Simple quaternion representation. More...

#include <quaternion.h>

Public Member Functions
	Quaternion ()
	Constructor. Creates a Quaternion with 0 rotatation (1, 0, 0, 0).
	Quaternion (const Quaternion &q)
	Copy constructor.
	Quaternion (const Point3D &p, const bool degrees=false)
	Creates the quaternion using Euler angles.
	Quaternion (const double x, const double y, const double z)
	Creates the quaternion using Euler angles.
	Quaternion (const Point3D &axis, const double angle, bool degrees=false)
	Constructor. Initializes a rotation quatnerion given an axis and angle.
	Quaternion (const double w, const double x, const double y, const double z)
	Constructor.
void	CreateRotation (const Point3D &axis, const double angle, bool degrees=false)
	Creates a rotation quaternion given an axis and angle.
void	CreateFromEuler (const double x, const double y, const double z, bool degrees=false)
	Creates the quaternion using Euler angles.
void	ConvertToEuler (double &x, double &y, double &z, bool degrees=false) const
	Converts the quaternion to Euler angles.
void	CreateFromEuler (const Point3D &p, bool degrees=false)
	Creates the quaternion using Euler angles.
void	ConvertToEuler (Point3D &p, bool degrees=false) const
	Converts the quaternion to Euler angles.
Point3D	ConvertToEuler (bool degrees=false) const
	Converts the quaternion to Euler angles.
void	SetRotationX (const double x, const bool degrees=false)
	Creates a rotation quaternion around the axis.
void	SetRotationY (const double y, const bool degrees=false)
	Creates a rotation quaternion around the axis.
void	SetRotationZ (const double z, const bool degrees=false)
	Creates a rotation quaternion around the axis.
void	Clear ()
	Sets all values to 0.
void	Print (const bool euler=false, const bool degrees=true) const
	Prints quaternion information to console.
double	Norm () const
double	Dot (const Quaternion &q) const
	Calculates dot product of quaternions.
Point3D	GetAxis () const
Quaternion	Normalize () const
	Normalizes the quaternion.
Quaternion	Conjugate () const
	Converts the quaternion to its' conjugate.
Quaternion	Invert () const
	Inverts the quaternion.
Point3D	Rotate (const Point3D &p) const
	Rotates the point.
Point3D	RotateInverse (const Point3D &p) const
	Rotates the point using the inverse of the quaternion.
Quaternion &	operator+= (const Quaternion &q)
	Performs addition of the quaternions.
Quaternion	operator+ (const Quaternion &q) const
	Performs addition of the quaternions.
Quaternion &	operator-= (const Quaternion &q)
	Performs subtraction of the quaternions.
Quaternion	operator- (const Quaternion &q) const
	Performs subtraction of the quaternions.
Quaternion &	operator*= (const Quaternion &q)
	Performs mulitiplication of the quaternions.
Quaternion	operator* (const Quaternion &q) const
	Performs mulitiplication of the quaternions.
Quaternion &	operator*= (const Point3D &p)
	Performs mulitiplication with point.
Quaternion	operator* (const Point3D &p) const
	Performs mulitiplication with point.
Quaternion &	operator/= (const Quaternion &q)
	Performs division of the quaternions.
Quaternion	operator/ (const Quaternion &q) const
	Performs division of the quaternions.
Quaternion &	operator= (const Quaternion &q)
	Sets equal to.
Quaternion &	operator= (const Point3D &p)
	Sets equal to.
Static Public Member Functions
static double	Norm (const Quaternion &q)
static double	Dot (const Quaternion &a, const Quaternion &b)
	Calculates dot product of quaternions.
static Quaternion	Normalize (const Quaternion &q)
	Calculates normalized quaternion.
static Quaternion	Conjugate (const Quaternion &q)
static Quaternion	Invert (const Quaternion &q)
static Quaternion	Rotate (const Quaternion &q1, const Quaternion &q2)
	Rotates the second quaternion over the first, and returns the resulting quaternion.
Public Attributes
double	mW
	Real number scalar of quaternion.
double	mX
	Part of vector (i).
double	mY
	Part of vector (j).
double	mZ
	Part of vector (k).

Detailed Description

Simple quaternion representation.

This quaternion data structure contains methods for most common operations involving quaternions including multiplication, division, rotation, etc.

Definition at line 58 of file quaternion.h.

Constructor & Destructor Documentation

Quaternion::Quaternion ( )

Constructor. Creates a Quaternion with 0 rotatation (1, 0, 0, 0).

Definition at line 64 of file quaternion.cpp.

Quaternion::Quaternion ( const Quaternion & q )

Copy constructor.

Definition at line 76 of file quaternion.cpp.

Quaternion::Quaternion	(	const Point3D &	p,
		const bool	degrees = `false`
	)

Creates the quaternion using Euler angles.

Parameters:

p	Euler angles.
degrees	If true angles are in degrees, otherwise radians.

Definition at line 153 of file quaternion.cpp.

Quaternion::Quaternion	(	const double	x,
		const double	y,
		const double	z
	)

Creates the quaternion using Euler angles.

