math::quaternion Class Reference

#include <quaternion.h>

Collaboration diagram for math::quaternion:

List of all members.

Public Member Functions

quaternion (void)

Default Constructor.

quaternion (const math::vector3 &v_, real_t w_)

Constructor to set x y z w.

quaternion (real_t x_, real_t y_, real_t z_, real_t w_)

Constructor to set a x y z w.

quaternion (const math::quaternion &p)

Copy Constructor.

math::quaternion & operator= (const math::quaternion &p)

Assignment Operator.

real_t w (void) const

Returns a copy of w.

real_t x (void) const

Returns a copy of x.

real_t y (void) const

Returns a copy of y.

real_t z (void) const

Returns a copy of z.

math::vector3 v (void) const

Returns a copy of x y z.

math::vector3 vec (void) const

Returns a copy of x y z.

real_t scalar (void) const

Returns a copy of w.

void set (real_t x_, real_t y_, real_t z_, real_t w_)

Sets the quaternion.

void set (const math::vector3 &v_, real_t w_)

Sets the quaternion.

math::quaternion conjugate (void) const

Returns the conjugate of the quaternion.

math::quaternion operator! (void) const

Returns the inverse of the quaternion.

double magnitude (void) const

Returns the magnitude of the quaternion.

void normalize (void)

Normalizes the quaternion.

void set_identity (void)

Sets the quaternion to the identity quaternion.

math::matrix4 get_rotation_matrix (void) const

Returns the rotation matrix that describes this quaternion.

void get_rotation_matrix (math::matrix4 &m) const

Sets a rotation matrix that describes this quaternion.

math::matrix4 get_transposed_rotation_matrix (void) const

Returns the transposed rotation matrix that describes this quaternion.

void get_transposed_rotation_matrix (math::matrix4 &m) const

Sets transposed rotation matrix that describes this quaternion.

math::quaternion operator* (const math::quaternion &rhs) const

Quaternion Multiplication.

math::vector3 operator* (const math::vector3 &rhs) const

Quaternion Vector Multiplication.

void from_angle_axis (real_t radians, const math::vector3 &axis)

Creates a rotation matrix given around an arbitrary axis.

void get_angle_axis (real_t &radians, math::vector3 &axis) const

Returns the angle and axis the quaternion describes.

void from_angles (real_t x_rad, real_t y_rad, real_t z_rad)

Creates a unit length quaternion from three Euler angles.

void from_matrix3 (const real_t *mat)

Creates a unit length quaternion from a 3x3 rotation matrix.

void from_matrix4 (const real_t *mat)

Creates a unit length quaternion from a 4x4 rotation matrix.

Static Public Member Functions

static math::quaternion slerp (real_t percent, const math::quaternion &qa, math::quaternion qb)

Spherical Linear Interpretation.

Static Public Attributes

static const math::quaternion IDENTITY

The identity quaternion.

Friends

std::ostream & math::operator<< (std::ostream &o, const math::quaternion &vec)

stream output operator.

Detailed Description

A quaternion.

Quaternions take on the form:

$(x,y,z,w)$

Note:: When sending the quaternion to OpenGL, use get_transposed_matrix().

Definition at line 46 of file quaternion.h.

Constructor & Destructor Documentation

math::quaternion::quaternion ( void ) [inline]

Default Constructor.

Sets quaternion to $(0,0,0,1)$ .

Definition at line 62 of file quaternion.h.

Referenced by conjugate(), operator!(), operator*(), and slerp().

math::quaternion::quaternion	(	const math::vector3 &	v_,
		real_t	w_
	)			`[inline]`

Constructor to set x y z w.

Parameters:

	v_	`vector` which defines the quaternion's x y z.
	w_	`real_t` which define the quaternion's w.

Definition at line 70 of file quaternion.h.

math::quaternion::quaternion	(	real_t	x_,
		real_t	y_,
		real_t	z_,
		real_t	w_
	)			`[inline]`

Constructor to set a x y z w.

Parameters:

	x_	`real_t` which defines the quaternion's x.
	y_	`real_t` which defines the quaternion's y.
	z_	`real_t` which defines the quaternion's z.
	w_	`real_t` which defines the quaternion's w.

Definition at line 80 of file quaternion.h.

Member Function Documentation

math::quaternion math::quaternion::conjugate ( void ) const [inline]

Returns the conjugate of the quaternion.

The conjugate of the quaternion is defined as:

$(x,y,z,-w)$

Note:: Do data within quaternion is modified. A copy of the quaternion is returned.

Definition at line 170 of file quaternion.h.

References quaternion().

void math::quaternion::from_angle_axis	(	real_t	radians,
		const math::vector3 &	axis
	)

Creates a rotation matrix given around an arbitrary axis.

Given an axis and an angle, this method will create a set this quaternion as the quaternion that describes the rotation around the axis by angle.

Note:: Rotations are right-handed.

Parameters:

	radians	A real number in radians.
	axis	A unit length vector describing the axis to rotate around.

Definition at line 164 of file quaternion.cpp.

