Quaternion (pythagoras 1.4.3 API)

java.lang.Object
- pythagoras.d.Quaternion

All Implemented Interfaces:

Serializable, IQuaternion
```
public class Quaternion
extends Object
implements IQuaternion, Serializable
```
A unit quaternion. Many of the formulas come from the Matrix and Quaternion FAQ.

See Also:

Serialized Form

Field Summary

Fields
Modifier and Type	Field and Description
`static IQuaternion`	`IDENTITY` The identity quaternion.
`double`	`w` The components of the quaternion.
`double`	`x` The components of the quaternion.
`double`	`y` The components of the quaternion.
`double`	`z` The components of the quaternion.

Constructor Summary

Constructors
Constructor and Description
`Quaternion()` Creates an identity quaternion.
`Quaternion(double[] values)` Creates a quaternion from an array of values.
`Quaternion(double x, double y, double z, double w)` Creates a quaternion from four components.
`Quaternion(IQuaternion other)` Copy constructor.

Method Summary

All Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`boolean`	`equals(Object other)`
`Quaternion`	`fromAngleAxis(double angle, double x, double y, double z)` Sets this quaternion to the rotation described by the given angle and normalized axis.
`Quaternion`	`fromAngleAxis(double angle, IVector3 axis)` Sets this quaternion to the rotation described by the given angle and normalized axis.
`Quaternion`	`fromAngles(double x, double y, double z)` Sets this quaternion to one that first rotates about x by the specified number of radians, then rotates about y, then about z.
`Quaternion`	`fromAngles(Vector3 angles)` Sets this quaternion to one that first rotates about x by the specified number of radians, then rotates about y, then about z.
`Quaternion`	`fromAnglesXY(double x, double y)` Sets this quaternion to one that first rotates about x by the specified number of radians, then rotates about y by the specified number of radians.
`Quaternion`	`fromAnglesXZ(double x, double z)` Sets this quaternion to one that first rotates about x by the specified number of radians, then rotates about z by the specified number of radians.
`Quaternion`	`fromAxes(IVector3 nx, IVector3 ny, IVector3 nz)` Sets this quaternion to one that rotates onto the given unit axes.
`Quaternion`	`fromVectorFromNegativeZ(double tx, double ty, double tz)` Sets this quaternion to the rotation of (0, 0, -1) onto the supplied normalized vector.
`Quaternion`	`fromVectorFromNegativeZ(IVector3 to)` Sets this quaternion to the rotation of (0, 0, -1) onto the supplied normalized vector.
`Quaternion`	`fromVectors(IVector3 from, IVector3 to)` Sets this quaternion to the rotation of the first normalized vector onto the second.
`void`	`get(double[] values)` Populates the supplied array with the contents of this quaternion.
`double`	`getRotationZ()` Returns the amount of rotation about the z axis (for the purpose of flattening the rotation).
`int`	`hashCode()`
`boolean`	`hasNaN()` Checks whether any of the components of this quaternion are not-numbers.
`Quaternion`	`integrate(IVector3 velocity, double t)` Integrates the provided angular velocity over the specified timestep.
`Quaternion`	`integrate(IVector3 velocity, double t, Quaternion result)` Integrates the provided angular velocity over the specified timestep, storing the result in the object provided.
`Quaternion`	`integrateLocal(IVector3 velocity, double t)` Integrates in-place the provided angular velocity over the specified timestep.
`Quaternion`	`invert()` Inverts this quaternion.
`Quaternion`	`invert(Quaternion result)` Inverts this quaternion, storing the result in the object provided.
`Quaternion`	`invertLocal()` Inverts this quaternion in-place.
`Quaternion`	`mult(IQuaternion other)` Multiplies this quaternion by another.
`Quaternion`	`mult(IQuaternion other, Quaternion result)` Multiplies this quaternion by another and stores the result in the provided object.
`Quaternion`	`multLocal(IQuaternion other)` Multiplies this quaternion in-place by another.
`Quaternion`	`normalize()` Normalizes this quaternion.
`Quaternion`	`normalize(Quaternion result)` Normalizes this quaternion, storing the result in the object provided.
`Quaternion`	`normalizeLocal()` Normalizes this quaternion in-place.
`Quaternion`	`randomize(Random rand)` Sets this to a random rotation obtained from a completely uniform distribution.
`Quaternion`	`set(double[] values)` Copies the elements of an array.
`Quaternion`	`set(double x, double y, double z, double w)` Sets all of the elements of the quaternion.
`Quaternion`	`set(IQuaternion other)` Copies the elements of another quaternion.
`Quaternion`	`slerp(IQuaternion other, double t)` Interpolates between this and the specified other quaternion.
`Quaternion`	`slerp(IQuaternion other, double t, Quaternion result)` Interpolates between this and the specified other quaternion, placing the result in the object provided.
`Quaternion`	`slerpLocal(IQuaternion other, double t)` Interpolates in-place between this and the specified other quaternion.
`Vector3`	`toAngles()` Computes and returns the angles to pass to `fromAngles(pythagoras.d.Vector3)` to reproduce this rotation.
`Vector3`	`toAngles(Vector3 result)` Computes the angles to pass to `fromAngles(pythagoras.d.Vector3)` to reproduce this rotation, placing them in the provided vector.
`String`	`toString()`
`Vector3`	`transform(IVector3 vector)` Transforms a vector by this quaternion.
`Vector3`	`transform(IVector3 vector, Vector3 result)` Transforms a vector by this quaternion and places the result in the provided object.
`Vector3`	`transformAndAdd(IVector3 vector, IVector3 add, Vector3 result)` Transforms a vector by this quaternion and adds another vector to it, placing the result in the object provided.
`Vector3`	`transformLocal(Vector3 vector)` Transforms a vector in-place by this quaternion.
`Vector3`	`transformScaleAndAdd(IVector3 vector, double scale, IVector3 add, Vector3 result)` Transforms a vector by this quaternion, applies a uniform scale, and adds another vector to it, placing the result in the object provided.
`Vector3`	`transformUnitX(Vector3 result)` Transforms the unit x vector by this quaternion, placing the result in the provided object.
`Vector3`	`transformUnitY(Vector3 result)` Transforms the unit y vector by this quaternion, placing the result in the provided object.
`Vector3`	`transformUnitZ(Vector3 result)` Transforms the unit z vector by this quaternion, placing the result in the provided object.
`double`	`transformZ(IVector3 vector)` Transforms a vector by this quaternion and returns the z coordinate of the result.
`double`	`w()` Returns the w-component of this quaternion.
`double`	`x()` Returns the x-component of this quaternion.
`double`	`y()` Returns the y-component of this quaternion.
`double`	`z()` Returns the z-component of this quaternion.

