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math::quaternion Class Reference

A quaternion. More...

#include <quaternion.h>

Collaboration diagram for math::quaternion:

[legend]List of all members.

Public Methods
	quaternion (void)
	Default Constructor. More...
	quaternion (const math::vector3 &v_, real_t w_)
	Constructor to set x y z w. More...
	quaternion (real_t x_, real_t y_, real_t z_, real_t w_)
	Constructor to set a x y z w. More...
	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. More...
math::vector3	vec (void) const
	Returns a copy of x y z. More...
real_t	scalar (void) const
	Returns a copy of w. More...
void	set (real_t x_, real_t y_, real_t z_, real_t w_)
	Sets the quaternion. More...
void	set (const math::vector3 &v_, real_t w_)
	Sets the quaternion. More...
math::quaternion	conjugate (void) const
	Returns the conjugate of the quaternion. More...
math::quaternion	operator! (void) const
	Returns the inverse of the quaternion. More...
double	magnitude (void) const
	Returns the magnitude of the quaternion. More...
void	normalize (void)
	Normalizes the quaternion. More...
void	set_identity (void)
	Sets the quaternion to the identity quaternion. More...
math::matrix4	get_rotation_matrix (void) const
	Returns the rotation matrix that describes this quaternion. More...
void	get_rotation_matrix (math::matrix4 &m) const
	Sets a rotation matrix that describes this quaternion. More...
math::matrix4	get_transposed_rotation_matrix (void) const
	Returns the transposed rotation matrix that describes this quaternion. More...
void	get_transposed_rotation_matrix (math::matrix4 &m) const
	Sets transposed rotation matrix that describes this quaternion. More...
math::quaternion	operator * (const math::quaternion &rhs) const
	Quaternion Multiplication.
math::vector3	operator * (const math::vector3 &rhs) const
	Quaternion Vector Multiplication. More...
void	from_angle_axis (real_t radians, const math::vector3 &axis)
	Creates a rotation matrix given around an arbitrary axis. More...
void	get_angle_axis (real_t &radians, math::vector3 &axis) const
	Returns the angle and axis the quaternion describes. More...
Static Public Methods
math::quaternion	slerp (real_t percent, const math::quaternion &qa, const math::quaternion &qb)
	Spherical Linear Interpretation. More...
Static Public Attributes
const math::quaternion	IDENTITY
	The identity quaternion. More...
Friends
std::ostream &	operator<< (std::ostream &o, const math::quaternion &vec)
	stream output operator. More...

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Detailed Description

A quaternion.

Quaternions take on the form:

Note:

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

Definition at line 25 of file quaternion.h.

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Constructor & Destructor Documentation

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

Default Constructor. Sets quaternion to . Definition at line 41 of file quaternion.h.

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 49 of file quaternion.h. References real_t.

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 59 of file quaternion.h. References real_t.

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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: Note: Do data within quaternion is modified. A copy of the quaternion is returned. Definition at line 149 of file quaternion.h.

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 142 of file quaternion.cpp. References math::vector3::length, and real_t.

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 154 of file quaternion.cpp. References math::equals, magnitude, real_t, 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 15 of file quaternion.cpp. References real_t, 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 56 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 65 of file quaternion.cpp. References real_t, 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 106 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: Definition at line 169 of file quaternion.h. Referenced by get_angle_axis.

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

Normalizes the quaternion. \warn If the quaternion has zero magnitude, a divide by zero may be possible. Definition at line 178 of file quaternion.h. References math::vector3::x, math::vector3::y, and math::vector3::z.

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 132 of file quaternion.cpp. References get_rotation_matrix.

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

Returns the inverse of the quaternion. The inverse of a normalized quaternion is defined as: Note: Assumes the quaternion is normalized. No normalization check is performed. Definition at line 159 of file quaternion.h.

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

Returns a copy of w. See also: w Definition at line 116 of file quaternion.h. References real_t.

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 138 of file quaternion.h. References real_t.

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 127 of file quaternion.h. References real_t, and math::vector3::set.

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

Sets the quaternion to the identity quaternion. The identity quaternion is defined as: Definition at line 192 of file quaternion.h. References math::vector3::set.

math::quaternion math::quaternion::slerp (  real_t    percent, const math::quaternion &    qa, const 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. Definition at line 180 of file quaternion.cpp. References math::equals, real_t, 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 99 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 108 of file quaternion.h.

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Friends And Related Function Documentation

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

stream output operator. Outputs quaternion as x y z w. Definition at line 207 of file quaternion.cpp.

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Member Data Documentation

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

The identity quaternion. The identity quaternion is described as:

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