java.lang.Object
- org.apache.commons.numbers.quaternion.Quaternion

All Implemented Interfaces:

Serializable
```
public final class Quaternion
extends Object
implements Serializable
```
This class implements quaternions (Hamilton's hypercomplex numbers).
Wherever quaternion components are listed in sequence, this class follows the convention of placing the scalar (w) component first, e.g. [w, x, y, z]. Other libraries and textbooks may place the w component last.

Instances of this class are guaranteed to be immutable.

See Also:

Serialized Form

Field Summary

Fields
Modifier and Type	Field	Description
`static Quaternion`	`I`	i.
`static Quaternion`	`J`	j.
`static Quaternion`	`K`	k.
`static Quaternion`	`ONE`	Identity quaternion.
`static Quaternion`	`ZERO`	Zero quaternion.

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method	Description
`Quaternion`	`add(Quaternion q)`	Computes the sum of the instance and another quaternion.
`static Quaternion`	`add(Quaternion q1, Quaternion q2)`	Computes the sum of two quaternions.
`Quaternion`	`conjugate()`	Returns the conjugate of this quaternion number.
`Quaternion`	`divide(double alpha)`	Divides the instance by a scalar.
`double`	`dot(Quaternion q)`	Computes the dot-product of the instance by a quaternion.
`static double`	`dot(Quaternion q1, Quaternion q2)`	Computes the dot-product of two quaternions.
`boolean`	`equals(Object other)`
`boolean`	`equals(Quaternion q, double eps)`	Checks whether this instance is equal to another quaternion within a given tolerance.
`double`	`getScalarPart()`	Gets the scalar part of the quaternion.
`double[]`	`getVectorPart()`	Gets the three components of the vector part of the quaternion.
`double`	`getW()`	Gets the first component of the quaternion (scalar part).
`double`	`getX()`	Gets the second component of the quaternion (first component of the vector part).
`double`	`getY()`	Gets the third component of the quaternion (second component of the vector part).
`double`	`getZ()`	Gets the fourth component of the quaternion (third component of the vector part).
`int`	`hashCode()`
`Quaternion`	`inverse()`	Returns the inverse of this instance.
`boolean`	`isPure(double eps)`	Checks whether the instance is a pure quaternion within a given tolerance.
`boolean`	`isUnit(double eps)`	Checks whether the instance is a unit quaternion within a given tolerance.
`Quaternion`	`multiply(double alpha)`	Multiplies the instance by a scalar.
`Quaternion`	`multiply(Quaternion q)`	Returns the Hamilton product of the instance by a quaternion.
`static Quaternion`	`multiply(Quaternion q1, Quaternion q2)`	Returns the Hamilton product of two quaternions.
`Quaternion`	`negate()`	Returns the opposite of this instance.
`double`	`norm()`	Computes the norm of the quaternion.
`Quaternion`	`normalize()`	Computes the normalized quaternion (the versor of the instance).
`double`	`normSq()`	Computes the square of the norm of the quaternion.
`static Quaternion`	`of(double[] v)`	Builds a pure quaternion from a vector (assuming that the scalar part is zero).
`static Quaternion`	`of(double scalar, double[] v)`	Builds a quaternion from scalar and vector parts.
`static Quaternion`	`of(double w, double x, double y, double z)`	Builds a quaternion from its components.
`static Quaternion`	`parse(String s)`	Parses a string that would be produced by `toString()` and instantiates the corresponding object.
`Quaternion`	`positivePolarForm()`	Returns the polar form of the quaternion.
`Quaternion`	`subtract(Quaternion q)`	Subtracts a quaternion from the instance.
`static Quaternion`	`subtract(Quaternion q1, Quaternion q2)`	Subtracts two quaternions.
`String`	`toString()`

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

- Field Detail
  - ZERO
```
public static final Quaternion ZERO
```
    Zero quaternion.
  - ONE
```
public static final Quaternion ONE
```
    Identity quaternion.
  - I
```
public static final Quaternion I
```
    i.
  - J
```
public static final Quaternion J
```
    j.
  - K
```
public static final Quaternion K
```
    k.
- Method Detail
  - of
```
public static Quaternion of(double w,
                            double x,
                            double y,
                            double z)
```
    Builds a quaternion from its components.
    
