numeric::Quaternion< typename > Class Template Reference

Unit quaternion 3-D orientation representation. More...

#include <Quaternion.hh>

Public Types
typedef T	Value
typedef T &	Reference
typedef T const &	ConstReference
typedef T *	Pointer
typedef T const *	ConstPointer
typedef T	value_type
typedef T &	reference
typedef T const &	const_reference
typedef T *	pointer
typedef T const *	const_pointer
typedef NumericTraits< T >	Traits
typedef xyzVector< T >	Axis

Public Member Functions
	Quaternion ()
	Default constructor. More...
	Quaternion (Value const &w_a, Value const &x_a, Value const &y_a, Value const &z_a, bool const precise=true)
	Coordinate constructor. More...
	Quaternion (Quaternion const &q)
	Copy constructor. More...
	~Quaternion ()
	Destructor. More...
Quaternion &	operator= (Quaternion const &q)
Value const &	w () const
	w More...
Value const &	x () const
	x More...
Value const &	y () const
	y More...
Value const &	z () const
	z More...
Value	w_squared () const
	w squared More...
Value	x_squared () const
	x squared More...
Value	y_squared () const
	y squared More...
Value	z_squared () const
	z squared More...
Value	norm () const
	Norm: Should be one. More...
Value	norm_squared () const
	Norm squared: Should be one. More...
Value	norm_error () const
	Norm error. More...
Value	norm_squared_error () const
	Norm squared error. More...
Value	magnitude () const
	Magnitude: Should be one. More...
Value	magnitude_squared () const
	Magnitude squared: Should be one. More...
Value	magnitude_error () const
	Magnitude error. More...
Value	magnitude_squared_error () const
	Magnitude squared error. More...
bool	is_normalized (Value const &tol=Traits::quaternion_tolerance()) const
	Magnitude squared error within tolerance? More...
bool	not_normalized (Value const &tol=Traits::quaternion_tolerance()) const
	Magnitude squared error exceeds tolerance? More...
Value	angle () const
	Principal angle of rotation (on [0,2*pi]) More...
Axis	axis () const
	Axis of Rotation unit vector (direction for angle on [0,2*pi]) More...
Axis &	axis (Axis &u) const
	Axis of rotation unit vector: Passed vector (direction for angle on [0,2*pi]) More...
Value	dot (Quaternion const &q) const
	Dot product. More...
Value	dot_product (Quaternion const &q) const
	Dot product. More...
Quaternion &	normalize ()
	Normalize. More...
Quaternion &	normalize_if_needed (Value const &tol=Traits::quaternion_tolerance())
	Normalize if magnitude squared error exceeds tolerance. More...
Quaternion &	to_identity ()
	Identity. More...
Quaternion &	conjugate ()
	Conjugate. More...
Quaternion &	invert ()
	Invert. More...
Quaternion &	apply (Quaternion const &q, bool const precise=true)
	Apply a successive Quaternion. More...
Quaternion &	left_multiply_by (Quaternion const &q, bool const precise=true)
	Left multiply by a Quaternion. More...
Quaternion &	right_multiply_by (Quaternion const &q, bool const precise=true)
	Right multiply by a Quaternion. More...
Quaternion &	left_multiply_by_inverse_of (Quaternion const &q, bool const precise=true)
	Left multiply by the inverse of a Quaternion. More...
Quaternion &	right_multiply_by_inverse_of (Quaternion const &q, bool const precise=true)
	Right multiply by the inverse of a Quaternion. More...
void	swap (Quaternion &q)
	Swap. More...
Quaternion	conjugated () const
	Conjugated. More...
Quaternion	inverse () const
	Inverse. More...

Static Public Member Functions
static Quaternion	identity ()
	Identity named constructor. More...
static Quaternion const &	I ()
	Identity Quaternion for expressions. More...

Private Attributes
Value	w_
	w coordinate More...
Value	x_
	x coordinate More...
Value	y_
	y coordinate More...
Value	z_
	z coordinate More...

