Module org.spongepowered.math

Package org.spongepowered.math.imaginary

Class Quaterniond

java.lang.Object

org.spongepowered.math.imaginary.Quaterniond

All Implemented Interfaces:

Serializable, Comparable<Quaterniond>, Imaginaryd

@Immutable
public final class Quaterniond
extends Object
implements Imaginaryd, Comparable<Quaterniond>, Serializable

Represent a quaternion of the form xi + yj + zk + w.

The x, y, z and w components are stored as doubles. This class is immutable.

See Also:

Serialized Form

Field Summary

Fields

Modifier and Type	Field	Description
static Quaterniond	IDENTITY	An immutable identity (0, 0, 0, 1) quaternion.
static Quaterniond	ZERO	An immutable identity (0, 0, 0, 0) quaternion.

Constructor Summary

Constructors

Constructor	Description
Quaterniond(double x, double y, double z, double w)	Constructs a new quaternion from the double components.
Quaterniond(float x, float y, float z, float w)	Constructs a new quaternion from the float components.

Method Summary

Modifier and Type	Method	Description
Quaterniond	add(double x, double y, double z, double w)	Adds the double components of another quaternion to this one.
Quaterniond	add(float x, float y, float z, float w)	Adds the float components of another quaternion to this one.
Quaterniond	add(Quaterniond q)	Adds another quaternion to this one.
Vector3d	axesAnglesDeg()	Returns the angles in degrees around the x, y and z axes that correspond to the rotation represented by this quaternion.
Vector3d	axesAnglesRad()	Returns the angles in radians around the x, y and z axes that correspond to the rotation represented by this quaternion.
Vector3d	axis()	Returns the axis of rotation for this quaternion.
int	compareTo(Quaterniond q)
Quaterniond	conjugate()	Conjugates the quaternion.
Vector3d	direction()	Returns a unit vector representing the direction of this quaternion, which is Vector3d.FORWARD rotated by this quaternion.
Quaterniond	div(double a)	Divides the components of this quaternion by a double scalar.
Quaterniond	div(double x, double y, double z, double w)	Divides this quaternions by the double components of another one.
Quaterniond	div(float a)	Divides the components of this quaternion by a float scalar.
Quaterniond	div(float x, float y, float z, float w)	Divides this quaternions by the float components of another one.
Quaterniond	div(Quaterniond q)	Divides this quaternions by another one.
double	dot(double x, double y, double z, double w)	Returns the dot product of this quaternion with the double components of another one.
double	dot(float x, float y, float z, float w)	Returns the dot product of this quaternion with the float components of another one.
double	dot(Quaterniond q)	Returns the dot product of this quaternion with another one.
boolean	equals(Object other)
static Quaterniond	from(double x, double y, double z, double w)	Creates a new quaternion from the double components.
static Quaterniond	fromAngleDegAxis(double angle, double x, double y, double z)	Creates a new quaternion from the rotation double angle in degrees around the axis vector double components.
static Quaterniond	fromAngleDegAxis(double angle, Vector3d axis)	Creates a new quaternion from the rotation double angle in degrees around the axis vector.
static Quaterniond	fromAngleDegAxis(float angle, float x, float y, float z)	Creates a new quaternion from the rotation float angle in degrees around the axis vector float components.
static Quaterniond	fromAngleDegAxis(float angle, Vector3d axis)	Creates a new quaternion from the rotation float angle in degrees around the axis vector.
static Quaterniond	fromAngleRadAxis(double angle, double x, double y, double z)	Creates a new quaternion from the rotation double angle in radians around the axis vector double components.
static Quaterniond	fromAngleRadAxis(double angle, Vector3d axis)	Creates a new quaternion from the rotation double angle in radians around the axis vector.
static Quaterniond	fromAngleRadAxis(float angle, float x, float y, float z)	Creates a new quaternion from the rotation float angle in radians around the axis vector float components.
