Rigid body 3-D position/transform. More...

#include <BodyPosition.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

typedef xyzVector< T >	Point

typedef xyzVector< T >	Vector

typedef xyzVector< T >	Translation

typedef xyzMatrix< T >	Rotation

typedef numeric::Quaternion< T >	Quaternion

Public Member Functions
	BodyPosition ()
	Default constructor. More...

	BodyPosition (Rotation const &R_a, Translation const &t_a)
	Rotation + Translation constructor. More...

	BodyPosition (Rotation const &R_a)
	Rotation constructor. More...

	BodyPosition (Quaternion const &q_a, Translation const &t_a)
	Quaternion + Translation constructor. More...

	BodyPosition (Quaternion const &q_a)
	Quaternion constructor. More...

	BodyPosition (Point const &, Vector const &x1, Vector const &u1, Point const &, Vector const &x2, Vector const &u2, Value const &cos, Value const &sin, Value const &csc)
	Point + Vector constructor. More...

	BodyPosition (BodyPosition const &bp)
	Copy constructor. More...

	~BodyPosition ()
	Destructor. More...

BodyPosition &	operator= (BodyPosition const &bp)
	Copy assignment. More...

Rotation const &	R () const
	Rotation. More...

Quaternion const &	q () const
	Quaternion. More...

Translation const &	t () const
	Translation. 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...

BodyPosition const &	operator() (Point &p) const
	Transform a Point. More...

BodyPosition const &	transform (Point &p) const
	Transform a Point. More...

BodyPosition const &	inverse_transform (Point &p) const
	Inverse transform a Point. More...

BodyPosition &	normalize ()
	Normalize. More...

BodyPosition &	normalize_if_needed (Value const &tol=Traits::quaternion_tolerance())
	Normalize if magnitude squared error exceeds tolerance. More...

BodyPosition &	to_identity ()
	Identity. More...

BodyPosition &	invert ()
	Invert. More...

BodyPosition &	apply (BodyPosition const &p, bool const precise=true)
	Apply a successive BodyPosition transformation. More...

BodyPosition &	left_transform_by (BodyPosition const &p, bool const precise=true)
	Left transform by a BodyPosition. More...

BodyPosition &	right_transform_by (BodyPosition const &p, bool const precise=true)
	Right transform by a BodyPosition. More...

BodyPosition &	left_transform_by_inverse_of (BodyPosition const &p, bool const precise=true)
	Left transform by the inverse of a BodyPosition. More...

BodyPosition &	right_transform_by_inverse_of (BodyPosition const &p, bool const precise=true)
	Right transform by the inverse of a BodyPosition. More...

BodyPosition	inverse () const
	Inverse. More...

Point	transformed (Point const &p) const
	Transformed Point. More...

Point	inverse_transformed (Point const &p) const
	Inverse transformed Point. More...

Translation	inverse_translation () const
	Inverse translation. More...

Static Public Member Functions
static BodyPosition	identity ()
	Identity named constructor. More...

static BodyPosition const &	I ()
	Identity BodyPosition for expressions. More...

Private Member Functions
BodyPosition const &	R_refresh (bool const precise=true) const
	Refresh rotation matrix from Quaternion. More...

BodyPosition const &	q_refresh (bool const precise=true) const
	Refresh Quaternion from rotation matrix. More...

Private Attributes
Rotation	R_
	Rotation matrix. More...

bool	R_fresh_
	Rotation matrix status. More...

Quaternion	q_
	Quaternion. More...

bool	q_fresh_
	Quaternion status. More...

Translation	t_
	Translation. More...

Friends
bool	operator== (BodyPosition const &p1, BodyPosition const &p2)
	BodyPosition == BodyPosition. More...

bool	operator!= (BodyPosition const &p1, BodyPosition const &p2)
	BodyPosition != BodyPosition. More...

Detailed Description

template<typename>
class numeric::BodyPosition< typename >

Rigid body 3-D position/transform.