Friends
class	BodyPosition< T >
Quaternion	operator* (Quaternion const &q2, Quaternion const &q1)
	Quaternion * Quaternion. More...
Quaternion	product (Quaternion const &q2, Quaternion const &q1, bool const precise=true)
	Product: Quaternion * Quaternion. More...
bool	operator== (Quaternion const &q1, Quaternion const &q2)
	Quaternion == Quaternion. More...
bool	operator!= (Quaternion const &q1, Quaternion const &q2)
	Quaternion != Quaternion. More...
Value	dot (Quaternion const &q1, Quaternion const &q2)
	Dot product. More...
Value	dot_product (Quaternion const &q1, Quaternion const &q2)
	Dot product. More...

Detailed Description

template<typename>
class numeric::Quaternion< typename >

Unit quaternion 3-D orientation representation.

Remarks

• Quaternion defined as ( w, x, y, z )
• Quaternions must be in the same coordinate frame to be used together
• Successive rotation convention: q2 * q1 means q1 followed by q2
• Performance-critical code can suppress normalization after every modification and use explicit normalization

Member Typedef Documentation

template<typename >

typedef xyzVector< T > numeric::Quaternion< typename >::Axis

template<typename >

typedef T const* numeric::Quaternion< typename >::const_pointer

template<typename >

typedef T const& numeric::Quaternion< typename >::const_reference

template<typename >

typedef T const* numeric::Quaternion< typename >::ConstPointer

template<typename >

typedef T const& numeric::Quaternion< typename >::ConstReference

template<typename >

typedef T* numeric::Quaternion< typename >::Pointer

template<typename >

typedef T* numeric::Quaternion< typename >::pointer

template<typename >

typedef T& numeric::Quaternion< typename >::Reference

template<typename >

typedef T& numeric::Quaternion< typename >::reference

template<typename >

typedef NumericTraits< T > numeric::Quaternion< typename >::Traits

template<typename >

typedef T numeric::Quaternion< typename >::Value

template<typename >

typedef T numeric::Quaternion< typename >::value_type

Constructor & Destructor Documentation

template<typename >

numeric::Quaternion< typename >::Quaternion ( )

inline

Default constructor.

Referenced by numeric::Quaternion< T >::conjugated(), numeric::Quaternion< T >::identity(), and numeric::Quaternion< T >::inverse().

template<typename >

numeric::Quaternion< typename >::Quaternion ( Value const &  w_a, Value const &  x_a, Value const &  y_a, Value const &  z_a, bool const  precise = true  )

inline

Coordinate constructor.

template<typename >

numeric::Quaternion< typename >::Quaternion ( Quaternion< typename > const &  q )

inline

Copy constructor.

template<typename >

numeric::Quaternion< typename >::~Quaternion ( )

inline

Destructor.

Member Function Documentation

template<typename >

Value numeric::Quaternion< typename >::angle ( ) const

inline

Principal angle of rotation (on [0,2*pi])

Referenced by numeric::BodyPosition< typename >::angle().

template<typename >

Quaternion& numeric::Quaternion< typename >::apply ( Quaternion< typename > const &  q, bool const  precise = true  )

inline

Apply a successive Quaternion.

Referenced by src.protocols.jd2.RosettaScriptWrapper::apply_to_failure().

template<typename >

Axis numeric::Quaternion< typename >::axis ( ) const

inline

Axis of Rotation unit vector (direction for angle on [0,2*pi])

Referenced by numeric::BodyPosition< typename >::axis().

template<typename >

Axis& numeric::Quaternion< typename >::axis ( Axis &  u ) const

inline

Axis of rotation unit vector: Passed vector (direction for angle on [0,2*pi])

template<typename >

Quaternion& numeric::Quaternion< typename >::conjugate ( )

inline

Conjugate.

template<typename >

Quaternion numeric::Quaternion< typename >::conjugated ( ) const

inline

Conjugated.

template<typename >

Value numeric::Quaternion< typename >::dot ( Quaternion< typename > const &  q ) const

inline

Dot product.

template<typename >

Value numeric::Quaternion< typename >::dot_product ( Quaternion< typename > const &  q ) const

inline

Dot product.

template<typename >

static Quaternion const& numeric::Quaternion< typename >::I ( )

inlinestatic

Identity Quaternion for expressions.