static Quaterniond	fromAngleRadAxis(float angle, Vector3d axis)	Creates a new quaternion from the rotation float angle in radians around the axis vector.
static Quaterniond	fromAxesAnglesDeg(double pitch, double yaw, double roll)	Creates a new quaternion from the double angles in degrees around the x, y and z axes.
static Quaterniond	fromAxesAnglesDeg(float pitch, float yaw, float roll)	Creates a new quaternion from the float angles in degrees around the x, y and z axes.
static Quaterniond	fromAxesAnglesRad(double pitch, double yaw, double roll)	Creates a new quaternion from the double angles in radians around the x, y and z axes.
static Quaterniond	fromAxesAnglesRad(float pitch, float yaw, float roll)	Creates a new quaternion from the float angles in radians around the x, y and z axes.
static Quaterniond	fromImaginary(double x, double y, double z)	Creates a new quaternion from the double imaginary components.
static Quaterniond	fromReal(double w)	Creates a new quaternion from the double real component.
static Quaterniond	fromRotationMatrix(Matrix3d matrix)	Creates a new quaternion from the rotation matrix.
static Quaterniond	fromRotationTo(Vector3d from, Vector3d to)	Creates a new quaternion from the angle-axis rotation defined from the first to the second vector.
int	hashCode()
Quaterniond	invert()	Inverts the quaternion.
double	length()	Returns the length of this quaternion.
double	lengthSquared()	Returns the square of the length of this quaternion.
Quaterniond	mul(double a)	Multiplies the components of this quaternion by a double scalar.
Quaterniond	mul(double x, double y, double z, double w)	Multiplies the double components of another quaternion with this one.
Quaterniond	mul(float a)	Multiplies the components of this quaternion by a float scalar.
Quaterniond	mul(float x, float y, float z, float w)	Multiplies the float components of another quaternion with this one.
Quaterniond	mul(Quaterniond q)	Multiplies another quaternion with this one.
Quaterniond	normalize()	Normalizes this quaternion.
Vector3d	rotate(double x, double y, double z)	Rotates the double components of a vector by this quaternion.
Vector3d	rotate(float x, float y, float z)	Rotates the float components of a vector by this quaternion.
Vector3d	rotate(Vector3d v)	Rotates a vector by this quaternion.
Quaterniond	sub(double x, double y, double z, double w)	Subtracts the double components of another quaternion from this one.
Quaterniond	sub(float x, float y, float z, float w)	Subtracts the float components of another quaternion from this one.
Quaterniond	sub(Quaterniond q)	Subtracts another quaternion from this one.
Complexd	toComplex()	Converts this quaternion to a complex by extracting the rotation around the axis and returning it as a rotation in the plane perpendicular to the rotation axis.
Quaterniond	toDouble()
Quaternionf	toFloat()
String	toString()
double	w()	Gets the w (real) component of this quaternion.
double	x()	Gets the x (imaginary) component of this quaternion.
double	y()	Gets the y (imaginary) component of this quaternion.
double	z()	Gets the z (imaginary) component of this quaternion.

Methods inherited from class java.lang.Object

clone, finalize, getClass, notify, notifyAll, wait, wait, wait

Field Detail

ZERO

public static final Quaterniond ZERO

An immutable identity (0, 0, 0, 0) quaternion.

IDENTITY

public static final Quaterniond IDENTITY

An immutable identity (0, 0, 0, 1) quaternion.

Constructor Detail

Quaterniond

public Quaterniond(float x,
                   float y,
                   float z,
                   float w)

Constructs a new quaternion from the float components.

Parameters:

x - The x (imaginary) component

y - The y (imaginary) component

z - The z (imaginary) component

w - The w (real) component

Quaterniond

public Quaterniond(double x,
                   double y,
                   double z,
                   double w)

Constructs a new quaternion from the double components.

Parameters:

x - The x (imaginary) component

y - The y (imaginary) component

z - The z (imaginary) component

w - The w (real) component

Method Detail

x

public double x()

Gets the x (imaginary) component of this quaternion.