    Parameters:
    
    w - Scalar component.
    
    x - First vector component.
    
    y - Second vector component.
    
    z - Third vector component.
    
    Returns:
    
    a quaternion instance.
  - of
```
public static Quaternion of(double scalar,
                            double[] v)
```
    Builds a quaternion from scalar and vector parts.
    
    Parameters:
    
    scalar - Scalar part of the quaternion.
    
    v - Components of the vector part of the quaternion.
    
    Returns:
    
    a quaternion instance.
    
    Throws:
    
    IllegalArgumentException - if the array length is not 3.
  - of
```
public static Quaternion of(double[] v)
```
    Builds a pure quaternion from a vector (assuming that the scalar part is zero).
    
    Parameters:
    
    v - Components of the vector part of the pure quaternion.
    
    Returns:
    
    a quaternion instance.
  - conjugate
```
public Quaternion conjugate()
```
    Returns the conjugate of this quaternion number. The conjugate of a + bi + cj + dk is a - bi -cj -dk.
    
    Returns:
    
    the conjugate of this quaternion object.
  - multiply
```
public static Quaternion multiply(Quaternion q1,
                                  Quaternion q2)
```
    Returns the Hamilton product of two quaternions.
    
    Parameters:
    
    q1 - First quaternion.
    
    q2 - Second quaternion.
    
    Returns:
    
    the product q1 and q2, in that order.
  - multiply
```
public Quaternion multiply(Quaternion q)
```
    Returns the Hamilton product of the instance by a quaternion.
    
    Parameters:
    
    q - Quaternion.
    
    Returns:
    
    the product of this instance with q, in that order.
  - add
```
public static Quaternion add(Quaternion q1,
                             Quaternion q2)
```
    Computes the sum of two quaternions.
    
    Parameters:
    
    q1 - Quaternion.
    
    q2 - Quaternion.
    
    Returns:
    
    the sum of q1 and q2.
  - add
```
public Quaternion add(Quaternion q)
```
    Computes the sum of the instance and another quaternion.
    
    Parameters:
    
    q - Quaternion.
    
    Returns:
    
    the sum of this instance and q.
  - subtract
```
public static Quaternion subtract(Quaternion q1,
                                  Quaternion q2)
```
    Subtracts two quaternions.
    
    Parameters:
    
    q1 - First Quaternion.
    
    q2 - Second quaternion.
    
    Returns:
    
    the difference between q1 and q2.
  - subtract
```
public Quaternion subtract(Quaternion q)
```
    Subtracts a quaternion from the instance.
    
    Parameters:
    
    q - Quaternion.
    
    Returns:
    
    the difference between this instance and q.
  - dot
```
public static double dot(Quaternion q1,
                         Quaternion q2)
```
    Computes the dot-product of two quaternions.
    
    Parameters:
    
    q1 - Quaternion.
    
    q2 - Quaternion.
    
    Returns:
    
    the dot product of q1 and q2.
  - dot
```
public double dot(Quaternion q)
```
    Computes the dot-product of the instance by a quaternion.
    
    Parameters:
    
    q - Quaternion.
    
    Returns:
    
    the dot product of this instance and q.
  - norm
```
public double norm()
```
    Computes the norm of the quaternion.
    
    Returns:
    
    the norm.
  - normSq
```
public double normSq()
```
    Computes the square of the norm of the quaternion.
    
    Returns:
    
    the square of the norm.
  - normalize
```
public Quaternion normalize()
```
    Computes the normalized quaternion (the versor of the instance). The norm of the quaternion must not be near zero.
    
    Returns:
    
    a normalized quaternion.
    
    Throws:
    
    IllegalStateException - if the norm of the quaternion is NaN, infinite, or near zero.
  - equals
```
public boolean equals(Object other)
```
    Overrides:
    
    equals in class Object
  - hashCode
```
public int hashCode()
```
    Overrides:
    
    hashCode in class Object
  - equals
```
public boolean equals(Quaternion q,
                      double eps)
```
    Checks whether this instance is equal to another quaternion within a given tolerance.
    
    Parameters:
    
    q - Quaternion with which to compare the current quaternion.
    
    eps - Tolerance.
    
    Returns:
    
    true if the each of the components are equal within the allowed absolute error.
  - isUnit
```
public boolean isUnit(double eps)
```
    Checks whether the instance is a unit quaternion within a given tolerance.
    
    Parameters:
    
    eps - Tolerance (absolute error).
    
    Returns:
    
    true if the norm is 1 within the given tolerance, false otherwise
  - isPure
```
public boolean isPure(double eps)
```
    Checks whether the instance is a pure quaternion within a given tolerance.
    
    Parameters:
    
    eps - Tolerance (absolute error).
    
    Returns:
    
    true if the scalar part of the quaternion is zero.
  - positivePolarForm
```
public Quaternion positivePolarForm()
```
    Returns the polar form of the quaternion.
    
    Returns:
    
    the unit quaternion with positive scalar part.
  - negate
```
public Quaternion negate()
```
    Returns the opposite of this instance.
    
    Returns:
    
    the quaternion for which all components have an opposite sign to this one.
  - inverse
```
public Quaternion inverse()
```
    Returns the inverse of this instance. The norm of the quaternion must not be zero.
    
    Returns:
    
    the inverse.
    
    Throws:
    
    IllegalStateException - if the norm (squared) of the quaternion is NaN, infinite, or near zero.
  - getW
```
public double getW()
```
    Gets the first component of the quaternion (scalar part).
    
    Returns:
    
    the scalar part.
  - getX
```
public double getX()
```
    Gets the second component of the quaternion (first component of the vector part).
    
    Returns:
    
    the first component of the vector part.
  - getY
```
public double getY()
```
    Gets the third component of the quaternion (second component of the vector part).
    
    Returns:
    
    the second component of the vector part.
  - getZ
```
public double getZ()
```
    Gets the fourth component of the quaternion (third component of the vector part).
    
    Returns:
    
    the third component of the vector part.
  - getScalarPart
```
public double getScalarPart()
```
    Gets the scalar part of the quaternion.
    
    Returns:
    
    the scalar part.
    
    See Also:
    
    getW()
  - getVectorPart
```
public double[] getVectorPart()
```
    Gets the three components of the vector part of the quaternion.
    
    Returns:
    
    the vector part.
    
    See Also:
    
    getX(), getY(), getZ()
  - multiply
```
public Quaternion multiply(double alpha)
```
    Multiplies the instance by a scalar.
    
    Parameters:
    
    alpha - Scalar factor.
    
    Returns:
    
    a scaled quaternion.
  - divide
```
public Quaternion divide(double alpha)
```
    Divides the instance by a scalar.
    
    Parameters:
    
    alpha - Scalar factor.
    
    Returns:
    
    a scaled quaternion.
  - parse
```
public static Quaternion parse(String s)
```
    Parses a string that would be produced by toString() and instantiates the corresponding object.
    
    Parameters:
    
    s - String representation.
    
    Returns:
    
    an instance.
    
    Throws:
    
    NumberFormatException - if the string does not conform to the specification.
  - toString
```
public String toString()
```
    Overrides:
    
    toString in class Object

Class Quaternion

Field Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

ZERO

ONE

I

J

K

Method Detail

of

of

of

conjugate

multiply

multiply

add

add

subtract

subtract

dot

dot

norm

normSq

normalize

equals

hashCode

equals

isUnit

isPure

positivePolarForm

negate

inverse

getW

getX

getY

getZ

getScalarPart

getVectorPart

multiply

divide

parse

toString