Quaternion

Documentation of 'jsci.maths.Quaternion' Java class Quaternion

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java.lang.Object
- jsci.maths.Quaternion

All Implemented Interfaces:

java.io.Serializable, Algebra.Member, BanachSpace.Member, CStarAlgebra.Member, Module.Member, VectorSpace.Member, Field.Member, Ring.Member, AbelianGroup.Member, Member
```
public final class Quaternion
extends java.lang.Object
implements Field.Member, CStarAlgebra.Member
```
The Quaternion class encapsulates quaternions.

See Also:

Serialized Form

Field Summary

Fields
Modifier and Type Field and Description

static Quaternion I

static Quaternion J

static Quaternion K

static Quaternion ONE

Fields
Modifier and Type	Field and Description
`static Quaternion`	`I`
`static Quaternion`	`J`
`static Quaternion`	`K`
`static Quaternion`	`ONE`

Constructor Summary

Constructors
Constructor and Description
`Quaternion(double real, Double3Vector imag)` Constructs a quaternion.
`Quaternion(double q0, double q1, double q2, double q3)` Constructs the quaternion q₀+iq₁+jq₂+kq₃.

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`AbelianGroup.Member`	`add(AbelianGroup.Member x)` Returns the addition of this number and another.
`Quaternion`	`add(Quaternion q)` Returns the addition of this quaternion and another.
`Quaternion`	`addImag(Double3Vector imag)` Returns the addition of this quaternion with an imaginary part.
`Quaternion`	`addReal(double real)` Returns the addition of this quaternion with a real part.
`Quaternion`	`conjugate()` Returns the conjugate of this quaternion.
`static Quaternion`	`cos(Quaternion q)`
`static Quaternion`	`cosh(Quaternion q)`
`Quaternion`	`divide(double x)` Returns the division of this quaternion by a scalar.
`Field.Member`	`divide(Field.Member x)` Returns the division of this number and another.
`Quaternion`	`divide(Quaternion q)` Returns the division of this quaternion by another.
`boolean`	`equals(java.lang.Object obj)` Compares two quaternions for equality.
`static Quaternion`	`exp(Quaternion q)`
`java.lang.Object`	`getSet()`
`int`	`hashCode()` Returns a hashcode for this quaternion.
`Double3Vector`	`imag()` Returns the imaginary part of this quaternion.
`Field.Member`	`inverse()` Returns the inverse of this quaternion.
`CStarAlgebra.Member`	`involution()` Returns the involution of this quaternion.
`boolean`	`isInfinite()` Returns true if either the real or imaginary part is infinite.
`boolean`	`isNaN()` Returns true if either the real or imaginary part is NaN.
`static Quaternion`	`log(Quaternion q)`
`Quaternion`	`multiply(double x)` Returns the multiplication of this quaternion by a scalar.
`Quaternion`	`multiply(Quaternion q)` Returns the multiplication of this quaternion and another.
`Ring.Member`	`multiply(Ring.Member x)` Returns the multiplication of this number and another.
`AbelianGroup.Member`	`negate()` Returns the negative of this quaternion.
`double`	`norm()` Returns the l²-norm (magnitude), which is also the C^* norm.
`Quaternion`	`normalize()`
`double`	`real()` Returns the real part of this quaternion.
`static Quaternion`	`rotation(AbstractDoubleSquareMatrix m)` Constructs a quaternion representing a rotation matrix.
`VectorSpace.Member`	`scalarDivide(Field.Member x)` Returns the division of this number by a real scalar.
`Module.Member`	`scalarMultiply(Ring.Member x)` Returns the multiplication of this number by a real scalar.
`static Quaternion`	`sin(Quaternion q)`
`static Quaternion`	`sinh(Quaternion q)`
`AbelianGroup.Member`	`subtract(AbelianGroup.Member x)` Returns the subtraction of this number and another.
`Quaternion`	`subtract(Quaternion q)` Returns the subtraction of this quaternion by another.
`Quaternion`	`subtractImag(Double3Vector imag)` Returns the subtraction of this quaternion by an imaginary part.
`Quaternion`	`subtractReal(double real)` Returns the subtraction of this quaternion by a real part.
`double`	`sumSquares()` Returns the sum of the squares of the components.
`static Quaternion`	`tan(Quaternion q)`
`static Quaternion`	`tanh(Quaternion q)`
`AbstractDoubleSquareMatrix`	`toRotationMatrix()` Returns a 3D rotation matrix representing this quaternion.
`java.lang.String`	`toString()` Returns a string representing the value of this quaternion.

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

- Field Detail
  - ONE
```
public static final Quaternion ONE
```
  - I
```
public static final Quaternion I
```
  - J
```
public static final Quaternion J
```
  - K
```
public static final Quaternion K
```
- Constructor Detail
  - Quaternion
```
public Quaternion(double real,
                  Double3Vector imag)
```
    Constructs a quaternion.
  - Quaternion
```
public Quaternion(double q0,
                  double q1,
                  double q2,
                  double q3)
```
    Constructs the quaternion q₀+iq₁+jq₂+kq₃.
- Method Detail
  - rotation
```
public static Quaternion rotation(AbstractDoubleSquareMatrix m)
```
    Constructs a quaternion representing a rotation matrix. Note: if the matrix is not orthogonal then the quaternion will not have unit norm. Note: unit quaternions are a double cover of SO(3).
    
    Parameters:
    
    m - a rotation matrix
  - toRotationMatrix
```
public AbstractDoubleSquareMatrix toRotationMatrix()
```
    Returns a 3D rotation matrix representing this quaternion. Note: if this quaternion does not have unit norm then the matrix will not be orthogonal.
  - equals
```
public boolean equals(java.lang.Object obj)
```
    Compares two quaternions for equality.
    
    Overrides:
    
    equals in class java.lang.Object
    
    Parameters:
    
    obj - a quaternion
  - toString
```
public java.lang.String toString()
```
    Returns a string representing the value of this quaternion.
    
    Overrides:
    
    toString in class java.lang.Object
  - hashCode
```
public int hashCode()
```
    Returns a hashcode for this quaternion.
    
    Overrides:
    
    hashCode in class java.lang.Object
  - isNaN
```
public boolean isNaN()
```
    Returns true if either the real or imaginary part is NaN.
  - isInfinite
```
public boolean isInfinite()
```
    Returns true if either the real or imaginary part is infinite.
  - real
```
public double real()
```
    Returns the real part of this quaternion.
  - imag
```
public Double3Vector imag()
```
    Returns the imaginary part of this quaternion.
  - getSet
```
public java.lang.Object getSet()
```
    Specified by:
    
    getSet in interface Member
  - norm
```
public double norm()
```
    Returns the l²-norm (magnitude), which is also the C^* norm.
    
    Specified by:
    
    norm in interface BanachSpace.Member
  - sumSquares
```
public double sumSquares()
```
    Returns the sum of the squares of the components.
  - negate
```
public AbelianGroup.Member negate()
```
    Returns the negative of this quaternion.
    
    Specified by:
    
    negate in interface AbelianGroup.Member
  - inverse
```
public Field.Member inverse()
```
    Returns the inverse of this quaternion.
    
    Specified by:
    
    inverse in interface Field.Member
  - involution
```
public CStarAlgebra.Member involution()
```
    Returns the involution of this quaternion.
    
    Specified by:
    
    involution in interface CStarAlgebra.Member
  - conjugate
```
public Quaternion conjugate()
```
    Returns the conjugate of this quaternion.
  - add
```
public AbelianGroup.Member add(AbelianGroup.Member x)
```
    Returns the addition of this number and another.
    
    Specified by:
    
    add in interface AbelianGroup.Member
    
    Parameters:
    
    x - a group member
  - add
```
public Quaternion add(Quaternion q)
```
    Returns the addition of this quaternion and another.
    
    Parameters:
    
    q - a quaternion
  - addReal
```
public Quaternion addReal(double real)
```
    Returns the addition of this quaternion with a real part.
    