Remarks

Dual personality: rotation matrix and quaternion representations
Rotation matrix is faster for transforming points
Quaternion is faster for successive frame transforms and easier to keep normalized
For quaternion q = ( w, x, y, z ) the equivalent rotation matrix is: 1-2( y^2 + z^2 ) 2( x y - w z ) 2( x z + w y ) 2( x y + w z ) 1-2( x^2 + z^2 ) 2( y z - w x ) 2( x z - w y ) 2( y z + w x ) 1-2( x^2 + y^2 )
Quaternions q and -q have the same rotation matrix
If an odd multiple of 2*pi is added to an angle the quaternion q is changed to -q
Invariant: The rotation matrix or quaternion or both must be "fresh" before and after every member function call

Member Typedef Documentation

template<typename >

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

template<typename >

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

template<typename >

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

template<typename >

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

template<typename >

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

template<typename >

typedef xyzVector< T > numeric::BodyPosition< typename >::Point

template<typename >

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

template<typename >

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

template<typename >

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

template<typename >

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

template<typename >

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

template<typename >

typedef xyzMatrix< T > numeric::BodyPosition< typename >::Rotation

template<typename >

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

template<typename >

typedef xyzVector< T > numeric::BodyPosition< typename >::Translation

template<typename >

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

template<typename >

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

template<typename >

typedef xyzVector< T > numeric::BodyPosition< typename >::Vector

Constructor & Destructor Documentation

template<typename >

numeric::BodyPosition< typename >::BodyPosition ( )

inline

Default constructor.

Referenced by numeric::BodyPosition< typename >::identity(), and numeric::BodyPosition< typename >::inverse().

template<typename >

numeric::BodyPosition< typename >::BodyPosition	(	Rotation const &	R_a,
		Translation const &	t_a
	)

inline

Rotation + Translation constructor.

template<typename >

numeric::BodyPosition< typename >::BodyPosition ( Rotation const & R_a )

inline

Rotation constructor.

template<typename >

numeric::BodyPosition< typename >::BodyPosition	(	Quaternion const &	q_a,
		Translation const &	t_a
	)

inline

Quaternion + Translation constructor.

template<typename >

numeric::BodyPosition< typename >::BodyPosition ( Quaternion const & q_a )

inline

Quaternion constructor.

template<typename >

numeric::BodyPosition< typename >::BodyPosition	(	Point const &	,
		Vector const &	x1,
		Vector const &	u1,
		Point const &	,
		Vector const &	x2,
		Vector const &	u2,
		Value const &	cos,
		Value const &	sin,
		Value const &	csc
	)

inline

Point + Vector constructor.

Note: Constructs the transform that takes a point p and unit vectors x and u bound to p and separated by an angle on (0,pi) from position 1 to 2

References numeric::csc(), numeric::xyzVector< typename >::is_normalized(), and basic::T().

template<typename >

numeric::BodyPosition< typename >::BodyPosition ( BodyPosition< typename > const & bp )

inline

Copy constructor.

template<typename >

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

inline

Destructor.

Member Function Documentation

template<typename >

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

inline

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

References numeric::Quaternion< typename >::angle(), numeric::BodyPosition< typename >::q_, numeric::BodyPosition< typename >::q_fresh_, and numeric::BodyPosition< typename >::q_refresh().

template<typename >

BodyPosition& numeric::BodyPosition< typename >::apply	(	BodyPosition< typename > const &	p,
		bool const	precise = `true`
	)

inline

Apply a successive BodyPosition transformation.

References numeric::BodyPosition< typename >::left_transform_by().

template<typename >

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

inline

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

References numeric::Quaternion< typename >::axis(), numeric::BodyPosition< typename >::q_, numeric::BodyPosition< typename >::q_fresh_, and numeric::BodyPosition< typename >::q_refresh().

template<typename >

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

inline

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

References numeric::Quaternion< typename >::axis(), numeric::BodyPosition< typename >::q_, numeric::BodyPosition< typename >::q_fresh_, and numeric::BodyPosition< typename >::q_refresh().

template<typename >

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

inlinestatic

Identity BodyPosition 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 BodyPosition numeric::BodyPosition< typename >::identity ( )

inlinestatic

Identity named constructor.

References numeric::BodyPosition< typename >::BodyPosition().

template<typename >

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

inline

Inverse.

References numeric::BodyPosition< typename >::BodyPosition().

template<typename >

BodyPosition const& numeric::BodyPosition< typename >::inverse_transform ( Point & p ) const

inline

Inverse transform a Point.

References numeric::inplace_transpose_product(), numeric::BodyPosition< typename >::R_, numeric::BodyPosition< typename >::R_fresh_, numeric::BodyPosition< typename >::R_refresh(), and numeric::BodyPosition< typename >::t_.

template<typename >

Point numeric::BodyPosition< typename >::inverse_transformed ( Point const & p ) const

inline

Inverse transformed Point.

References numeric::BodyPosition< typename >::R_, numeric::BodyPosition< typename >::R_fresh_, numeric::BodyPosition< typename >::R_refresh(), numeric::BodyPosition< typename >::t_, and numeric::transpose_product().

template<typename >

Translation numeric::BodyPosition< typename >::inverse_translation ( ) const

inline

Inverse translation.

References numeric::BodyPosition< typename >::R_, numeric::BodyPosition< typename >::R_fresh_, numeric::BodyPosition< typename >::R_refresh(), numeric::BodyPosition< typename >::t_, and numeric::transpose_product().

template<typename >

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

inline

Invert.

References numeric::inplace_product(), numeric::Quaternion< typename >::invert(), numeric::BodyPosition< typename >::q_, numeric::BodyPosition< typename >::q_fresh_, numeric::BodyPosition< typename >::R_, numeric::BodyPosition< typename >::R_fresh_, numeric::BodyPosition< typename >::R_refresh(), basic::T(), numeric::BodyPosition< typename >::t_, and numeric::xyzMatrix< typename >::transpose().

template<typename >

BodyPosition& numeric::BodyPosition< typename >::left_transform_by	(	BodyPosition< typename > const &	p,
		bool const	precise = `true`
	)

inline

Left transform by a BodyPosition.

References numeric::Quaternion< typename >::left_multiply_by(), numeric::BodyPosition< typename >::q_, numeric::BodyPosition< typename >::q_fresh_, numeric::BodyPosition< typename >::q_refresh(), numeric::BodyPosition< typename >::R_fresh_, and numeric::BodyPosition< typename >::t_.

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

template<typename >

BodyPosition& numeric::BodyPosition< typename >::left_transform_by_inverse_of	(	BodyPosition< typename > const &	p,
		bool const	precise = `true`
	)

inline

Left transform by the inverse of a BodyPosition.

References numeric::Quaternion< typename >::left_multiply_by_inverse_of(), numeric::BodyPosition< typename >::q_, numeric::BodyPosition< typename >::q_fresh_, numeric::BodyPosition< typename >::q_refresh(), numeric::BodyPosition< typename >::R_fresh_, and numeric::BodyPosition< typename >::t_.

template<typename >

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

inline

Normalize.

References numeric::Quaternion< typename >::normalize(), numeric::BodyPosition< typename >::q_, numeric::BodyPosition< typename >::q_fresh_, numeric::BodyPosition< typename >::q_refresh(), and numeric::BodyPosition< typename >::R_fresh_.

template<typename >

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

inline

Normalize if magnitude squared error exceeds tolerance.

References numeric::Quaternion< typename >::normalize_if_needed(), numeric::BodyPosition< typename >::q_, numeric::BodyPosition< typename >::q_fresh_, numeric::BodyPosition< typename >::q_refresh(), and numeric::BodyPosition< typename >::R_fresh_.

template<typename >

BodyPosition const& numeric::BodyPosition< typename >::operator() ( Point & p ) const

inline

Transform a Point.

References numeric::inplace_product(), numeric::BodyPosition< typename >::R_, numeric::BodyPosition< typename >::R_fresh_, numeric::BodyPosition< typename >::R_refresh(), and numeric::BodyPosition< typename >::t_.

template<typename >

BodyPosition& numeric::BodyPosition< typename >::operator= ( BodyPosition< typename > const & bp )

inline

Copy assignment.

References numeric::BodyPosition< typename >::q_, numeric::BodyPosition< typename >::q_fresh_, numeric::BodyPosition< typename >::R_, numeric::BodyPosition< typename >::R_fresh_, and numeric::BodyPosition< typename >::t_.

template<typename >

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

inline

Quaternion.

References numeric::BodyPosition< typename >::q_, numeric::BodyPosition< typename >::q_fresh_, and numeric::BodyPosition< typename >::q_refresh().

template<typename >

BodyPosition const& numeric::BodyPosition< typename >::q_refresh ( bool const precise = true ) const

inlineprivate

Refresh Quaternion from rotation matrix.

Referenced by numeric::BodyPosition< typename >::angle(), numeric::BodyPosition< typename >::axis(), numeric::BodyPosition< typename >::left_transform_by(), numeric::BodyPosition< typename >::left_transform_by_inverse_of(), numeric::BodyPosition< typename >::normalize(), numeric::BodyPosition< typename >::normalize_if_needed(), numeric::BodyPosition< typename >::q(), numeric::BodyPosition< typename >::right_transform_by(), and numeric::BodyPosition< typename >::right_transform_by_inverse_of().

template<typename >

Rotation const& numeric::BodyPosition< typename >::R ( ) const

inline

Rotation.

References numeric::BodyPosition< typename >::R_, numeric::BodyPosition< typename >::R_fresh_, and numeric::BodyPosition< typename >::R_refresh().

template<typename >

BodyPosition const& numeric::BodyPosition< typename >::R_refresh ( bool const precise = true ) const

inlineprivate

Refresh rotation matrix from Quaternion.

Referenced by numeric::BodyPosition< typename >::inverse_transform(), numeric::BodyPosition< typename >::inverse_transformed(), numeric::BodyPosition< typename >::inverse_translation(), numeric::BodyPosition< typename >::invert(), numeric::BodyPosition< typename >::operator()(), numeric::BodyPosition< typename >::q_refresh(), numeric::BodyPosition< typename >::R(), numeric::BodyPosition< typename >::transform(), and numeric::BodyPosition< typename >::transformed().

template<typename >

BodyPosition& numeric::BodyPosition< typename >::right_transform_by	(	BodyPosition< typename > const &	p,
		bool const	precise = `true`
	)

inline

Right transform by a BodyPosition.

References numeric::BodyPosition< typename >::q_, numeric::BodyPosition< typename >::q_fresh_, numeric::BodyPosition< typename >::q_refresh(), numeric::BodyPosition< typename >::R_fresh_, numeric::Quaternion< typename >::right_multiply_by(), numeric::BodyPosition< typename >::t_, and numeric::BodyPosition< typename >::transformed().

template<typename >

BodyPosition& numeric::BodyPosition< typename >::right_transform_by_inverse_of	(	BodyPosition< typename > const &	p,
		bool const	precise = `true`
	)

inline

Right transform by the inverse of a BodyPosition.

References numeric::BodyPosition< typename >::q_, numeric::BodyPosition< typename >::q_fresh_, numeric::BodyPosition< typename >::q_refresh(), numeric::BodyPosition< typename >::R_fresh_, numeric::Quaternion< typename >::right_multiply_by_inverse_of(), numeric::BodyPosition< typename >::t_, and numeric::BodyPosition< typename >::transform().

template<typename >

Translation const& numeric::BodyPosition< typename >::t ( ) const

inline

Translation.

References numeric::BodyPosition< typename >::t_.

template<typename >

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

inline

Identity.

References numeric::BodyPosition< typename >::q_, numeric::BodyPosition< typename >::q_fresh_, numeric::BodyPosition< typename >::R_, numeric::BodyPosition< typename >::R_fresh_, basic::T(), numeric::BodyPosition< typename >::t_, numeric::Quaternion< typename >::to_identity(), and numeric::xyzMatrix< typename >::to_identity().

template<typename >

BodyPosition const& numeric::BodyPosition< typename >::transform ( Point & p ) const

inline

Transform a Point.

References numeric::inplace_product(), numeric::BodyPosition< typename >::R_, numeric::BodyPosition< typename >::R_fresh_, numeric::BodyPosition< typename >::R_refresh(), and numeric::BodyPosition< typename >::t_.

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

template<typename >

Point numeric::BodyPosition< typename >::transformed ( Point const & p ) const

inline

Transformed Point.

References numeric::product(), numeric::BodyPosition< typename >::R_, numeric::BodyPosition< typename >::R_fresh_, numeric::BodyPosition< typename >::R_refresh(), and numeric::BodyPosition< typename >::t_.

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

Friends And Related Function Documentation

template<typename >

bool operator!=	(	BodyPosition< typename > const &	p1,
		BodyPosition< typename > const &	p2
	)

friend

BodyPosition != BodyPosition.

template<typename >

bool operator==	(	BodyPosition< typename > const &	p1,
		BodyPosition< typename > const &	p2
	)

friend

BodyPosition == BodyPosition.

Member Data Documentation

template<typename >

Quaternion numeric::BodyPosition< typename >::q_

mutableprivate

Quaternion.

template<typename >

bool numeric::BodyPosition< typename >::q_fresh_

mutableprivate

Quaternion status.

template<typename >

Rotation numeric::BodyPosition< typename >::R_

mutableprivate

Rotation matrix.

template<typename >

bool numeric::BodyPosition< typename >::R_fresh_

mutableprivate

Rotation matrix status.

template<typename >

Translation numeric::BodyPosition< typename >::t_

private

Translation.

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

src/numeric/BodyPosition.fwd.hh
src/numeric/BodyPosition.hh

Public Types

Public Member Functions

Static Public Member Functions

Private Member Functions

Private Attributes

Friends

Detailed Description

template<typename> class numeric::BodyPosition< typename >

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation

Member Data Documentation

template<typename>
class numeric::BodyPosition< typename >