\( N \times N \) rotation matrix backed by a unit quaternion (or an axis-angle representation). More...

#include <AffineTransform.hpp>

Inheritance diagram for CDPL::Math::RotationMatrix< T >:

Public Types
typedef T	ValueType
	The scalar value type. More...

typedef const T	Reference
	Reference type (always a `const` reference — elements are computed). More...

typedef const T	ConstReference
	Constant reference type to an element. More...

typedef std::size_t	SizeType
	The unsigned size type. More...

typedef std::ptrdiff_t	DifferenceType
	The signed difference type. More...

typedef MatrixReference< SelfType >	ClosureType
	Closure type used when this matrix appears inside another expression. More...

typedef const MatrixReference< const SelfType >	ConstClosureType
	Constant closure type used when this matrix appears inside another expression. More...

typedef Matrix< T, std::vector< T > >	MatrixTemporaryType
	Concrete temporary matrix type used by expression-template machinery. More...

typedef Vector< T, std::vector< T > >	VectorTemporaryType
	Concrete temporary vector type used when assembling vectors from this matrix. More...

Public Types inherited from CDPL::Math::MatrixContainer< RotationMatrix< T > >
typedef RotationMatrix< T >	ContainerType
	The derived matrix container type. More...

Public Types inherited from CDPL::Math::MatrixExpression< E >
typedef E	ExpressionType
	The derived matrix expression type. More...

Public Types inherited from CDPL::Math::Expression< E >
typedef E	ExpressionType
	The derived expression type (made available to expression-template machinery). More...

Public Member Functions
template<typename E >
	RotationMatrix (SizeType n, const QuaternionExpression< E > &q)
	Constructs an \( N \times N \) rotation matrix from the unit quaternion q. More...

template<typename T1 , typename T2 , typename T3 , typename T4 >
	RotationMatrix (SizeType n, const T1 &w, const T2 &ux, const T3 &uy, const T4 &uz)
	Constructs an \( N \times N \) rotation matrix from an axis-angle representation. More...

	RotationMatrix (const RotationMatrix &m)
	Constructs a copy of the rotation matrix m. More...

template<typename E >
void	set (const QuaternionExpression< E > &q)
	Sets the rotation from the unit quaternion q. More...

template<typename T1 , typename T2 , typename T3 , typename T4 >
void	set (const T1 &w, const T2 &ux, const T3 &uy, const T4 &uz)
	Sets the rotation from an axis-angle representation. More...

ConstReference	operator() (SizeType i, SizeType j) const
	Returns the rotation-matrix entry at (i, j). More...

bool	isEmpty () const
	Tells whether the matrix is empty (size zero). More...

SizeType	getSize1 () const
	Returns the dimension N (the row count). More...

SizeType	getSize2 () const
	Returns the dimension N (the column count). More...

SizeType	getMaxSize1 () const
	Returns the maximum representable row count. More...

SizeType	getMaxSize2 () const
	Returns the maximum representable column count. More...

RotationMatrix &	operator= (const RotationMatrix &m)
	Copy-assigns the dimension and the underlying quaternion components from m. More...

void	swap (RotationMatrix &m)
	Swaps the dimension and the underlying quaternion components with m. More...

void	resize (SizeType n)
	Resizes the matrix dimension to n (the underlying quaternion is left unchanged). More...

Public Member Functions inherited from CDPL::Math::MatrixContainer< RotationMatrix< T > >
const ContainerType &	operator() () const
	Returns a `const` reference to the derived matrix container. More...

ContainerType &	operator() ()
	Returns a reference to the derived matrix container. More...

Public Member Functions inherited from CDPL::Math::MatrixExpression< E >
const ExpressionType &	operator() () const
	Returns a `const` reference to the derived matrix expression. More...

ExpressionType &	operator() ()
	Returns a reference to the derived matrix expression. More...

Friends
void	swap (RotationMatrix &m1, RotationMatrix &m2)
	ADL-enabled free-function form of swap(). More...