Parameters:

x	Rotation around the X-axis in radians (roll [-PI, PI]).
y	Rotation around the Y-axis in radians (pitch [-PI/2, PI/2]).
z	Rotation around the Z-axis in radians (yaw [-PI, PI]). Positive rotation is clockwise.

Definition at line 137 of file quaternion.cpp.

Quaternion::Quaternion	(	const Point3D &	axis,
		const double	angle,
		bool	degrees = `false`
	)

Constructor. Initializes a rotation quatnerion given an axis and angle.

Parameters:

axis	The axis for rotation.
angle	The angle of rotation.
degrees	If true angle is in degrees, otherwise radians.

Definition at line 95 of file quaternion.cpp.

Quaternion::Quaternion	(	const double	w,
		const double	x,
		const double	y,
		const double	z
	)

Constructor.

Definition at line 115 of file quaternion.cpp.

Member Function Documentation

void Quaternion::Clear ( )

Sets all values to 0.

Definition at line 359 of file quaternion.cpp.

Quaternion Quaternion::Conjugate ( ) const

Converts the quaternion to its' conjugate.

Definition at line 498 of file quaternion.cpp.

Quaternion Quaternion::Conjugate ( const Quaternion & q ) [static]

Parameters:

q	The quaternion to get the conjugate of.

Returns:: The conjugate of the quaternion.

Definition at line 511 of file quaternion.cpp.

void Quaternion::ConvertToEuler	(	double &	x,
		double &	y,
		double &	z,
		bool	degrees = `false`
	)		const

Converts the quaternion to Euler angles.

Parameters:

x	Rotation around the X-axis (roll [-PI, PI]).
y	Rotation around the Y-axis (pitch [-PI/2, PI/2]).
z	Rotation around the Z-axis (yaw [-PI, PI]).
degrees	If true, angles are provided in degrees, otherwise radians.

Definition at line 300 of file quaternion.cpp.

void Quaternion::ConvertToEuler	(	Point3D &	p,
		bool	degrees = `false`
	)		const

Converts the quaternion to Euler angles.

Parameters:

p	Euler angles.
degrees	If true, angles are provided in degrees, otherwise radians.

Definition at line 331 of file quaternion.cpp.

Point3D Quaternion::ConvertToEuler ( bool degrees = false ) const

Converts the quaternion to Euler angles.

Parameters:

degrees If true, angles are provided in degrees, otherwise radians.

Returns:: Euler angles as a Point3D(x, y, z);

Definition at line 346 of file quaternion.cpp.

void Quaternion::CreateFromEuler	(	const Point3D &	p,
		bool	degrees = `false`
	)

Creates the quaternion using Euler angles.

Parameters:

p	Euler angles.
degrees	If true angles are in degrees, otherwise radians.

Definition at line 232 of file quaternion.cpp.

void Quaternion::CreateFromEuler	(	const double	x,
		const double	y,
		const double	z,
		bool	degrees = `false`
	)

Creates the quaternion using Euler angles.

Parameters:

x	Rotation around the X-axis (roll [-PI, PI]).
y	Rotation around the Y-axis (pitch [-PI/2, PI/2]).
z	Rotation around the Z-axis (yaw [-PI, PI]). (positive is clockwise).
degrees	If true angles are in degrees, otherwise radians.

Definition at line 194 of file quaternion.cpp.

void Quaternion::CreateRotation	(	const Point3D &	axis,
		const double	angle,
		bool	degrees = `false`
	)

Creates a rotation quaternion given an axis and angle.

Parameters:

axis	The axis for rotation.
angle	The angle of rotation.
degrees	If true angle is in degrees, otherwise radians.

Definition at line 169 of file quaternion.cpp.

double Quaternion::Dot	(	const Quaternion &	a,
		const Quaternion &	b
	)		`[static]`

Calculates dot product of quaternions.

Parameters:

a	Quaternion 1.
b	Quaternion 2.

Returns:: Dot product of 2 quaternions.

Definition at line 437 of file quaternion.cpp.

double Quaternion::Dot ( const Quaternion & q ) const

Calculates dot product of quaternions.

Parameters:

q	The quaternion to calculate dot product with.

Returns:: Dot product.

Definition at line 421 of file quaternion.cpp.

Point3D Quaternion::GetAxis ( ) const

Returns:: The Axis of the quaternion.

Definition at line 448 of file quaternion.cpp.

Quaternion Quaternion::Invert ( ) const

Inverts the quaternion.

Definition at line 527 of file quaternion.cpp.

Quaternion Quaternion::Invert ( const Quaternion & q ) [static]

Parameters:

q	The quaternion to get the inverse of.

Returns:: The inverse of the quaternion.

Definition at line 544 of file quaternion.cpp.

double Quaternion::Norm ( const Quaternion & q ) [static]

Parameters:

q	The quaternion to calculate norm for.

Returns:: Norm of the quaternion.

Definition at line 406 of file quaternion.cpp.

double Quaternion::Norm ( ) const

Returns:: Norm of the quaternion.

Definition at line 393 of file quaternion.cpp.