    Parameters:
    
    real - a real part
  - addImag
```
public Quaternion addImag(Double3Vector imag)
```
    Returns the addition of this quaternion with an imaginary part.
    
    Parameters:
    
    imag - an imaginary part
  - subtract
```
public AbelianGroup.Member subtract(AbelianGroup.Member x)
```
    Returns the subtraction of this number and another.
    
    Specified by:
    
    subtract in interface AbelianGroup.Member
    
    Parameters:
    
    x - a group member
  - subtract
```
public Quaternion subtract(Quaternion q)
```
    Returns the subtraction of this quaternion by another.
    
    Parameters:
    
    q - a quaternion
  - subtractReal
```
public Quaternion subtractReal(double real)
```
    Returns the subtraction of this quaternion by a real part.
    
    Parameters:
    
    real - a real part
  - subtractImag
```
public Quaternion subtractImag(Double3Vector imag)
```
    Returns the subtraction of this quaternion by an imaginary part.
    
    Parameters:
    
    imag - an imaginary part
  - scalarMultiply
```
public Module.Member scalarMultiply(Ring.Member x)
```
    Returns the multiplication of this number by a real scalar.
    
    Specified by:
    
    scalarMultiply in interface Module.Member
    
    Parameters:
    
    x - a ring member
  - multiply
```
public Ring.Member multiply(Ring.Member x)
```
    Returns the multiplication of this number and another.
    
    Specified by:
    
    multiply in interface Ring.Member
    
    Parameters:
    
    x - a ring member
  - multiply
```
public Quaternion multiply(Quaternion q)
```
    Returns the multiplication of this quaternion and another.
    
    Parameters:
    
    q - a quaternion
  - multiply
```
public Quaternion multiply(double x)
```
    Returns the multiplication of this quaternion by a scalar.
    
    Parameters:
    
    x - a real number
  - scalarDivide
```
public VectorSpace.Member scalarDivide(Field.Member x)
```
    Returns the division of this number by a real scalar.
    
    Specified by:
    
    scalarDivide in interface VectorSpace.Member
    
    Parameters:
    
    x - a field member
  - divide
```
public Field.Member divide(Field.Member x)
```
    Returns the division of this number and another.
    
    Specified by:
    
    divide in interface Field.Member
    
    Parameters:
    
    x - a field member
  - divide
```
public Quaternion divide(Quaternion q)
```
    Returns the division of this quaternion by another.
    
    Parameters:
    
    q - a quaternion
    
    Throws:
    
    java.lang.ArithmeticException - If divide by zero.
  - divide
```
public Quaternion divide(double x)
```
    Returns the division of this quaternion by a scalar.
    
    Parameters:
    
    x - a real number
    
    Throws:
    
    java.lang.ArithmeticException - If divide by zero.
  - normalize
```
public Quaternion normalize()
```
  - exp
```
public static Quaternion exp(Quaternion q)
```
  - log
```
public static Quaternion log(Quaternion q)
```
  - sin
```
public static Quaternion sin(Quaternion q)
```
  - cos
```
public static Quaternion cos(Quaternion q)
```
  - tan
```
public static Quaternion tan(Quaternion q)
```
  - sinh
```
public static Quaternion sinh(Quaternion q)
```
  - cosh
```
public static Quaternion cosh(Quaternion q)
```
  - tanh
```
public static Quaternion tanh(Quaternion q)
```

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All Classes

Summary:
Nested |
Field |
Constr |
Method

Detail:
Field |
Constr |
Method

Class Quaternion

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

ONE

I

J

K

Constructor Detail

Quaternion

Quaternion

Method Detail

rotation

toRotationMatrix

equals

toString

hashCode

isNaN

isInfinite

real

imag

getSet

norm

sumSquares

negate

inverse

involution

conjugate

add

add

addReal

addImag

subtract

subtract

subtractReal

subtractImag

scalarMultiply

multiply

multiply

multiply

scalarDivide

divide

divide

divide

normalize

exp

log

sin

cos

tan

sinh

cosh

tanh