Quaternion (Apache Commons Math 3.6.1 API)

java.lang.Object
- org.apache.commons.math3.complex.Quaternion

All Implemented Interfaces:

Serializable
```
public final class Quaternion
extends Object
implements Serializable
```
This class implements quaternions (Hamilton's hypercomplex numbers).
Instance of this class are guaranteed to be immutable.

Since:

3.1

See Also:
Serialized Form

Field Summary

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

Constructor Summary

Constructors
Constructor and Description
`Quaternion(double[] v)` Builds a pure quaternion from a vector (assuming that the scalar part is zero).
`Quaternion(double scalar, double[] v)` Builds a quaternion from scalar and vector parts.
`Quaternion(double a, double b, double c, double d)` Builds a quaternion from its components.

Method Summary

Methods
Modifier and Type	Method and 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.
`double`	`dotProduct(Quaternion q)` Computes the dot-product of the instance by a quaternion.
`static double`	`dotProduct(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.
`Quaternion`	`getConjugate()` Returns the conjugate quaternion of the instance.
`Quaternion`	`getInverse()` Returns the inverse of this instance.
`double`	`getNorm()` Computes the norm of the quaternion.
`Quaternion`	`getPositivePolarForm()` Returns the polar form of the quaternion.
`double`	`getQ0()` Gets the first component of the quaternion (scalar part).
`double`	`getQ1()` Gets the second component of the quaternion (first component of the vector part).
`double`	`getQ2()` Gets the third component of the quaternion (second component of the vector part).
`double`	`getQ3()` Gets the fourth component of the quaternion (third component of the vector part).
`double`	`getScalarPart()` Gets the scalar part of the quaternion.
`double[]`	`getVectorPart()` Gets the three components of the vector part of the quaternion.
`int`	`hashCode()`
`boolean`	`isPureQuaternion(double eps)` Checks whether the instance is a pure quaternion within a given tolerance.
`boolean`	`isUnitQuaternion(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`	`normalize()` Computes the normalized quaternion (the versor of the instance).
`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
  - IDENTITY
```
public static final Quaternion IDENTITY
```
    Identity quaternion.
  - ZERO
```
public static final Quaternion ZERO
```
    Zero quaternion.
  - I
```
public static final Quaternion I
```
    i
  - J
```
public static final Quaternion J
```
    j
  - K
```
public static final Quaternion K
```
    k
- Constructor Detail
  - Quaternion
```
public Quaternion(double a,
          double b,
          double c,
          double d)
```
    Builds a quaternion from its components.
    
    Parameters:
    a - Scalar component.
    b - First vector component.
    c - Second vector component.
    d - Third vector component.
  - Quaternion
```
public Quaternion(double scalar,
          double[] v)
           throws DimensionMismatchException
```
    Builds a quaternion from scalar and vector parts.
    
    Parameters:
    scalar - Scalar part of the quaternion.
    v - Components of the vector part of the quaternion.
    
    Throws:
    
    DimensionMismatchException - if the array length is not 3.
  - Quaternion
```
public Quaternion(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.
- Method Detail
  - getConjugate
```
public Quaternion getConjugate()
```
    Returns the conjugate quaternion of the instance.
    
    Returns:
    the conjugate quaternion
  - 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.
  - dotProduct
```
public static double dotProduct(Quaternion q1,
                Quaternion q2)
```
    Computes the dot-product of two quaternions.
    
    Parameters:
    q1 - Quaternion.
    q2 - Quaternion.
    
    Returns:
    the dot product of q1 and q2.
  - dotProduct
```
public double dotProduct(Quaternion q)
```
    Computes the dot-product of the instance by a quaternion.
    
    Parameters:
    q - Quaternion.
    
    Returns:
    the dot product of this instance and q.
  - getNorm
```
public double getNorm()
```
    Computes the norm of the quaternion.
    
    Returns:
    the norm.
  - normalize
```
public Quaternion normalize()
```
    Computes the normalized quaternion (the versor of the instance). The norm of the quaternion must not be zero.
    
    Returns:
    a normalized quaternion.
    
    Throws:
    
    ZeroException - if the norm of the quaternion is 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.
  - isUnitQuaternion
```
public boolean isUnitQuaternion(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
  - isPureQuaternion
```
public boolean isPureQuaternion(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.
  - getPositivePolarForm
```
public Quaternion getPositivePolarForm()
```
    Returns the polar form of the quaternion.
    
    Returns:
    the unit quaternion with positive scalar part.
  - getInverse
```
public Quaternion getInverse()
```
    Returns the inverse of this instance. The norm of the quaternion must not be zero.
    
    Returns:
    the inverse.
    
    Throws:
    
    ZeroException - if the norm (squared) of the quaternion is zero.
  - getQ0
```
public double getQ0()
```
    Gets the first component of the quaternion (scalar part).
    
    Returns:
    the scalar part.
  - getQ1
```
public double getQ1()
```
    Gets the second component of the quaternion (first component of the vector part).
    
    Returns:
    the first component of the vector part.
  - getQ2
```
public double getQ2()
```
    Gets the third component of the quaternion (second component of the vector part).
    
    Returns:
    the second component of the vector part.
  - getQ3
```
public double getQ3()
```
    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:
    getQ0()
  - getVectorPart
```
public double[] getVectorPart()
```
    Gets the three components of the vector part of the quaternion.
    
    Returns:
    the vector part.
    See Also:
    getQ1(), getQ2(), getQ3()
  - multiply
```
public Quaternion multiply(double alpha)
```
    Multiplies the instance by a scalar.
    
    Parameters:
    alpha - Scalar factor.
    
    Returns:
    a scaled quaternion.
  - toString
```
public String toString()
```
    Overrides:
    
    toString in class Object

Class Quaternion

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

IDENTITY

ZERO

I

J

K

Constructor Detail

Quaternion

Quaternion

Quaternion

Method Detail

getConjugate

multiply

multiply

add

add

subtract

subtract

dotProduct

dotProduct

getNorm

normalize

equals

hashCode

equals

isUnitQuaternion

isPureQuaternion

getPositivePolarForm

getInverse

getQ0

getQ1

getQ2

getQ3

getScalarPart

getVectorPart

multiply

toString