Methods inherited from class java.lang.Object
getClass, notify, notifyAll, wait, wait, wait

- Field Detail
  - IDENTITY
```
public static final IQuaternion IDENTITY
```
    The identity quaternion.
  - x
```
public double x
```
    The components of the quaternion.
  - y
```
public double y
```
    The components of the quaternion.
  - z
```
public double z
```
    The components of the quaternion.
  - w
```
public double w
```
    The components of the quaternion.
- Constructor Detail
  - Quaternion
```
public Quaternion(double x,
                  double y,
                  double z,
                  double w)
```
    Creates a quaternion from four components.
  - Quaternion
```
public Quaternion(double[] values)
```
    Creates a quaternion from an array of values.
  - Quaternion
```
public Quaternion(IQuaternion other)
```
    Copy constructor.
  - Quaternion
```
public Quaternion()
```
    Creates an identity quaternion.
- Method Detail
  - set
```
public Quaternion set(IQuaternion other)
```
    Copies the elements of another quaternion.
    
    Returns:
    
    a reference to this quaternion, for chaining.
  - set
```
public Quaternion set(double[] values)
```
    Copies the elements of an array.
    
    Returns:
    
    a reference to this quaternion, for chaining.
  - set
```
public Quaternion set(double x,
                      double y,
                      double z,
                      double w)
```
    Sets all of the elements of the quaternion.
    
    Returns:
    
    a reference to this quaternion, for chaining.
  - fromVectors
```
public Quaternion fromVectors(IVector3 from,
                              IVector3 to)
```
    Sets this quaternion to the rotation of the first normalized vector onto the second.
    
    Returns:
    
    a reference to this quaternion, for chaining.
  - fromVectorFromNegativeZ
```
public Quaternion fromVectorFromNegativeZ(IVector3 to)
```
    Sets this quaternion to the rotation of (0, 0, -1) onto the supplied normalized vector.
    
    Returns:
    
    a reference to the quaternion, for chaining.
  - fromVectorFromNegativeZ
```
public Quaternion fromVectorFromNegativeZ(double tx,
                                          double ty,
                                          double tz)
```
    Sets this quaternion to the rotation of (0, 0, -1) onto the supplied normalized vector.
    
    Returns:
    
    a reference to the quaternion, for chaining.
  - fromAxes
```
public Quaternion fromAxes(IVector3 nx,
                           IVector3 ny,
                           IVector3 nz)
```
    Sets this quaternion to one that rotates onto the given unit axes.
    
    Returns:
    
    a reference to this quaternion, for chaining.
  - fromAngleAxis
```
public Quaternion fromAngleAxis(double angle,
                                IVector3 axis)
```
    Sets this quaternion to the rotation described by the given angle and normalized axis.
    
    Returns:
    
    a reference to this quaternion, for chaining.
  - fromAngleAxis
```
public Quaternion fromAngleAxis(double angle,
                                double x,
                                double y,
                                double z)
```
    Sets this quaternion to the rotation described by the given angle and normalized axis.
    
    Returns:
    
    a reference to this quaternion, for chaining.
  - randomize
```
public Quaternion randomize(Random rand)
```
    Sets this to a random rotation obtained from a completely uniform distribution.
  - fromAnglesXZ
```
public Quaternion fromAnglesXZ(double x,
                               double z)
```
    Sets this quaternion to one that first rotates about x by the specified number of radians, then rotates about z by the specified number of radians.
  - fromAnglesXY
```
public Quaternion fromAnglesXY(double x,
                               double y)
```
    Sets this quaternion to one that first rotates about x by the specified number of radians, then rotates about y by the specified number of radians.
  - fromAngles
```
public Quaternion fromAngles(Vector3 angles)
```
    Sets this quaternion to one that first rotates about x by the specified number of radians, then rotates about y, then about z.
  - fromAngles
```
public Quaternion fromAngles(double x,
                             double y,
                             double z)
```
    Sets this quaternion to one that first rotates about x by the specified number of radians, then rotates about y, then about z.
  - normalizeLocal
```
public Quaternion normalizeLocal()
```
    Normalizes this quaternion in-place.
    
    Returns:
    
    a reference to this quaternion, for chaining.
  - invertLocal
```
public Quaternion invertLocal()
```
    Inverts this quaternion in-place.
    
    Returns:
    
    a reference to this quaternion, for chaining.
  - multLocal
```
public Quaternion multLocal(IQuaternion other)
```
    Multiplies this quaternion in-place by another.
    
    Returns:
    
    a reference to this quaternion, for chaining.
  - slerpLocal
```
public Quaternion slerpLocal(IQuaternion other,
                             double t)
```
    Interpolates in-place between this and the specified other quaternion.
    
    Returns:
    
    a reference to this quaternion, for chaining.
  - transformLocal
```
public Vector3 transformLocal(Vector3 vector)
```
    Transforms a vector in-place by this quaternion.
    
    Returns:
    
    a reference to the vector, for chaining.
  - integrateLocal
```
public Quaternion integrateLocal(IVector3 velocity,
                                 double t)
```
    Integrates in-place the provided angular velocity over the specified timestep.
    
    Returns:
    
    a reference to this quaternion, for chaining.
  - x
```
public double x()
```
    Description copied from interface: IQuaternion
    
    Returns the x-component of this quaternion.
    
    Specified by:
    
    x in interface IQuaternion
  - y
```
public double y()
```
    Description copied from interface: IQuaternion
    
    Returns the y-component of this quaternion.
    
    Specified by:
    
    y in interface IQuaternion
  - z
```
public double z()
```
    Description copied from interface: IQuaternion
    
    Returns the z-component of this quaternion.
    
    Specified by:
    
    z in interface IQuaternion
  - w
```
public double w()
```
    Description copied from interface: IQuaternion
    
    Returns the w-component of this quaternion.
    