Note

Default and identity() named constructors can be faster for construction

Can be safely used in construction of global objects

template<typename >

static Quaternion numeric::Quaternion< typename >::identity ( )

inlinestatic

Identity named constructor.

template<typename >

Quaternion numeric::Quaternion< typename >::inverse ( ) const

inline

Inverse.

template<typename >

Quaternion& numeric::Quaternion< typename >::invert ( )

inline

Invert.

Referenced by numeric::BodyPosition< typename >::invert().

template<typename >

bool numeric::Quaternion< typename >::is_normalized ( Value const &  tol = Traits::quaternion_tolerance() ) const

inline

Magnitude squared error within tolerance?

Referenced by numeric::Quaternion< T >::Quaternion().

template<typename >

Quaternion& numeric::Quaternion< typename >::left_multiply_by ( Quaternion< typename > const &  q, bool const  precise = true  )

inline

Left multiply by a Quaternion.

Referenced by numeric::Quaternion< T >::apply(), and numeric::BodyPosition< typename >::left_transform_by().

template<typename >

Quaternion& numeric::Quaternion< typename >::left_multiply_by_inverse_of ( Quaternion< typename > const &  q, bool const  precise = true  )

inline

Left multiply by the inverse of a Quaternion.

Referenced by numeric::BodyPosition< typename >::left_transform_by_inverse_of().

template<typename >

Value numeric::Quaternion< typename >::magnitude ( ) const

inline

Magnitude: Should be one.

Referenced by numeric::Quaternion< T >::magnitude_error().

template<typename >

Value numeric::Quaternion< typename >::magnitude_error ( ) const

inline

Magnitude error.

template<typename >

Value numeric::Quaternion< typename >::magnitude_squared ( ) const

inline

Magnitude squared: Should be one.

Referenced by numeric::Quaternion< T >::magnitude_squared_error().

template<typename >

Value numeric::Quaternion< typename >::magnitude_squared_error ( ) const

inline

Magnitude squared error.

template<typename >

Value numeric::Quaternion< typename >::norm ( ) const

inline

Norm: Should be one.

Referenced by numeric::Quaternion< T >::norm_error().

template<typename >

Value numeric::Quaternion< typename >::norm_error ( ) const

inline

Norm error.

template<typename >

Value numeric::Quaternion< typename >::norm_squared ( ) const

inline

Norm squared: Should be one.

Referenced by numeric::Quaternion< T >::norm_squared_error(), numeric::Quaternion< T >::normalize(), and numeric::Quaternion< T >::normalize_if_needed().

template<typename >

Value numeric::Quaternion< typename >::norm_squared_error ( ) const

inline

Norm squared error.

Referenced by numeric::Quaternion< T >::is_normalized(), and numeric::Quaternion< T >::not_normalized().

template<typename >

Quaternion& numeric::Quaternion< typename >::normalize ( )

inline

Normalize.

Referenced by numeric::Quaternion< T >::left_multiply_by(), numeric::Quaternion< T >::left_multiply_by_inverse_of(), numeric::BodyPosition< typename >::normalize(), numeric::BodyPosition< typename >::q_refresh(), numeric::Quaternion< T >::Quaternion(), numeric::BodyPosition< typename >::R_refresh(), numeric::Quaternion< T >::right_multiply_by(), and numeric::Quaternion< T >::right_multiply_by_inverse_of().

template<typename >

Quaternion& numeric::Quaternion< typename >::normalize_if_needed ( Value const &  tol = Traits::quaternion_tolerance() )

inline

Normalize if magnitude squared error exceeds tolerance.

Referenced by numeric::BodyPosition< typename >::normalize_if_needed().

template<typename >

bool numeric::Quaternion< typename >::not_normalized ( Value const &  tol = Traits::quaternion_tolerance() ) const

inline

Magnitude squared error exceeds tolerance?

template<typename >

Quaternion& numeric::Quaternion< typename >::operator= ( Quaternion< typename > const &  q )

inline

template<typename >

Quaternion& numeric::Quaternion< typename >::right_multiply_by ( Quaternion< typename > const &  q, bool const  precise = true  )

inline

Right multiply by a Quaternion.