Returns:

The x (imaginary) component

y

public double y()

Gets the y (imaginary) component of this quaternion.

Returns:

The y (imaginary) component

z

public double z()

Gets the z (imaginary) component of this quaternion.

Returns:

The z (imaginary) component

w

public double w()

Gets the w (real) component of this quaternion.

Returns:

The w (real) component

add

public Quaterniond add(Quaterniond q)

Adds another quaternion to this one.

Parameters:

q - The quaternion to add

Returns:

A new quaternion, which is the sum of both

add

public Quaterniond add(float x,
                       float y,
                       float z,
                       float w)

Adds the float components of another quaternion to this one.

Parameters:

x - The x (imaginary) component of the quaternion to add

y - The y (imaginary) component of the quaternion to add

z - The z (imaginary) component of the quaternion to add

w - The w (real) component of the quaternion to add

Returns:

A new quaternion, which is the sum of both

add

public Quaterniond add(double x,
                       double y,
                       double z,
                       double w)

Adds the double components of another quaternion to this one.

Parameters:

x - The x (imaginary) component of the quaternion to add

y - The y (imaginary) component of the quaternion to add

z - The z (imaginary) component of the quaternion to add

w - The w (real) component of the quaternion to add

Returns:

A new quaternion, which is the sum of both

sub

public Quaterniond sub(Quaterniond q)

Subtracts another quaternion from this one.

Parameters:

q - The quaternion to subtract

Returns:

A new quaternion, which is the difference of both

sub

public Quaterniond sub(float x,
                       float y,
                       float z,
                       float w)

Subtracts the float components of another quaternion from this one.

Parameters:

x - The x (imaginary) component of the quaternion to subtract

y - The y (imaginary) component of the quaternion to subtract

z - The z (imaginary) component of the quaternion to subtract

w - The w (real) component of the quaternion to subtract

Returns:

A new quaternion, which is the difference of both

sub

public Quaterniond sub(double x,
                       double y,
                       double z,
                       double w)

Subtracts the double components of another quaternion from this one.

Parameters:

x - The x (imaginary) component of the quaternion to subtract

y - The y (imaginary) component of the quaternion to subtract

z - The z (imaginary) component of the quaternion to subtract

w - The w (real) component of the quaternion to subtract

Returns:

A new quaternion, which is the difference of both

mul

public Quaterniond mul(float a)

Multiplies the components of this quaternion by a float scalar.

Parameters:

a - The multiplication scalar

Returns:

A new quaternion, which has each component multiplied by the scalar

mul

public Quaterniond mul(double a)

Multiplies the components of this quaternion by a double scalar.

Specified by:

mul in interface Imaginaryd

Parameters:

a - The multiplication scalar

Returns:

A new quaternion, which has each component multiplied by the scalar

mul

public Quaterniond mul(Quaterniond q)

Multiplies another quaternion with this one.

Parameters:

q - The quaternion to multiply with

Returns:

A new quaternion, which is the product of both

mul

public Quaterniond mul(float x,
                       float y,
                       float z,
                       float w)

Multiplies the float components of another quaternion with this one.

Parameters:

x - The x (imaginary) component of the quaternion to multiply with

y - The y (imaginary) component of the quaternion to multiply with

z - The z (imaginary) component of the quaternion to multiply with

w - The w (real) component of the quaternion to multiply with

Returns:

A new quaternion, which is the product of both

mul

public Quaterniond mul(double x,
                       double y,
                       double z,
                       double w)

Multiplies the double components of another quaternion with this one.

Parameters:

x - The x (imaginary) component of the quaternion to multiply with

y - The y (imaginary) component of the quaternion to multiply with

z - The z (imaginary) component of the quaternion to multiply with

w - The w (real) component of the quaternion to multiply with

Returns:

A new quaternion, which is the product of both

div

public Quaterniond div(float a)

Divides the components of this quaternion by a float scalar.

Parameters:

a - The division scalar

Returns:

A new quaternion, which has each component divided by the scalar

div

public Quaterniond div(double a)

Divides the components of this quaternion by a double scalar.

Specified by:

div in interface Imaginaryd

Parameters:

a - The division scalar

Returns:

A new quaternion, which has each component divided by the scalar

div

public Quaterniond div(Quaterniond q)

Divides this quaternions by another one.

Parameters:

q - The quaternion to divide with

Returns:

The quotient of the two quaternions

div

public Quaterniond div(float x,
                       float y,
                       float z,
                       float w)

Divides this quaternions by the float components of another one.

Parameters:

x - The x (imaginary) component of the quaternion to divide with

y - The y (imaginary) component of the quaternion to divide with

z - The z (imaginary) component of the quaternion to divide with

w - The w (real) component of the quaternion to divide with

Returns:

The quotient of the two quaternions

div

public Quaterniond div(double x,
                       double y,
                       double z,
                       double w)

Divides this quaternions by the double components of another one.

Parameters:

x - The x (imaginary) component of the quaternion to divide with

y - The y (imaginary) component of the quaternion to divide with

z - The z (imaginary) component of the quaternion to divide with

w - The w (real) component of the quaternion to divide with

Returns:

The quotient of the two quaternions

dot

public double dot(Quaterniond q)

Returns the dot product of this quaternion with another one.

Parameters:

q - The quaternion to calculate the dot product with

Returns:

The dot product of the two quaternions

dot

public double dot(float x,
                  float y,
                  float z,
                  float w)

Returns the dot product of this quaternion with the float components of another one.

Parameters:

x - The x (imaginary) component of the quaternion to calculate the dot product with

y - The y (imaginary) component of the quaternion to calculate the dot product with

z - The z (imaginary) component of the quaternion to calculate the dot product with

w - The w (real) component of the quaternion to calculate the dot product with

Returns:

The dot product of the two quaternions

dot

public double dot(double x,
                  double y,
                  double z,
                  double w)

Returns the dot product of this quaternion with the double components of another one.

Parameters:

x - The x (imaginary) component of the quaternion to calculate the dot product with

y - The y (imaginary) component of the quaternion to calculate the dot product with

z - The z (imaginary) component of the quaternion to calculate the dot product with

w - The w (real) component of the quaternion to calculate the dot product with

Returns:

The dot product of the two quaternions

rotate

public Vector3d rotate(Vector3d v)

Rotates a vector by this quaternion.

Parameters:

v - The vector to rotate

Returns:

The rotated vector

rotate

public Vector3d rotate(float x,
                       float y,
                       float z)

Rotates the float components of a vector by this quaternion.

Parameters:

x - The x component of the vector

y - The y component of the vector

z - The z component of the vector

Returns:

The rotated vector

rotate

public Vector3d rotate(double x,
                       double y,
                       double z)

Rotates the double components of a vector by this quaternion.

Parameters:

x - The x component of the vector

y - The y component of the vector

z - The z component of the vector

Returns:

The rotated vector

direction

public Vector3d direction()

Returns a unit vector representing the direction of this quaternion, which is Vector3d.FORWARD rotated by this quaternion.

Returns:

The vector representing the direction this quaternion is pointing to

axis

public Vector3d axis()

Returns the axis of rotation for this quaternion.

Returns:

The axis of rotation

axesAnglesDeg

public Vector3d axesAnglesDeg()

Returns the angles in degrees around the x, y and z axes that correspond to the rotation represented by this quaternion.

Returns:

The angle in degrees for each axis, stored in a vector, in the corresponding component

axesAnglesRad

public Vector3d axesAnglesRad()

Returns the angles in radians around the x, y and z axes that correspond to the rotation represented by this quaternion.

Returns:

The angle in radians for each axis, stored in a vector, in the corresponding component

conjugate

public Quaterniond conjugate()

Conjugates the quaternion.

Conjugation of a quaternion a is an operation returning quaternion a' such that a' * a = a * a' = |a|<sup>2</sup> where |a|<sup>2</sup> is squared length of a.

Specified by:

conjugate in interface Imaginaryd

Returns:

the conjugated quaternion

invert

public Quaterniond invert()

Inverts the quaternion.

Inversion of a quaternion a returns quaternion a<sup>-1</sup> = a' / |a|<sup>2</sup> where a' is conjugation of a, and |a|<sup>2</sup> is squared length of a.

For any quaternions a, b, c such that a * b = c, the equations a<sup>-1</sup> * c = b and c * b<sup>-1</sup> = a are true.

Specified by:

invert in interface Imaginaryd

Returns:

the inverted quaternion

lengthSquared

public double lengthSquared()

Returns the square of the length of this quaternion.

Specified by:

lengthSquared in interface Imaginaryd

Returns:

The square of the length

length

public double length()

Returns the length of this quaternion.

Specified by:

length in interface Imaginaryd

Returns:

The length

normalize

public Quaterniond normalize()

Normalizes this quaternion.

Specified by:

normalize in interface Imaginaryd

Returns:

A new quaternion of unit length

toComplex

public Complexd toComplex()

Converts this quaternion to a complex by extracting the rotation around the axis and returning it as a rotation in the plane perpendicular to the rotation axis.

Returns:

The rotation without the axis as a complex

toFloat

public Quaternionf toFloat()

Specified by:

toFloat in interface Imaginaryd

toDouble

public Quaterniond toDouble()

Specified by:

toDouble in interface Imaginaryd

equals

public boolean equals(Object other)

Overrides:

equals in class Object

hashCode

public int hashCode()

Overrides:

hashCode in class Object

compareTo

public int compareTo(Quaterniond q)

Specified by:

compareTo in interface Comparable<Quaterniond>

toString

public String toString()

Overrides:

toString in class Object

fromReal

public static Quaterniond fromReal(double w)

Creates a new quaternion from the double real component.

The ZERO constant is re-used when w is 0.

Parameters:

w - The w (real) component

Returns:

The quaternion created from the double real component

fromImaginary

public static Quaterniond fromImaginary(double x,
                                        double y,
                                        double z)

Creates a new quaternion from the double imaginary components.

The ZERO constant is re-used when x, y, and z are 0.

Parameters:

x - The x (imaginary) component

y - The y (imaginary) component

z - The z (imaginary) component

Returns:

The quaternion created from the double imaginary components

from

public static Quaterniond from(double x,
                               double y,
                               double z,
                               double w)

Creates a new quaternion from the double components.

The ZERO constant is re-used when x, y, z, and w are 0.

Parameters:

x - The x (imaginary) component

y - The y (imaginary) component

z - The z (imaginary) component

w - The w (real) component

Returns:

The quaternion created from the double components

fromAxesAnglesDeg

public static Quaterniond fromAxesAnglesDeg(float pitch,
                                            float yaw,
                                            float roll)

Creates a new quaternion from the float angles in degrees around the x, y and z axes.

Parameters:

pitch - The rotation around x

yaw - The rotation around y

roll - The rotation around z

Returns:

The quaternion defined by the rotations around the axes

fromAxesAnglesRad

public static Quaterniond fromAxesAnglesRad(float pitch,
                                            float yaw,
                                            float roll)

Creates a new quaternion from the float angles in radians around the x, y and z axes.

Parameters:

pitch - The rotation around x

yaw - The rotation around y

roll - The rotation around z

Returns:

The quaternion defined by the rotations around the axes

fromAxesAnglesDeg

public static Quaterniond fromAxesAnglesDeg(double pitch,
                                            double yaw,
                                            double roll)

Creates a new quaternion from the double angles in degrees around the x, y and z axes.

Parameters:

pitch - The rotation around x

yaw - The rotation around y

roll - The rotation around z

Returns:

The quaternion defined by the rotations around the axes

fromAxesAnglesRad

public static Quaterniond fromAxesAnglesRad(double pitch,
                                            double yaw,
                                            double roll)

Creates a new quaternion from the double angles in radians around the x, y and z axes.

Parameters:

pitch - The rotation around x

yaw - The rotation around y

roll - The rotation around z

Returns:

The quaternion defined by the rotations around the axes

fromRotationTo

public static Quaterniond fromRotationTo(Vector3d from,
                                         Vector3d to)

Creates a new quaternion from the angle-axis rotation defined from the first to the second vector.

Parameters:

from - The first vector

to - The second vector

Returns:

The quaternion defined by the angle-axis rotation between the vectors

fromAngleDegAxis

public static Quaterniond fromAngleDegAxis(float angle,
                                           Vector3d axis)

Creates a new quaternion from the rotation float angle in degrees around the axis vector.

Parameters:

angle - The rotation angle in degrees

axis - The axis of rotation

Returns:

The quaternion defined by the rotation around the axis

fromAngleRadAxis

public static Quaterniond fromAngleRadAxis(float angle,
                                           Vector3d axis)

Creates a new quaternion from the rotation float angle in radians around the axis vector.

Parameters:

angle - The rotation angle in radians

axis - The axis of rotation

Returns:

The quaternion defined by the rotation around the axis

fromAngleDegAxis

public static Quaterniond fromAngleDegAxis(double angle,
                                           Vector3d axis)

Creates a new quaternion from the rotation double angle in degrees around the axis vector.

Parameters:

angle - The rotation angle in degrees

axis - The axis of rotation

Returns:

The quaternion defined by the rotation around the axis

fromAngleRadAxis

public static Quaterniond fromAngleRadAxis(double angle,
                                           Vector3d axis)

Creates a new quaternion from the rotation double angle in radians around the axis vector.

Parameters:

angle - The rotation angle in radians

axis - The axis of rotation

Returns:

The quaternion defined by the rotation around the axis

fromAngleDegAxis

public static Quaterniond fromAngleDegAxis(float angle,
                                           float x,
                                           float y,
                                           float z)

Creates a new quaternion from the rotation float angle in degrees around the axis vector float components.

Parameters:

angle - The rotation angle in degrees

x - The x component of the axis vector

y - The y component of the axis vector

z - The z component of the axis vector

Returns:

The quaternion defined by the rotation around the axis

fromAngleRadAxis

public static Quaterniond fromAngleRadAxis(float angle,
                                           float x,
                                           float y,
                                           float z)

Creates a new quaternion from the rotation float angle in radians around the axis vector float components.

Parameters:

angle - The rotation angle in radians

x - The x component of the axis vector

y - The y component of the axis vector

z - The z component of the axis vector

Returns:

The quaternion defined by the rotation around the axis

fromAngleDegAxis

public static Quaterniond fromAngleDegAxis(double angle,
                                           double x,
                                           double y,
                                           double z)

Creates a new quaternion from the rotation double angle in degrees around the axis vector double components.

Parameters:

angle - The rotation angle in degrees

x - The x component of the axis vector

y - The y component of the axis vector

z - The z component of the axis vector

Returns:

The quaternion defined by the rotation around the axis

fromAngleRadAxis

public static Quaterniond fromAngleRadAxis(double angle,
                                           double x,
                                           double y,
                                           double z)

Creates a new quaternion from the rotation double angle in radians around the axis vector double components.

Parameters:

angle - The rotation angle in radians

x - The x component of the axis vector

y - The y component of the axis vector

z - The z component of the axis vector

Returns:

The quaternion defined by the rotation around the axis

fromRotationMatrix

public static Quaterniond fromRotationMatrix(Matrix3d matrix)

Creates a new quaternion from the rotation matrix. The matrix will be interpreted as a rotation matrix even if it is not.

Parameters:

matrix - The rotation matrix

Returns:

The quaternion defined by the rotation matrix