    Specified by:
    
    w in interface IQuaternion
  - get
```
public void get(double[] values)
```
    Description copied from interface: IQuaternion
    
    Populates the supplied array with the contents of this quaternion.
    
    Specified by:
    
    get in interface IQuaternion
  - hasNaN
```
public boolean hasNaN()
```
    Description copied from interface: IQuaternion
    
    Checks whether any of the components of this quaternion are not-numbers.
    
    Specified by:
    
    hasNaN in interface IQuaternion
  - toAngles
```
public Vector3 toAngles(Vector3 result)
```
    Description copied from interface: IQuaternion
    
    Computes the angles to pass to fromAngles(pythagoras.d.Vector3) to reproduce this rotation, placing them in the provided vector. This uses the factorization method described in David Eberly's Euler Angle Formulas.
    
    Specified by:
    
    toAngles in interface IQuaternion
    
    Returns:
    
    a reference to the result vector, for chaining.
  - toAngles
```
public Vector3 toAngles()
```
    Description copied from interface: IQuaternion
    
    Computes and returns the angles to pass to fromAngles(pythagoras.d.Vector3) to reproduce this rotation.
    
    Specified by:
    
    toAngles in interface IQuaternion
    
    Returns:
    
    a new vector containing the resulting angles.
  - normalize
```
public Quaternion normalize()
```
    Description copied from interface: IQuaternion
    
    Normalizes this quaternion.
    
    Specified by:
    
    normalize in interface IQuaternion
    
    Returns:
    
    a new quaternion containing the result.
  - normalize
```
public Quaternion normalize(Quaternion result)
```
    Description copied from interface: IQuaternion
    
    Normalizes this quaternion, storing the result in the object provided.
    
    Specified by:
    
    normalize in interface IQuaternion
    
    Returns:
    
    a reference to the result, for chaining.
  - invert
```
public Quaternion invert()
```
    Description copied from interface: IQuaternion
    
    Inverts this quaternion.
    
    Specified by:
    
    invert in interface IQuaternion
    
    Returns:
    
    a new quaternion containing the result.
  - invert
```
public Quaternion invert(Quaternion result)
```
    Description copied from interface: IQuaternion
    
    Inverts this quaternion, storing the result in the object provided.
    
    Specified by:
    
    invert in interface IQuaternion
    
    Returns:
    
    a reference to the result, for chaining.
  - mult
```
public Quaternion mult(IQuaternion other)
```
    Description copied from interface: IQuaternion
    
    Multiplies this quaternion by another.
    
    Specified by:
    
    mult in interface IQuaternion
    
    Returns:
    
    a new quaternion containing the result.
  - mult
```
public Quaternion mult(IQuaternion other,
                       Quaternion result)
```
    Description copied from interface: IQuaternion
    
    Multiplies this quaternion by another and stores the result in the provided object.
    
    Specified by:
    
    mult in interface IQuaternion
    
    Returns:
    
    a reference to the result, for chaining.
  - slerp
```
public Quaternion slerp(IQuaternion other,
                        double t)
```
    Description copied from interface: IQuaternion
    
    Interpolates between this and the specified other quaternion.
    
    Specified by:
    
    slerp in interface IQuaternion
    
    Returns:
    
    a new quaternion containing the result.
  - slerp
```
public Quaternion slerp(IQuaternion other,
                        double t,
                        Quaternion result)
```
    Description copied from interface: IQuaternion
    
    Interpolates between this and the specified other quaternion, placing the result in the object provided. Based on the code in Nick Bobick's article, Rotating Objects Using Quaternions.
    
    Specified by:
    
    slerp in interface IQuaternion
    
    Returns:
    
    a reference to the result quaternion, for chaining.
  - transform
```
public Vector3 transform(IVector3 vector)
```
    Description copied from interface: IQuaternion
    
    Transforms a vector by this quaternion.
    
    Specified by:
    
    transform in interface IQuaternion
    
    Returns:
    
    a new vector containing the result.
  - transform
```
public Vector3 transform(IVector3 vector,
                         Vector3 result)
```
    Description copied from interface: IQuaternion
    
    Transforms a vector by this quaternion and places the result in the provided object.
    