Referenced by numeric::BodyPosition< typename >::right_transform_by().

template<typename >

Quaternion& numeric::Quaternion< typename >::right_multiply_by_inverse_of ( Quaternion< typename > const &  q, bool const  precise = true  )

inline

Right multiply by the inverse of a Quaternion.

Referenced by numeric::BodyPosition< typename >::right_transform_by_inverse_of().

template<typename >

void numeric::Quaternion< typename >::swap ( Quaternion< typename > &  q )

inline

Swap.

template<typename >

Quaternion& numeric::Quaternion< typename >::to_identity ( )

inline

Identity.

Referenced by numeric::BodyPosition< typename >::to_identity().

template<typename >

Value const& numeric::Quaternion< typename >::w ( ) const

inline

w

Referenced by numeric::operator>>(), and numeric::random::random_rotation().

template<typename >

Value numeric::Quaternion< typename >::w_squared ( ) const

inline

w squared

template<typename >

Value const& numeric::Quaternion< typename >::x ( ) const

inline

x

Referenced by numeric::operator>>(), and numeric::random::random_rotation().

template<typename >

Value numeric::Quaternion< typename >::x_squared ( ) const

inline

x squared

template<typename >

Value const& numeric::Quaternion< typename >::y ( ) const

inline

y

Referenced by numeric::operator>>(), and numeric::random::random_rotation().

template<typename >

Value numeric::Quaternion< typename >::y_squared ( ) const

inline

y squared

template<typename >

Value const& numeric::Quaternion< typename >::z ( ) const

inline

z

Referenced by numeric::operator>>(), and numeric::random::random_rotation().

template<typename >

Value numeric::Quaternion< typename >::z_squared ( ) const

inline

z squared

Friends And Related Function Documentation

template<typename >

friend class BodyPosition< T >

friend

template<typename >

Value dot ( Quaternion< typename > const &  q1, Quaternion< typename > const &  q2  )

friend

Dot product.

template<typename >

Value dot_product ( Quaternion< typename > const &  q1, Quaternion< typename > const &  q2  )

friend

Dot product.

template<typename >

bool operator!= ( Quaternion< typename > const &  q1, Quaternion< typename > const &  q2  )

friend

Quaternion != Quaternion.

template<typename >

Quaternion operator* ( Quaternion< typename > const &  q2, Quaternion< typename > const &  q1  )

friend

Quaternion * Quaternion.

template<typename >

bool operator== ( Quaternion< typename > const &  q1, Quaternion< typename > const &  q2  )

friend

Quaternion == Quaternion.

template<typename >

Quaternion product ( Quaternion< typename > const &  q2, Quaternion< typename > const &  q1, bool const  precise = true  )

friend

Product: Quaternion * Quaternion.

Member Data Documentation

template<typename >

Value numeric::Quaternion< typename >::w_

private

w coordinate

Referenced by numeric::Quaternion< T >::angle(), numeric::Quaternion< T >::conjugated(), numeric::Quaternion< T >::dot(), numeric::Quaternion< T >::dot_product(), numeric::Quaternion< T >::inverse(), numeric::Quaternion< T >::left_multiply_by(), numeric::Quaternion< T >::left_multiply_by_inverse_of(), numeric::Quaternion< T >::magnitude(), numeric::Quaternion< T >::magnitude_squared(), numeric::Quaternion< T >::norm(), numeric::Quaternion< T >::norm_squared(), numeric::Quaternion< T >::normalize(), numeric::Quaternion< T >::normalize_if_needed(), numeric::Quaternion< T >::operator=(), numeric::BodyPosition< typename >::q_refresh(), numeric::BodyPosition< typename >::R_refresh(), numeric::Quaternion< T >::right_multiply_by(), numeric::Quaternion< T >::right_multiply_by_inverse_of(), numeric::Quaternion< T >::swap(), numeric::Quaternion< T >::to_identity(), numeric::Quaternion< T >::w(), and numeric::Quaternion< T >::w_squared().

template<typename >

Value numeric::Quaternion< typename >::x_

private

x coordinate

Referenced by numeric::Quaternion< T >::axis(), numeric::Quaternion< T >::conjugate(), numeric::Quaternion< T >::conjugated(), numeric::Quaternion< T >::dot(), numeric::Quaternion< T >::dot_product(), numeric::Quaternion< T >::inverse(), numeric::Quaternion< T >::invert(), numeric::Quaternion< T >::left_multiply_by(), numeric::Quaternion< T >::left_multiply_by_inverse_of(), numeric::Quaternion< T >::magnitude(), numeric::Quaternion< T >::magnitude_squared(), numeric::Quaternion< T >::norm(), numeric::Quaternion< T >::norm_squared(), numeric::Quaternion< T >::normalize(), numeric::Quaternion< T >::normalize_if_needed(), numeric::Quaternion< T >::operator=(), numeric::BodyPosition< typename >::q_refresh(), numeric::BodyPosition< typename >::R_refresh(), numeric::Quaternion< T >::right_multiply_by(), numeric::Quaternion< T >::right_multiply_by_inverse_of(), numeric::Quaternion< T >::swap(), numeric::Quaternion< T >::to_identity(), numeric::Quaternion< T >::x(), and numeric::Quaternion< T >::x_squared().

template<typename >

Value numeric::Quaternion< typename >::y_

private

y coordinate

Referenced by numeric::Quaternion< T >::axis(), numeric::Quaternion< T >::conjugate(), numeric::Quaternion< T >::conjugated(), numeric::Quaternion< T >::dot(), numeric::Quaternion< T >::dot_product(), numeric::Quaternion< T >::inverse(), numeric::Quaternion< T >::invert(), numeric::Quaternion< T >::left_multiply_by(), numeric::Quaternion< T >::left_multiply_by_inverse_of(), numeric::Quaternion< T >::magnitude(), numeric::Quaternion< T >::magnitude_squared(), numeric::Quaternion< T >::norm(), numeric::Quaternion< T >::norm_squared(), numeric::Quaternion< T >::normalize(), numeric::Quaternion< T >::normalize_if_needed(), numeric::Quaternion< T >::operator=(), numeric::BodyPosition< typename >::q_refresh(), numeric::BodyPosition< typename >::R_refresh(), numeric::Quaternion< T >::right_multiply_by(), numeric::Quaternion< T >::right_multiply_by_inverse_of(), numeric::Quaternion< T >::swap(), numeric::Quaternion< T >::to_identity(), numeric::Quaternion< T >::y(), and numeric::Quaternion< T >::y_squared().

template<typename >

Value numeric::Quaternion< typename >::z_

private

z coordinate

Referenced by numeric::Quaternion< T >::axis(), numeric::Quaternion< T >::conjugate(), numeric::Quaternion< T >::conjugated(), numeric::Quaternion< T >::dot(), numeric::Quaternion< T >::dot_product(), numeric::Quaternion< T >::inverse(), numeric::Quaternion< T >::invert(), numeric::Quaternion< T >::left_multiply_by(), numeric::Quaternion< T >::left_multiply_by_inverse_of(), numeric::Quaternion< T >::magnitude(), numeric::Quaternion< T >::magnitude_squared(), numeric::Quaternion< T >::norm(), numeric::Quaternion< T >::norm_squared(), numeric::Quaternion< T >::normalize(), numeric::Quaternion< T >::normalize_if_needed(), numeric::Quaternion< T >::operator=(), numeric::BodyPosition< typename >::q_refresh(), numeric::BodyPosition< typename >::R_refresh(), numeric::Quaternion< T >::right_multiply_by(), numeric::Quaternion< T >::right_multiply_by_inverse_of(), numeric::Quaternion< T >::swap(), numeric::Quaternion< T >::to_identity(), numeric::Quaternion< T >::z(), and numeric::Quaternion< T >::z_squared().

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

• src/numeric/Quaternion.fwd.hh
• src/numeric/Quaternion.hh