numeric::Quaternion< typename > Class Template Reference

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

#include <Quaternion.fwd.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

Definition at line 23 of file Quaternion.fwd.hh.

Member Typedef Documentation

template<typename >

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

Definition at line 75 of file Quaternion.hh.

template<typename >

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

Definition at line 69 of file Quaternion.hh.

template<typename >

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

Definition at line 67 of file Quaternion.hh.

template<typename >

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

Definition at line 62 of file Quaternion.hh.

template<typename >

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

Definition at line 60 of file Quaternion.hh.

template<typename >

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

Definition at line 61 of file Quaternion.hh.

template<typename >

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

Definition at line 68 of file Quaternion.hh.

template<typename >

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

Definition at line 59 of file Quaternion.hh.

template<typename >

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

Definition at line 66 of file Quaternion.hh.

template<typename >

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

Definition at line 72 of file Quaternion.hh.

template<typename >

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

Definition at line 58 of file Quaternion.hh.

template<typename >

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

Definition at line 65 of file Quaternion.hh.

Constructor & Destructor Documentation

template<typename >

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

inline

Default constructor.

Definition at line 83 of file Quaternion.hh.

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.

Definition at line 93 of file Quaternion.hh.

template<typename >

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

inline

Copy constructor.

Definition at line 122 of file Quaternion.hh.

template<typename >

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

inline

Destructor.

Definition at line 132 of file Quaternion.hh.

Member Function Documentation

template<typename >

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

inline

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

Definition at line 320 of file Quaternion.hh.

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.

Definition at line 444 of file Quaternion.hh.

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])

Definition at line 329 of file Quaternion.hh.

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])

Definition at line 338 of file Quaternion.hh.

template<typename >

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

inline

Conjugate.

Definition at line 420 of file Quaternion.hh.

template<typename >

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

inline

Conjugated.

Definition at line 537 of file Quaternion.hh.

template<typename >

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

inline

Dot product.

Definition at line 350 of file Quaternion.hh.

template<typename >

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

inline

Dot product.

Definition at line 359 of file Quaternion.hh.

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

Definition at line 597 of file Quaternion.hh.

template<typename >

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

inlinestatic

Identity named constructor.

Definition at line 114 of file Quaternion.hh.

template<typename >

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

inline

Inverse.

Definition at line 546 of file Quaternion.hh.

template<typename >

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

inline

Invert.

Definition at line 432 of file Quaternion.hh.

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?

Definition at line 302 of file Quaternion.hh.

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.

Definition at line 453 of file Quaternion.hh.

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.

Definition at line 487 of file Quaternion.hh.

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

template<typename >

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

inline

Magnitude: Should be one.

Definition at line 266 of file Quaternion.hh.

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

template<typename >

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

inline

Magnitude error.

Definition at line 284 of file Quaternion.hh.

template<typename >

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

inline

Magnitude squared: Should be one.

Definition at line 275 of file Quaternion.hh.

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

template<typename >

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

inline

Magnitude squared error.

Definition at line 293 of file Quaternion.hh.

template<typename >

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

inline

Norm: Should be one.

Definition at line 230 of file Quaternion.hh.

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

template<typename >

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

inline

Norm error.

Definition at line 248 of file Quaternion.hh.

template<typename >

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

inline

Norm squared: Should be one.

Definition at line 239 of file Quaternion.hh.

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.

Definition at line 257 of file Quaternion.hh.

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

template<typename >

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

inline

Normalize.

Definition at line 371 of file Quaternion.hh.

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.

Definition at line 389 of file Quaternion.hh.

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?

Definition at line 311 of file Quaternion.hh.

template<typename >

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

inline

Definition at line 140 of file Quaternion.hh.

template<typename >

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

inline

Right multiply by a Quaternion.

Definition at line 470 of file Quaternion.hh.

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.

Definition at line 504 of file Quaternion.hh.

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

template<typename >

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

inline

Swap.

Definition at line 521 of file Quaternion.hh.

template<typename >

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

inline

Identity.

Definition at line 407 of file Quaternion.hh.

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

template<typename >

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

inline

w

Definition at line 158 of file Quaternion.hh.

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

template<typename >

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

inline

w squared

Definition at line 194 of file Quaternion.hh.

template<typename >

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

inline

x

Definition at line 167 of file Quaternion.hh.

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

template<typename >

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

inline

x squared

Definition at line 203 of file Quaternion.hh.

template<typename >

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

inline

y

Definition at line 176 of file Quaternion.hh.

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

template<typename >

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

inline

y squared

Definition at line 212 of file Quaternion.hh.

template<typename >

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

inline

z

Definition at line 185 of file Quaternion.hh.

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

template<typename >

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

inline

z squared

Definition at line 221 of file Quaternion.hh.

Friends And Related Function Documentation

template<typename >

friend class BodyPosition< T >

friend

Definition at line 51 of file Quaternion.hh.

template<typename >

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

friend

Dot product.

Definition at line 631 of file Quaternion.hh.

template<typename >

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

friend

Dot product.

Definition at line 641 of file Quaternion.hh.

template<typename >

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

friend

Quaternion != Quaternion.

Definition at line 621 of file Quaternion.hh.

template<typename >

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

friend

Quaternion * Quaternion.

Definition at line 556 of file Quaternion.hh.

template<typename >

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

friend

Quaternion == Quaternion.

Definition at line 611 of file Quaternion.hh.

template<typename >

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

friend

Product: Quaternion * Quaternion.

Definition at line 571 of file Quaternion.hh.

Member Data Documentation

template<typename >

Value numeric::Quaternion< typename >::w_

private

w coordinate

Definition at line 651 of file Quaternion.hh.

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

Definition at line 654 of file Quaternion.hh.

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

Definition at line 657 of file Quaternion.hh.

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

Definition at line 660 of file Quaternion.hh.

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