Additional Inherited Members
Protected Member Functions inherited from CDPL::Math::MatrixContainer< RotationMatrix< T > >
	MatrixContainer ()

	~MatrixContainer ()

Protected Member Functions inherited from CDPL::Math::MatrixExpression< E >
	MatrixExpression ()

	~MatrixExpression ()

Protected Member Functions inherited from CDPL::Math::Expression< E >
	Expression ()

	~Expression ()

Detailed Description

template<typename T>
class CDPL::Math::RotationMatrix< T >

\( N \times N \) rotation matrix backed by a unit quaternion (or an axis-angle representation).

The first \( 3 \times 3 \) block holds the rotation; the remaining diagonal entries are 1 (identity) and all other entries are 0. The size \( N \) is configurable and typically chosen to fit the surrounding coordinate system (e.g. 4 for homogeneous transformations).

Template Parameters

T	The scalar value type.

Member Typedef Documentation

◆ ValueType

template<typename T >

typedef T CDPL::Math::RotationMatrix< T >::ValueType

The scalar value type.

◆ Reference

template<typename T >

typedef const T CDPL::Math::RotationMatrix< T >::Reference

Reference type (always a const reference — elements are computed).

◆ ConstReference

template<typename T >

typedef const T CDPL::Math::RotationMatrix< T >::ConstReference

Constant reference type to an element.

◆ SizeType

template<typename T >

typedef std::size_t CDPL::Math::RotationMatrix< T >::SizeType

The unsigned size type.

◆ DifferenceType

template<typename T >

typedef std::ptrdiff_t CDPL::Math::RotationMatrix< T >::DifferenceType

The signed difference type.

◆ ClosureType

template<typename T >

typedef MatrixReference<SelfType> CDPL::Math::RotationMatrix< T >::ClosureType

Closure type used when this matrix appears inside another expression.

◆ ConstClosureType

template<typename T >

typedef const MatrixReference<const SelfType> CDPL::Math::RotationMatrix< T >::ConstClosureType

Constant closure type used when this matrix appears inside another expression.

◆ MatrixTemporaryType

template<typename T >

typedef Matrix<T, std::vector<T> > CDPL::Math::RotationMatrix< T >::MatrixTemporaryType

Concrete temporary matrix type used by expression-template machinery.

◆ VectorTemporaryType

template<typename T >

typedef Vector<T, std::vector<T> > CDPL::Math::RotationMatrix< T >::VectorTemporaryType

Concrete temporary vector type used when assembling vectors from this matrix.

Constructor & Destructor Documentation

◆ RotationMatrix() [1/3]

template<typename T >

template<typename E >

CDPL::Math::RotationMatrix< T >::RotationMatrix	(	SizeType	n,
		const QuaternionExpression< E > &	q
	)

inline

Constructs an \( N \times N \) rotation matrix from the unit quaternion q.

Template Parameters

E	The quaternion expression type.

Parameters

n	The matrix dimension N.
q	The unit quaternion expressing the rotation.

◆ RotationMatrix() [2/3]

template<typename T >

template<typename T1 , typename T2 , typename T3 , typename T4 >

CDPL::Math::RotationMatrix< T >::RotationMatrix	(	SizeType	n,
		const T1 &	w,
		const T2 &	ux,
		const T3 &	uy,
		const T4 &	uz
	)

inline

Constructs an \( N \times N \) rotation matrix from an axis-angle representation.

Template Parameters

T1	The rotation-angle scalar type.
T2	The x-axis component scalar type.
T3	The y-axis component scalar type.
T4	The z-axis component scalar type.

Parameters

n	The matrix dimension N.
w	The rotation angle (in radians).
ux	The x-component of the rotation axis (unit vector).
uy	The y-component of the rotation axis (unit vector).
uz	The z-component of the rotation axis (unit vector).

◆ RotationMatrix() [3/3]

template<typename T >

CDPL::Math::RotationMatrix< T >::RotationMatrix ( const RotationMatrix< T > & m )

inline

Constructs a copy of the rotation matrix m.

Parameters

m	The rotation matrix to copy.

Member Function Documentation

◆ set() [1/2]

template<typename T >

template<typename E >

void CDPL::Math::RotationMatrix< T >::set ( const QuaternionExpression< E > & q )

inline

Sets the rotation from the unit quaternion q.

Template Parameters

E	The quaternion expression type.

Parameters

q	The unit quaternion expressing the rotation.

