Quaternion (Libbulletjme API)

java.lang.Object
- com.jme3.math.Quaternion

All Implemented Interfaces:

java.io.Serializable, java.lang.Cloneable
```
public final class Quaternion
extends java.lang.Object
implements java.lang.Cloneable, java.io.Serializable
```
Used to efficiently represent rotations and orientations in 3-dimensional space, without risk of gimbal lock. Each instance has 4 single-precision components: 3 imaginary components (X, Y, and Z) and a real component (W).
Mathematically, quaternions are an extension of complex numbers. In mathematics texts, W often appears first, but in JME it always comes last.

See Also:

Serialized Form

Field Summary

Fields
Modifier and Type	Field and Description
`static Quaternion`	`DIRECTION_Z` Another shared instance of the identity quaternion (0, 0, 0, 1).
`static Quaternion`	`IDENTITY` Shared instance of the identity quaternion (0, 0, 0, 1).
`protected float`	`w` The real (W) component.
`protected float`	`x` The first imaginary (X) component.
`protected float`	`y` The 2nd imaginary (Y) component.
`protected float`	`z` The 3rd imaginary (Z) component.
`static Quaternion`	`ZERO` Shared instance of the zero quaternion (0, 0, 0, 0).

Constructor Summary

Constructors
Constructor and Description
`Quaternion()` Instantiates an identity quaternion: all components zeroed except `w`, which is set to 1.
`Quaternion(float x, float y, float z, float w)` Instantiates a quaternion with the specified components.
`Quaternion(Quaternion q)` Instantiates a copy of the argument.

Method Summary

All Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`Quaternion`	`addLocal(Quaternion q)` Adds the argument and returns the (modified) current instance.
`Quaternion`	`clone()` Creates a copy.
`boolean`	`equals(java.lang.Object o)` Tests for exact equality with the argument, distinguishing -0 from 0.
`Quaternion`	`fromAngleNormalAxis(float angle, Vector3f axis)` Sets the quaternion from the specified rotation angle and normalized axis of rotation.
`Quaternion`	`fromAngles(float xAngle, float yAngle, float zAngle)` Sets the quaternion from the specified Tait-Bryan angles, applying the rotations in x-z-y extrinsic order or y-z'-x" intrinsic order.
`Quaternion`	`fromAxes(Vector3f xAxis, Vector3f yAxis, Vector3f zAxis)` Sets the quaternion from the specified orthonormal basis.
`Quaternion`	`fromRotationMatrix(float m00, float m01, float m02, float m10, float m11, float m12, float m20, float m21, float m22)` Sets the quaternion from a rotation matrix with the specified elements.
`Quaternion`	`fromRotationMatrix(Matrix3f matrix)` Sets the quaternion from the specified rotation matrix.
`float`	`getW()` Returns the W (real) component.
`float`	`getX()` Returns the X component.
`float`	`getY()` Returns the Y component.
`float`	`getZ()` Returns the Z component.
`int`	`hashCode()` Returns a hash code.
`Quaternion`	`inverse()` Returns the multiplicative inverse.
`void`	`loadIdentity()` Sets all components to zero except `w`, which is set to 1.
`Quaternion`	`mult(Quaternion q)` Multiplies by the argument and returns the product as a new instance.
`Quaternion`	`mult(Quaternion q, Quaternion storeResult)` Multiplies by the specified quaternion and returns the product in a 3rd quaternion.
`Quaternion`	`multLocal(float scalar)` Multiplies by the scalar argument and returns the (modified) current instance.
`Quaternion`	`multLocal(float qx, float qy, float qz, float qw)` Multiplies by a quaternion with the specified components and returns the (modified) current instance.
`Quaternion`	`multLocal(Quaternion q)` Multiplies by the argument and returns the (modified) current instance.
`float`	`norm()` Returns the norm, defined as the dot product of the quaternion with itself.
`Quaternion`	`normalizeLocal()` Scales the quaternion to have norm=1 and returns the (modified) current instance.
`Quaternion`	`set(float x, float y, float z, float w)` Sets all 4 components to specified values.
`Quaternion`	`set(Quaternion q)` Copies all 4 components from the argument.
`Matrix3f`	`toRotationMatrix()` Converts to an equivalent rotation matrix.
`Matrix3f`	`toRotationMatrix(Matrix3f result)` Converts to an equivalent rotation matrix.
`Matrix4f`	`toRotationMatrix(Matrix4f result)` Sets the rotation component of the specified transform matrix.
`java.lang.String`	`toString()` Returns a string representation of the quaternion, which is unaffected.
`Matrix4f`	`toTransformMatrix(Matrix4f store)` Sets the rotation component of the specified transform matrix.

