The Quaternion Javascript class. Defines a 4 dimensional value. More...

Public Slots
void	setWXYZ (const double w, const double x, const double y, const double z)
	Sets the w, x, y, z values to the given values. More...

Quaternion	getConjugate ()
	Returns the conjugate of the Quaternion. More...

Quaternion	getInverse ()
	Returns the inverse of the Quaternion. More...

bool	isIdentity () const
	Returns true if the Quaternion is the identity Quaternion. More...

bool	isEqual (const Quaternion q2) const
	Returns true if two Quaternions are equal. More...

bool	isNotEqual (const Quaternion q2) const
	Returns true if two Quaternions are NOT equal. More...

Point3d	toEuler (bool degrees=true) const
	Returns a Point3d loaded with the Euler Angles corresponding to the Quaternion. More...

void	fromEuler (double eulerX, double eulerY, double eulerZ, bool degree=true)
	Initialize the quaternion from a trio of 3 successive Euler angles(degrees or radians). More...

Matrix4x4	toMatrix () const
	Returns a Matrix4x4 loaded with the Rotation Matrix corresponding to the Quaternion. More...

double	getNorm () const
	Returns the norm of the Quaternion. More...

double	getDotProduct (const Quaternion q2) const
	Returns the dot product of the given Quaternion parameters. More...

Quaternion	multiply (const Quaternion q2) const
	Returns the multiplication product of the given Quaternion parameters. More...

Quaternion	getNormalized ()
	Returns the normalized Quaternion. More...

Vector3d	rotateVector (const Vector3d vect)
	Rotates a vector by the angle the Quaternion represents. More...

Public Member Functions
	Quaternion ()
	Create a new identity Quaternion. More...

	Quaternion (double w, double x, double y, double z)
	Create a new Quaternion. More...

Properties
double	w
	The w value. More...

double	x
	The x value. More...

double	y
	The y value. More...

double	z
	The z value. More...

Detailed Description

The Quaternion Javascript class. Defines a 4 dimensional value.

The Quaternion class defines a 4 dimensional value container, and is used to represent a rotation of a 3-D object.

Constructor & Destructor Documentation

◆ Quaternion() [1/2]

Quaternion::Quaternion ( )

Create a new identity Quaternion.

The identity Quaternion is [1, 0, 0, 0].

◆ Quaternion() [2/2]

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

Create a new Quaternion.

Parameters

w	: W value.
x	: X value.
y	: Y value.
z	: Z value.

Member Function Documentation

◆ fromEuler

void Quaternion::fromEuler	(	double	eulerX,
		double	eulerY,
		double	eulerZ,
		bool	degree = `true`
	)

slot

Initialize the quaternion from a trio of 3 successive Euler angles(degrees or radians).

var newRotation = new Quaternion;

newRotation.setEuler(90, 45, 45, true); // set the initial values of a quaternion from angles in degrees.

Parameters

eulerX	: The angle around the x axis
eulerY	: The angle around the y axis
eulerZ	: The angle around the z axis
degree	: True if the given angles are in degrees, false if they are in radians.

◆ getConjugate

Quaternion Quaternion::getConjugate ( )

slot

Returns the conjugate of the Quaternion.

Changes the Quaternion to its inverse. When the norm of a Quaternion is 1, this is the same as invert().

Returns: The conjugate of the Quaternion.

◆ getDotProduct

double Quaternion::getDotProduct ( const Quaternion q2 ) const

slot

Returns the dot product of the given Quaternion parameters.

The dot product of two Quaternions is the angle between the two rotations.

Parameters

q2	: The second Quaternion to use in the calculation.

Returns: The dot product of the two Quaternions.

◆ getInverse

Quaternion Quaternion::getInverse ( )

slot

Returns the inverse of the Quaternion.

Changes the Quaternion to its inverse. When the norm of a Quaternion is 1, this is the same as conjugate(), but less efficient.

Returns: The inverse of the Quaternion.

◆ getNorm

double Quaternion::getNorm ( ) const

slot

Returns the norm of the Quaternion.

The norm is the 4 dimensional euclidean length of the Quaternion.

Returns: The norm of the Quaternion.

◆ getNormalized

Quaternion Quaternion::getNormalized ( )

slot

Returns the normalized Quaternion.

Normalizing a Quaternion eliminates any errors in its calculation caused by floating-point precision.

A normalized Quaternion is one with a euclidean length (norm) of 1 (Unit length).

Returns: The normalized Quaternion.

◆ isEqual

bool Quaternion::isEqual ( const Quaternion q2 ) const

slot

Returns true if two Quaternions are equal.

Parameters

q2	: The Quaternion to compare to.

Returns: true if the two Quaternion are equal.

◆ isIdentity

bool Quaternion::isIdentity ( ) const

slot

Returns true if the Quaternion is the identity Quaternion.

The identity Quaternion is [1, 0, 0, 0].

Returns: true if the Quaternion is the identity Quaternion.

◆ isNotEqual

bool Quaternion::isNotEqual ( const Quaternion q2 ) const

slot

Returns true if two Quaternions are NOT equal.

Parameters

q2	: The Quaternion to compare to.

Returns: true if the two Quaternion are NOT equal.

◆ multiply

Quaternion Quaternion::multiply ( const Quaternion q2 ) const

slot

Returns the multiplication product of the given Quaternion parameters.

The multiplication of two Quaternions is the combination of the 2 angles of the quaternions.

Parameters

q2	: The second Quaternion to use in the calculation.

Returns: The combined rotation of the two Quaternions.

◆ rotateVector

Vector3d Quaternion::rotateVector ( const Vector3d vect )

slot

Rotates a vector by the angle the Quaternion represents.

Parameters

vect	: The Vector3d to be rotated.

Returns: The rotated Vector3d.

Note: This returns a new Vector3d, and does not modify the Vector3d in the parameter.

◆ setWXYZ

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

slot

Sets the w, x, y, z values to the given values.

Parameters

w	: W value.
x	: X value.
y	: Y value.
z	: Z value.

◆ toEuler

Point3d Quaternion::toEuler ( bool degrees = true ) const

slot

Returns a Point3d loaded with the Euler Angles corresponding to the Quaternion.

Parameters

degrees : Whether or not the Euler Angles are in degrees or radians. (true for degrees)

Returns: A Point3d loaded with the Euler Angles corresponding to the Quaternion.

◆ toMatrix

Matrix4x4 Quaternion::toMatrix ( ) const

slot

Returns a Matrix4x4 loaded with the Rotation Matrix corresponding to the Quaternion.

The Rotation Matrix is a 3x3 matrix used for rotating vectors.

Returns: A Matrix4x4 loaded with the Rotation Matrix corresponding to the Quaternion.

Property Documentation

◆ w

double Quaternion::w

readwrite

The w value.

◆ x

double Quaternion::x

readwrite

The x value.

◆ y

double Quaternion::y

readwrite

The y value.

◆ z

double Quaternion::z

readwrite

The z value.

Public Slots

Public Member Functions

Properties

Detailed Description

Constructor & Destructor Documentation

◆ Quaternion() [1/2]

◆ Quaternion() [2/2]

Member Function Documentation

◆ fromEuler

◆ getConjugate

◆ getDotProduct

◆ getInverse

◆ getNorm

◆ getNormalized

◆ isEqual

◆ isIdentity

◆ isNotEqual

◆ multiply

◆ rotateVector

◆ setWXYZ

◆ toEuler

◆ toMatrix

Property Documentation

◆ w

◆ x

◆ y

◆ z