References math::equals(), and math::vector3::length().

Referenced by from_angles().

void math::quaternion::from_angles	(	real_t	x_rad,
		real_t	y_rad,
		real_t	z_rad
	)

Creates a unit length quaternion from three Euler angles.

Parameters:

	x_rad	Rotation around x axis in radians.
	y_rad	Rotation around y axis in radians.
	z_rad	Rotation around z axis in radians.

Definition at line 203 of file quaternion.cpp.

References from_angle_axis(), normalize(), math::vector3::X_AXIS, math::vector3::Y_AXIS, and math::vector3::Z_AXIS.

void math::quaternion::from_matrix3 ( const real_t * mat )

Creates a unit length quaternion from a 3x3 rotation matrix.

Parameters:

mat

Pointer to an real_t[ 9 ] representing a rotation matrix. Matrix is assumed to be stored in row major format.

Definition at line 221 of file quaternion.cpp.

References math::vector3::x(), math::vector3::y(), and math::vector3::z().

void math::quaternion::from_matrix4 ( const real_t * mat )

Creates a unit length quaternion from a 4x4 rotation matrix.

Parameters:

mat

Pointer to an real_t[ 16 ] representing a rotation matrix. Matrix is assumed to be stored in row major format.

Definition at line 262 of file quaternion.cpp.

References math::vector3::x(), math::vector3::y(), and math::vector3::z().

void math::quaternion::get_angle_axis	(	real_t &	radians,
		math::vector3 &	axis
	)			const

Returns the angle and axis the quaternion describes.

Parameters:

	radians	The angle about axis in radians (output).
	axis	The axis the quaternion's rotation is aroiund (output).

Returns:: Sets radians and axis.

Definition at line 176 of file quaternion.cpp.

References math::equals(), magnitude(), math::vector3::set(), math::vector3::x(), math::vector3::y(), and math::vector3::z().

void math::quaternion::get_rotation_matrix ( math::matrix4 & m ) const

Sets a rotation matrix that describes this quaternion.

Parameters:

m A matrix4 where the rotation matrix will be written.

Definition at line 37 of file quaternion.cpp.

References math::matrix4::set(), math::vector3::x(), math::vector3::y(), and math::vector3::z().

math::matrix4 math::quaternion::get_rotation_matrix ( void ) const

Returns the rotation matrix that describes this quaternion.

Returns:: A matrix4 that describes the rotation this quaternion represents.

Definition at line 78 of file quaternion.cpp.

Referenced by operator*().

void math::quaternion::get_transposed_rotation_matrix ( math::matrix4 & m ) const

Sets transposed rotation matrix that describes this quaternion.

Parameters:

m A matrix4 where the rotation matrix will be written.

Note:: Use this method to send the quaternion to OpenGL functions such as glMultMatrix().

Definition at line 87 of file quaternion.cpp.

References math::matrix4::set(), math::vector3::x(), math::vector3::y(), and math::vector3::z().

math::matrix4 math::quaternion::get_transposed_rotation_matrix ( void ) const

Returns the transposed rotation matrix that describes this quaternion.

Note:: Use this method to send the quaternion to OpenGL functions such as glMultMatrix().

Returns:: A transposed matrix4 that describes the rotation this quaternion represents.

Definition at line 128 of file quaternion.cpp.

double math::quaternion::magnitude ( void ) const [inline]

Returns the magnitude of the quaternion.

The magnitude of the quaternion is defined as:

$\sqrt{x^2+y^2+z^2+w^2}$

Definition at line 190 of file quaternion.h.

Referenced by get_angle_axis(), and normalize().

void math::quaternion::normalize ( void ) [inline]

Normalizes the quaternion.

Warning:: If the quaternion has zero magnitude, a divide by zero may be possible.

Definition at line 199 of file quaternion.h.

References magnitude(), math::vector3::x(), math::vector3::y(), and math::vector3::z().

Referenced by from_angles().

math::quaternion math::quaternion::operator! ( void ) const [inline]

Returns the inverse of the quaternion.

The inverse of a normalized quaternion is defined as:

$(x,y,z,-w)$

Note:: Assumes the quaternion is normalized. No normalization check is performed.

Definition at line 180 of file quaternion.h.

References quaternion().

math::vector3 math::quaternion::operator* ( const math::vector3 & rhs ) const

Quaternion Vector Multiplication.

Multiplies the matrix that this quaternion describes by the vector rhs.

Definition at line 154 of file quaternion.cpp.

References get_rotation_matrix().

real_t math::quaternion::scalar ( void ) const [inline]

Returns a copy of w.

See also:: w

Definition at line 137 of file quaternion.h.

void math::quaternion::set	(	const math::vector3 &	v_,
		real_t	w_
	)			`[inline]`

Sets the quaternion.

Parameters:

	v_	`vector` which defines the quaternion's x y z.
	w_	`real_t` which define the quaternion's w.

Definition at line 159 of file quaternion.h.

void math::quaternion::set	(	real_t	x_,
		real_t	y_,
		real_t	z_,
		real_t	w_
	)			`[inline]`

Sets the quaternion.

Parameters:

	x_	`real_t` which defines the quaternion's x.
	y_	`real_t` which defines the quaternion's y.
	z_	`real_t` which defines the quaternion's z.
	w_	`real_t` which defines the quaternion's w.

Definition at line 148 of file quaternion.h.

References math::vector3::set().

void math::quaternion::set_identity ( void ) [inline]

Sets the quaternion to the identity quaternion.

The identity quaternion is defined as:

$(0,0,0,1)$

Definition at line 213 of file quaternion.h.

References math::vector3::set().

math::quaternion math::quaternion::slerp	(	real_t	percent,
		const math::quaternion &	qa,
		math::quaternion	qb
	)			`[static]`

Spherical Linear Interpretation.

Interprets the between the two rotations that qa and qb describe.

Parameters:

	percent	A real_t between [0-1] descibing how much to interpret between qa and qb.
	qa	Initial orientation.
	qb	Ending orientation.

Definition at line 301 of file quaternion.cpp.

References math::equals(), m_v, m_w, math::vector3::negate(), quaternion(), v(), w(), x(), y(), and z().

math::vector3 math::quaternion::v ( void ) const [inline]

Returns a copy of x y z.

See also:: vec

Returns:: A vector containing x y z.

Definition at line 120 of file quaternion.h.

Referenced by slerp().

math::vector3 math::quaternion::vec ( void ) const [inline]

Returns a copy of x y z.

See also:: v

Returns:: A vector containing x y z.

Definition at line 129 of file quaternion.h.

Referenced by fob::bird::get_quaternion().

Friends And Related Function Documentation

std::ostream& math::operator<<	(	std::ostream &	o,
		const math::quaternion &	vec
	)			`[friend]`

stream output operator.

Outputs quaternion as x y z w.

Member Data Documentation

const math::quaternion math::quaternion::IDENTITY [static]

The identity quaternion.

The identity quaternion is described as:

$(0,0,0,1)$

Definition at line 321 of file quaternion.h.


Public Member Functions
	quaternion (void)
	Default Constructor.
	quaternion (const math::vector3 &v_, real_t w_)
	Constructor to set x y z w.
	quaternion (real_t x_, real_t y_, real_t z_, real_t w_)
	Constructor to set a x y z w.
	quaternion (const math::quaternion &p)
	Copy Constructor.
math::quaternion &	operator= (const math::quaternion &p)
	Assignment Operator.
real_t	w (void) const
	Returns a copy of w.
real_t	x (void) const
	Returns a copy of x.
real_t	y (void) const
	Returns a copy of y.
real_t	z (void) const
	Returns a copy of z.
math::vector3	v (void) const
	Returns a copy of x y z.
math::vector3	vec (void) const
	Returns a copy of x y z.
real_t	scalar (void) const
	Returns a copy of w.
void	set (real_t x_, real_t y_, real_t z_, real_t w_)
	Sets the quaternion.
void	set (const math::vector3 &v_, real_t w_)
	Sets the quaternion.
math::quaternion	conjugate (void) const
	Returns the conjugate of the quaternion.
math::quaternion	operator! (void) const
	Returns the inverse of the quaternion.
double	magnitude (void) const
	Returns the magnitude of the quaternion.
void	normalize (void)
	Normalizes the quaternion.
void	set_identity (void)
	Sets the quaternion to the identity quaternion.
math::matrix4	get_rotation_matrix (void) const
	Returns the rotation matrix that describes this quaternion.
void	get_rotation_matrix (math::matrix4 &m) const
	Sets a rotation matrix that describes this quaternion.
math::matrix4	get_transposed_rotation_matrix (void) const
	Returns the transposed rotation matrix that describes this quaternion.
void	get_transposed_rotation_matrix (math::matrix4 &m) const
	Sets transposed rotation matrix that describes this quaternion.
math::quaternion	operator* (const math::quaternion &rhs) const
	Quaternion Multiplication.
math::vector3	operator* (const math::vector3 &rhs) const
	Quaternion Vector Multiplication.
void	from_angle_axis (real_t radians, const math::vector3 &axis)
	Creates a rotation matrix given around an arbitrary axis.
void	get_angle_axis (real_t &radians, math::vector3 &axis) const
	Returns the angle and axis the quaternion describes.
void	from_angles (real_t x_rad, real_t y_rad, real_t z_rad)
	Creates a unit length quaternion from three Euler angles.
void	from_matrix3 (const real_t *mat)
	Creates a unit length quaternion from a 3x3 rotation matrix.
void	from_matrix4 (const real_t *mat)
	Creates a unit length quaternion from a 4x4 rotation matrix.
Static Public Member Functions
static math::quaternion	slerp (real_t percent, const math::quaternion &qa, math::quaternion qb)
	Spherical Linear Interpretation.
Static Public Attributes
static const math::quaternion	IDENTITY
	The identity quaternion.
Friends
std::ostream &	math::operator<< (std::ostream &o, const math::quaternion &vec)
	`stream` output operator.