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

- Field Detail
  - IDENTITY
```
public static final Quaternion IDENTITY
```
    Shared instance of the identity quaternion (0, 0, 0, 1). Do not modify!
    This is the usual representation for a null rotation.
  - DIRECTION_Z
```
public static final Quaternion DIRECTION_Z
```
    Another shared instance of the identity quaternion (0, 0, 0, 1). Do not modify!
  - ZERO
```
public static final Quaternion ZERO
```
    Shared instance of the zero quaternion (0, 0, 0, 0). Do not modify!
    The zero quaternion doesn't represent any valid rotation.
  - x
```
protected float x
```
    The first imaginary (X) component. Not an angle!
  - y
```
protected float y
```
    The 2nd imaginary (Y) component. Not an angle!
  - z
```
protected float z
```
    The 3rd imaginary (Z) component. Not an angle!
  - w
```
protected float w
```
    The real (W) component. Not an angle!
- Constructor Detail
  - Quaternion
```
public Quaternion()
```
    Instantiates an identity quaternion: all components zeroed except w, which is set to 1.
  - Quaternion
```
public Quaternion(float x,
                  float y,
                  float z,
                  float w)
```
    Instantiates a quaternion with the specified components.
    
    Parameters:
    
    x - the desired X component
    
    y - the desired Y component
    
    z - the desired Z component
    
    w - the desired W component
  - Quaternion
```
public Quaternion(Quaternion q)
```
    Instantiates a copy of the argument.
    
    Parameters:
    
    q - the quaternion to copy (not null, unaffected)
- Method Detail
  - getX
```
public float getX()
```
    Returns the X component. The quaternion is unaffected.
    
    Returns:
    
    the value of the x component
  - getY
```
public float getY()
```
    Returns the Y component. The quaternion is unaffected.
    
    Returns:
    
    the value of the y component
  - getZ
```
public float getZ()
```
    Returns the Z component. The quaternion is unaffected.
    
    Returns:
    
    the value of the z component
  - getW
```
public float getW()
```
    Returns the W (real) component. The quaternion is unaffected.
    
    Returns:
    
    the value of the w component
  - set
```
public Quaternion set(float x,
                      float y,
                      float z,
                      float w)
```
    Sets all 4 components to specified values.
    
    Parameters:
    
    x - the desired X component
    
    y - the desired Y component
    
    z - the desired Z component
    
    w - the desired W component
    
    Returns:
    
    the (modified) current instance (for chaining)
  - set
```
public Quaternion set(Quaternion q)
```
    Copies all 4 components from the argument.
    
    Parameters:
    
    q - the quaternion to copy (not null, unaffected)
    
    Returns:
    
    the (modified) current instance (for chaining)
  - loadIdentity
```
public void loadIdentity()
```
    Sets all components to zero except w, which is set to 1.
  - fromAngles
```
public Quaternion fromAngles(float xAngle,
                             float yAngle,
                             float zAngle)
```
    Sets the quaternion from the specified Tait-Bryan angles, applying the rotations in x-z-y extrinsic order or y-z'-x" intrinsic order.
    
    Parameters:
    
    xAngle - the X angle (in radians)
    
    yAngle - the Y angle (in radians)
    
    zAngle - the Z angle (in radians)
    
    Returns:
    
    the (modified) current instance (for chaining)
    
    See Also:
    
    http://www.euclideanspace.com/maths/geometry/rotations/conversions/eulerToQuaternion/index.htm
  - fromRotationMatrix
```
public Quaternion fromRotationMatrix(Matrix3f matrix)
```
    Sets the quaternion from the specified rotation matrix.
    Does not verify that the argument is a valid rotation matrix. Positive scaling is compensated for, but not reflection or shear.
    
    Parameters:
    
    matrix - the input matrix (not null, unaffected)
    
    Returns:
    
    the (modified) current instance (for chaining)
  - fromRotationMatrix
```
public Quaternion fromRotationMatrix(float m00,
                                     float m01,
                                     float m02,
                                     float m10,
                                     float m11,
                                     float m12,
                                     float m20,
                                     float m21,
                                     float m22)
```
    Sets the quaternion from a rotation matrix with the specified elements.
    Does not verify that the arguments form a valid rotation matrix. Positive scaling is compensated for, but not reflection or shear.
    
    Parameters:
    
    m00 - the matrix element in row 0, column 0
    
    m01 - the matrix element in row 0, column 1
    
    m02 - the matrix element in row 0, column 2
    
    m10 - the matrix element in row 1, column 0
    
    m11 - the matrix element in row 1, column 1
    
    m12 - the matrix element in row 1, column 2
    
    m20 - the matrix element in row 2, column 0
    
    m21 - the matrix element in row 2, column 1
    
    m22 - the matrix element in row 2, column 2
    
    Returns:
    
    the (modified) current instance (for chaining)
  - toRotationMatrix
```
public Matrix3f toRotationMatrix()
```
    Converts to an equivalent rotation matrix. The current instance is unaffected.
    Note: the result is created from a normalized version of the current instance.
    
    Returns:
    
    a new 3x3 rotation matrix
  - toRotationMatrix
```
public Matrix3f toRotationMatrix(Matrix3f result)
```
    Converts to an equivalent rotation matrix. The current instance is unaffected.
    Note: the result is created from a normalized version of the current instance.
    
    Parameters:
    
    result - storage for the result (not null)
    
    Returns:
    
    result, configured as a 3x3 rotation matrix
  - toTransformMatrix
```
public Matrix4f toTransformMatrix(Matrix4f store)
```
    Sets the rotation component of the specified transform matrix. The current instance is unaffected.
    Note: preserves the translation component of store but not its scaling component.
    Note: the result is created from a normalized version of the current instance.
    
    Parameters:
    
    store - storage for the result (not null)
    
    Returns:
    
    store, with 9 of its 16 elements modified
  - toRotationMatrix
```
public Matrix4f toRotationMatrix(Matrix4f result)
```
    Sets the rotation component of the specified transform matrix. The current instance is unaffected.
    Note: preserves the translation and scaling components of result unless result includes reflection.
    Note: the result is created from a normalized version of the current instance.
    
    Parameters:
    
    result - storage for the result (not null)
    
    Returns:
    
    result, with 9 of its 16 elements modified
  - fromAngleNormalAxis
```
public Quaternion fromAngleNormalAxis(float angle,
                                      Vector3f axis)
```
    Sets the quaternion from the specified rotation angle and normalized axis of rotation.
    
    Parameters:
    
    angle - the desired rotation angle (in radians)
    
    axis - the desired axis of rotation (not null, length=1, unaffected)
    
    Returns:
    
    the (modified) current instance (for chaining)
  - addLocal
```
public Quaternion addLocal(Quaternion q)
```
    Adds the argument and returns the (modified) current instance.
    Seldom used. To combine rotations, use multLocal(com.jme3.math.Quaternion) or mult(com.jme3.math.Quaternion, com.jme3.math.Quaternion) instead of this method.
    
    Parameters:
    
    q - the quaternion to add (not null, unaffected unless it's this)
    
    Returns:
    
    the (modified) current instance (for chaining)
  - mult
```
public Quaternion mult(Quaternion q)
```
    Multiplies by the argument and returns the product as a new instance. The current instance is unaffected.
    This method is used to combine rotations. Note that quaternion multiplication is noncommutative, so generally q * p != p * q.
    
    Parameters:
    
    q - the right factor (not null, unaffected)
    
    Returns:
    
    this * q (a new Quaternion)
  - mult
```
public Quaternion mult(Quaternion q,
                       Quaternion storeResult)
```
    Multiplies by the specified quaternion and returns the product in a 3rd quaternion. The current instance is unaffected, unless it's storeResult.
    This method is used to combine rotations. Note that quaternion multiplication is noncommutative, so generally q * p != p * q.
    It is safe for q and storeResult to be the same object. However, if this and storeResult are the same object, the result is undefined.
    
    Parameters:
    
    q - the right factor (not null, unaffected unless it's storeResult)
    
    storeResult - storage for the product, or null for a new Quaternion
    
    Returns:
    
    this * q (either storeResult or a new Quaternion)
  - fromAxes
```
public Quaternion fromAxes(Vector3f xAxis,
                           Vector3f yAxis,
                           Vector3f zAxis)
```
    Sets the quaternion from the specified orthonormal basis.
    The 3 basis vectors describe the axes of a rotated coordinate system. They are assumed to be normalized, mutually orthogonal, and in right-hand order. No error checking is performed; the caller must ensure that the specified vectors represent a right-handed coordinate system.
    
    Parameters:
    
    xAxis - the X axis of the desired coordinate system (not null, length=1, unaffected)
    
    yAxis - the Y axis of the desired coordinate system (not null, length=1, unaffected)
    
    zAxis - the Z axis of the desired coordinate system (not null, length=1, unaffected)
    
    Returns:
    
    the (modified) current instance (for chaining)
  - multLocal
```
public Quaternion multLocal(Quaternion q)
```
    Multiplies by the argument and returns the (modified) current instance.
    This method is used to combine rotations. Note that quaternion multiplication is noncommutative, so generally q * p != p * q.
    
    Parameters:
    
    q - the right factor (not null, unaffected unless it's this)
    
    Returns:
    
    the (modified) current instance (for chaining)
  - multLocal
```
public Quaternion multLocal(float qx,
                            float qy,
                            float qz,
                            float qw)
```
    Multiplies by a quaternion with the specified components and returns the (modified) current instance.
    This method is used to combine rotations. Note that quaternion multiplication is noncommutative, so generally q * p != p * q.
    
    Parameters:
    
    qx - the X component of the right factor
    
    qy - the Y component of the right factor
    
    qz - the Z component of the right factor
    
    qw - the W component of the right factor
    
    Returns:
    
    the (modified) current instance (for chaining)
  - multLocal
```
public Quaternion multLocal(float scalar)
```
    Multiplies by the scalar argument and returns the (modified) current instance.
    
    Parameters:
    
    scalar - the scaling factor
    
    Returns:
    
    the (modified) current instance (for chaining)
  - norm
```
public float norm()
```
    Returns the norm, defined as the dot product of the quaternion with itself. The current instance is unaffected.
    
    Returns:
    
    the sum of the squared components (not negative)
  - normalizeLocal
```
public Quaternion normalizeLocal()
```
    Scales the quaternion to have norm=1 and returns the (modified) current instance. For a quaternion with norm=0, the result is undefined.
    
    Returns:
    
    the (modified) current instance (for chaining)
  - inverse
```
public Quaternion inverse()
```
    Returns the multiplicative inverse. For a quaternion with norm=0, null is returned. Either way, the current instance is unaffected.
    
    Returns:
    
    a new Quaternion or null
  - toString
```
public java.lang.String toString()
```
    Returns a string representation of the quaternion, which is unaffected. For example, the identity quaternion is represented by:
```
 (0.0, 0.0, 0.0, 1.0)
 
```
    Overrides:
    
    toString in class java.lang.Object
    
    Returns:
    
    the string representation (not null, not empty)
  - equals
```
public boolean equals(java.lang.Object o)
```
    Tests for exact equality with the argument, distinguishing -0 from 0. If o is null, false is returned. Either way, the current instance is unaffected.
    
    Overrides:
    
    equals in class java.lang.Object
    
    Parameters:
    
    o - the object to compare (may be null, unaffected)
    
    Returns:
    
    true if this and o have identical values, otherwise false
  - hashCode
```
public int hashCode()
```
    Returns a hash code. If two quaternions have identical values, they will have the same hash code. The current instance is unaffected.
    
    Overrides:
    
    hashCode in class java.lang.Object
    
    Returns:
    
    a 32-bit value for use in hashing
    
    See Also:
    
    Object.hashCode()
  - clone
```
public Quaternion clone()
```
    Creates a copy. The current instance is unaffected.
    
    Overrides:
    
    clone in class java.lang.Object
    
    Returns:
    
    a new instance, equivalent to the current one

Class Quaternion

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

IDENTITY

DIRECTION_Z

ZERO

x

y

z

w

Constructor Detail

Quaternion

Quaternion

Quaternion

Method Detail

getX

getY

getZ

getW

set

set

loadIdentity

fromAngles

fromRotationMatrix

fromRotationMatrix

toRotationMatrix

toRotationMatrix

toTransformMatrix

toRotationMatrix

fromAngleNormalAxis

addLocal

mult

mult

fromAxes

multLocal

multLocal

multLocal

norm

normalizeLocal

inverse

toString

equals

hashCode

clone