Quaternion Quaternion::Normalize ( const Quaternion & q ) [static]

Calculates normalized quaternion.

Parameters:

q	The quaternion to get the normalization of.

Returns:: The normalized quaternion.

Definition at line 478 of file quaternion.cpp.

Quaternion Quaternion::Normalize ( ) const

Normalizes the quaternion.

Definition at line 459 of file quaternion.cpp.

Quaternion Quaternion::operator* ( const Point3D & p ) const

Performs mulitiplication with point.

Definition at line 725 of file quaternion.cpp.

Quaternion Quaternion::operator* ( const Quaternion & q ) const

Performs mulitiplication of the quaternions.

Definition at line 696 of file quaternion.cpp.

Quaternion & Quaternion::operator*= ( const Quaternion & q )

Performs mulitiplication of the quaternions.

Definition at line 676 of file quaternion.cpp.

Quaternion & Quaternion::operator*= ( const Point3D & p )

Performs mulitiplication with point.

Definition at line 712 of file quaternion.cpp.

Quaternion Quaternion::operator+ ( const Quaternion & q ) const

Performs addition of the quaternions.

Definition at line 629 of file quaternion.cpp.

Quaternion & Quaternion::operator+= ( const Quaternion & q )

Performs addition of the quaternions.

Definition at line 614 of file quaternion.cpp.

Quaternion Quaternion::operator- ( const Quaternion & q ) const

Performs subtraction of the quaternions.

Definition at line 660 of file quaternion.cpp.

Quaternion & Quaternion::operator-= ( const Quaternion & q )

Performs subtraction of the quaternions.

Definition at line 645 of file quaternion.cpp.

Quaternion Quaternion::operator/ ( const Quaternion & q ) const

Performs division of the quaternions.

Definition at line 762 of file quaternion.cpp.

Quaternion & Quaternion::operator/= ( const Quaternion & q )

Performs division of the quaternions.

Definition at line 737 of file quaternion.cpp.

Quaternion & Quaternion::operator= ( const Quaternion & q )

Sets equal to.

Definition at line 782 of file quaternion.cpp.

Quaternion & Quaternion::operator= ( const Point3D & p )

Sets equal to.

Definition at line 797 of file quaternion.cpp.

void Quaternion::Print	(	const bool	euler = `false`,
		const bool	degrees = `true`
	)		const

Prints quaternion information to console.

Parameters:

euler	If true than quaternion is converted to Euler angles for display.
degrees	If Euler angles are beingn displayed, set to true for degrees instead of radians.

Definition at line 375 of file quaternion.cpp.

Quaternion Quaternion::Rotate	(	const Quaternion &	q1,
		const Quaternion &	q2
	)		`[static]`

Rotates the second quaternion over the first, and returns the resulting quaternion.

Parameters:

q1	The quaternion to rotate around.
q2	The quaternion rotating.

Returns:: The result of the rotation.

Definition at line 603 of file quaternion.cpp.

Point3D Quaternion::Rotate ( const Point3D & p ) const

Rotates the point.

Parameters:

p	The point to rotate.

Returns:: The result of the rotation.

Definition at line 570 of file quaternion.cpp.

Point3D Quaternion::RotateInverse ( const Point3D & p ) const

Rotates the point using the inverse of the quaternion.

Parameters:

p	The p to rotate with.

Returns:: The result of the rotation.

Definition at line 585 of file quaternion.cpp.

void Quaternion::SetRotationX	(	const double	x,
		const bool	degrees = `false`
	)

Creates a rotation quaternion around the axis.

Parameters:

x	Rotation around X-axis (roll [-PI, PI]).
degrees	If true the angle is in degrees, otherwise radians.

Definition at line 281 of file quaternion.cpp.

void Quaternion::SetRotationY	(	const double	y,
		const bool	degrees = `false`
	)

Creates a rotation quaternion around the axis.

Parameters:

y	Rotation around Y-axis (pitch [-PI/2, PI/2]).
degrees	If true the angle is in degrees, otherwise radians.

Definition at line 264 of file quaternion.cpp.

void Quaternion::SetRotationZ	(	const double	z,
		const bool	degrees = `false`
	)

Creates a rotation quaternion around the axis.

Parameters:

z	Rotation around Z-axis (yaw [-PI, PI]).
degrees	If true the angle is in degrees, otherwise radians.

Definition at line 247 of file quaternion.cpp.

Member Data Documentation

double CxUtils::Quaternion::mW

Real number scalar of quaternion.

Definition at line 121 of file quaternion.h.

double CxUtils::Quaternion::mX

Part of vector (i).

Definition at line 122 of file quaternion.h.

double CxUtils::Quaternion::mY

Part of vector (j).

Definition at line 123 of file quaternion.h.

double CxUtils::Quaternion::mZ

Part of vector (k).

Definition at line 124 of file quaternion.h.

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

C:/Active/libraries/cxutils/2.0/include/cxutils/math/quaternion.h
C:/Active/libraries/cxutils/2.0/src/cxutils/math/quaternion.cpp

CxUtils::Quaternion Class Reference

Public Member Functions

Static Public Member Functions

Public Attributes

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation