with unit length if the rotation is valid

data() [1/2]

template<typename T >

T * Ocean::RotationT< T >::data ( )

inline

Returns a pointer to the internal values.

Returns

Pointer to the internal values

data() [2/2]

template<typename T >

const T * Ocean::RotationT< T >::data ( ) const

inline

Returns a pointer to the internal values.

Returns

Pointer to the internal values

invert()

template<typename T >

void Ocean::RotationT< T >::invert

(

)

Inverts this rotation, this rotation must be valid.

See also

isValid(), inverted().

inverted()

template<typename T >

RotationT< T > Ocean::RotationT< T >::inverted

(

)

const

Returns the inverted rotation, this rotation must be valid.

Returns

Inverted rotation

See also

isValid(), invert().

isValid()

template<typename T >

bool Ocean::RotationT< T >::isValid

(

)

const

Returns whether this rotation has valid parameters.

Returns

True, if so

operator!=()

template<typename T >

bool Ocean::RotationT< T >::operator!= ( const RotationT< T > &  right ) const

inline

Returns whether two rotations are not identical up to a small epsilon.

Parameters

right

The right operand

Returns

True, if so

operator()() [1/4]

template<typename T >

T * Ocean::RotationT< T >::operator() ( )

inline

Access operator.

Returns

Pointer to the internal elements.

operator()() [2/4]

template<typename T >

const T * Ocean::RotationT< T >::operator() ( ) const

inline

Access operator.

Returns

Pointer to the internal elements.

operator()() [3/4]

template<typename T >

T & Ocean::RotationT< T >::operator() ( unsigned int  index )

inline

Element access operator.

Parameters

index

The index of the element to return, with range [0, 3]

Returns

Internal element

operator()() [4/4]

template<typename T >

T Ocean::RotationT< T >::operator() ( unsigned int  index ) const

inline

Element access operator.

Parameters

index

The index of the element to return, with range [0, 3]

Returns

Internal element

operator*() [1/3]

template<typename T >

RotationT< T > Ocean::RotationT< T >::operator*

(

const QuaternionT< T > &

quaternion

)

const

Multiplies two rotations, this rotation must be valid.

Parameters

quaternion

The right rotation as unit quaternion, must be valid

Returns

Resulting rotation

operator*() [2/3]

template<typename T >

RotationT< T > Ocean::RotationT< T >::operator*

(

const RotationT< T > &

right

)

const

Multiplies two rotations, this rotation must be valid.

Parameters

right

The right rotation to multiply, must be valid

Returns

Resulting rotation

operator*() [3/3]

template<typename T >

VectorT3< T > Ocean::RotationT< T >::operator*

(

const VectorT3< T > &

vector

)

const

Rotates a 3D vector with this rotation, this rotation must be valid.

Parameters

vector

The vector to rotate

Returns

Rotated vector

operator*=() [1/2]

template<typename T >

RotationT< T > & Ocean::RotationT< T >::operator*=

(

const QuaternionT< T > &

quaternion

)

Multiplies and assign two rotations, this rotation must be valid.

Parameters

quaternion

The right rotation as unit quaternion, must be valid

Returns

Reference to this rotation

operator*=() [2/2]

template<typename T >

RotationT< T > & Ocean::RotationT< T >::operator*=

(

const RotationT< T > &

right

)

Multiplies and assign two rotations, this rotation must be valid.

Parameters

right

The right rotation to multiply, must be valid

Returns

Reference to this rotation

operator-()

template<typename T >

RotationT< T > Ocean::RotationT< T >::operator-

(

)

const

Returns the inverse rotation, this rotation must be valid.

Returns

Inverse rotation

operator==()

template<typename T >

bool Ocean::RotationT< T >::operator==

(

const RotationT< T > &

right

)

const

Returns whether two rotations are identical up to a small epsilon.

Parameters

right

The right operand

Returns

True, if so

operator[]() [1/2]

template<typename T >

T & Ocean::RotationT< T >::operator[] ( unsigned int  index )

inline

Element access operator.

Parameters

index

The index of the element to return, with range [0, 3]

Returns

Internal element

operator[]() [2/2]

template<typename T >

T Ocean::RotationT< T >::operator[] ( unsigned int  index ) const

inline

Element access operator.

Parameters

index

The index of the element to return, with range [0, 3]

Returns

Internal element

setAngle()

template<typename T >

void Ocean::RotationT< T >::setAngle

(

const T

angle

)

Sets the angle of the rotation.

Parameters

angle

The angle of rotation in radian, with range (-infinity, infinity), however will be converted to the range [0.0, 2 * PI)

setAxis()

template<typename T >

void Ocean::RotationT< T >::setAxis

(

const VectorT3< T > &

axis

)

Sets the axis of the rotation.

Parameters

axis	The axis with length 1

Field Documentation

values_

template<typename T >

T Ocean::RotationT< T >::values_[4] = {T(0), T(1), T(0), T(0)}

protected

The four values of the angle-axis rotation.

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

• Euler.h
• Rotation.h