◆ set() [2/2]

template<typename T >

template<typename T1 , typename T2 , typename T3 , typename T4 >

void CDPL::Math::RotationMatrix< T >::set	(	const T1 &	w,
		const T2 &	ux,
		const T3 &	uy,
		const T4 &	uz
	)

inline

Sets the rotation from an axis-angle representation.

Template Parameters

T1	The rotation-angle scalar type.
T2	The x-axis component scalar type.
T3	The y-axis component scalar type.
T4	The z-axis component scalar type.

Parameters

w	The rotation angle (in radians).
ux	The x-component of the rotation axis (unit vector).
uy	The y-component of the rotation axis (unit vector).
uz	The z-component of the rotation axis (unit vector).

◆ operator()()

template<typename T >

ConstReference CDPL::Math::RotationMatrix< T >::operator()	(	SizeType	i,
		SizeType	j
	)		const

inline

Returns the rotation-matrix entry at (i, j).

Parameters

i	The zero-based row index.
j	The zero-based column index.

Returns: The matrix entry (computed from the stored unit quaternion).

Exceptions

Base::IndexError if either index is out of range.

◆ isEmpty()

template<typename T >

bool CDPL::Math::RotationMatrix< T >::isEmpty ( ) const

inline

Tells whether the matrix is empty (size zero).

Returns: true if N is zero, and false otherwise.

◆ getSize1()

template<typename T >

SizeType CDPL::Math::RotationMatrix< T >::getSize1 ( ) const

inline

Returns the dimension N (the row count).

Returns: N.

◆ getSize2()

template<typename T >

SizeType CDPL::Math::RotationMatrix< T >::getSize2 ( ) const

inline

Returns the dimension N (the column count).

Returns: N.

◆ getMaxSize1()

template<typename T >

SizeType CDPL::Math::RotationMatrix< T >::getMaxSize1 ( ) const

inline

Returns the maximum representable row count.

Returns: The maximum row count.

◆ getMaxSize2()

template<typename T >

SizeType CDPL::Math::RotationMatrix< T >::getMaxSize2 ( ) const

inline

Returns the maximum representable column count.

Returns: The maximum column count.

◆ operator=()

template<typename T >

RotationMatrix& CDPL::Math::RotationMatrix< T >::operator= ( const RotationMatrix< T > & m )

inline

Copy-assigns the dimension and the underlying quaternion components from m.

Parameters

m	The source rotation matrix.

Returns: A reference to itself.

◆ swap()

template<typename T >

void CDPL::Math::RotationMatrix< T >::swap ( RotationMatrix< T > & m )

inline

Swaps the dimension and the underlying quaternion components with m.

Parameters

m	The rotation matrix to swap with.

◆ resize()

template<typename T >

void CDPL::Math::RotationMatrix< T >::resize ( SizeType n )

inline

Resizes the matrix dimension to n (the underlying quaternion is left unchanged).

Parameters

n	The new dimension.

Friends And Related Function Documentation

◆ swap

template<typename T >

void swap	(	RotationMatrix< T > &	m1,
		RotationMatrix< T > &	m2
	)

friend

ADL-enabled free-function form of swap().

Parameters

m1	The first rotation matrix.
m2	The second rotation matrix.

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

AffineTransform.hpp

Public Types

Public Member Functions

Friends

Additional Inherited Members

Detailed Description

template<typename T> class CDPL::Math::RotationMatrix< T >

Member Typedef Documentation

◆ ValueType

◆ Reference

◆ ConstReference

◆ SizeType

◆ DifferenceType

◆ ClosureType

◆ ConstClosureType

◆ MatrixTemporaryType

◆ VectorTemporaryType

Constructor & Destructor Documentation

◆ RotationMatrix() [1/3]

◆ RotationMatrix() [2/3]

◆ RotationMatrix() [3/3]

Member Function Documentation

◆ set() [1/2]

◆ set() [2/2]

◆ operator()()

◆ isEmpty()

◆ getSize1()

◆ getSize2()

◆ getMaxSize1()

◆ getMaxSize2()

◆ operator=()

◆ swap()

◆ resize()

Friends And Related Function Documentation

◆ swap

template<typename T>
class CDPL::Math::RotationMatrix< T >