    Specified by:
    
    transform in interface IQuaternion
    
    Returns:
    
    a reference to the result, for chaining.
  - transformUnitX
```
public Vector3 transformUnitX(Vector3 result)
```
    Description copied from interface: IQuaternion
    
    Transforms the unit x vector by this quaternion, placing the result in the provided object.
    
    Specified by:
    
    transformUnitX in interface IQuaternion
    
    Returns:
    
    a reference to the result, for chaining.
  - transformUnitY
```
public Vector3 transformUnitY(Vector3 result)
```
    Description copied from interface: IQuaternion
    
    Transforms the unit y vector by this quaternion, placing the result in the provided object.
    
    Specified by:
    
    transformUnitY in interface IQuaternion
    
    Returns:
    
    a reference to the result, for chaining.
  - transformUnitZ
```
public Vector3 transformUnitZ(Vector3 result)
```
    Description copied from interface: IQuaternion
    
    Transforms the unit z vector by this quaternion, placing the result in the provided object.
    
    Specified by:
    
    transformUnitZ in interface IQuaternion
    
    Returns:
    
    a reference to the result, for chaining.
  - transformAndAdd
```
public Vector3 transformAndAdd(IVector3 vector,
                               IVector3 add,
                               Vector3 result)
```
    Description copied from interface: IQuaternion
    
    Transforms a vector by this quaternion and adds another vector to it, placing the result in the object provided.
    
    Specified by:
    
    transformAndAdd in interface IQuaternion
    
    Returns:
    
    a reference to the result, for chaining.
  - transformScaleAndAdd
```
public Vector3 transformScaleAndAdd(IVector3 vector,
                                    double scale,
                                    IVector3 add,
                                    Vector3 result)
```
    Description copied from interface: IQuaternion
    
    Transforms a vector by this quaternion, applies a uniform scale, and adds another vector to it, placing the result in the object provided.
    
    Specified by:
    
    transformScaleAndAdd in interface IQuaternion
    
    Returns:
    
    a reference to the result, for chaining.
  - transformZ
```
public double transformZ(IVector3 vector)
```
    Description copied from interface: IQuaternion
    
    Transforms a vector by this quaternion and returns the z coordinate of the result.
    
    Specified by:
    
    transformZ in interface IQuaternion
  - getRotationZ
```
public double getRotationZ()
```
    Description copied from interface: IQuaternion
    
    Returns the amount of rotation about the z axis (for the purpose of flattening the rotation).
    
    Specified by:
    
    getRotationZ in interface IQuaternion
  - integrate
```
public Quaternion integrate(IVector3 velocity,
                            double t)
```
    Description copied from interface: IQuaternion
    
    Integrates the provided angular velocity over the specified timestep.
    
    Specified by:
    
    integrate in interface IQuaternion
    
    Returns:
    
    a new quaternion containing the result.
  - integrate
```
public Quaternion integrate(IVector3 velocity,
                            double t,
                            Quaternion result)
```
    Description copied from interface: IQuaternion
    
    Integrates the provided angular velocity over the specified timestep, storing the result in the object provided.
    
    Specified by:
    
    integrate in interface IQuaternion
    
    Returns:
    
    a reference to the result object, for chaining.
  - toString
```
public String toString()
```
    Overrides:
    
    toString in class Object
  - hashCode
```
public int hashCode()
```
    Overrides:
    
    hashCode in class Object
  - equals
```
public boolean equals(Object other)
```
    Overrides:
    
    equals in class Object

Class Quaternion

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

IDENTITY

x

y

z

w

Constructor Detail

Quaternion

Quaternion

Quaternion

Quaternion

Method Detail

set

set

set

fromVectors

fromVectorFromNegativeZ

fromVectorFromNegativeZ

fromAxes

fromAngleAxis

fromAngleAxis

randomize

fromAnglesXZ

fromAnglesXY

fromAngles

fromAngles

normalizeLocal

invertLocal

multLocal

slerpLocal

transformLocal

integrateLocal

x

y

z

w

get

hasNaN

toAngles

toAngles

normalize

normalize

invert

invert

mult

mult

slerp

slerp

transform

transform

transformUnitX

transformUnitY

transformUnitZ

transformAndAdd

transformScaleAndAdd

transformZ

getRotationZ

integrate

integrate

toString

hashCode

equals