java.lang.Object
- org.robwork.sdurw_math.Rotation3DVector
- - org.robwork.sdurw_math.Quaternion

```
public class Quaternion
extends Rotation3DVector
```
A Quaternion \mathbf{q}\in \mathbb{R}^4 a complex
number used to describe rotations in 3-dimensional space.
q_w+{\bf i}\ q_x+ {\bf j} q_y+ {\bf k}\ q_z

Quaternions can be added and multiplied in a similar way as usual
algebraic numbers. Though there are differences. Quaternion
multiplication is not commutative which means
Q\cdot P \neq P\cdot Q

Constructor Summary

Constructors
Constructor	Description
`Quaternion()`	constuct Quaterinion of {0,0,0,1}
`Quaternion(double qx, double qy, double qz, double qw)`	Creates a Quaternion
`Quaternion(long cPtr, boolean cMemoryOwn)`
`Quaternion(EigenQuaterniond r)`	Creates a Quaternion from a Eigen quaternion
`Quaternion(Quaternion quat)`	Creates a Quaternion from another Quaternion
`Quaternion(Rotation3D rot)`	Extracts a Quaternion from Rotation matrix using setRotation(const Rotation3D<R>& rot)
`Quaternion(Rotation3DVector rot)`	Creates a Quaternion from another Rotation3DVector type

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method	Description
`Quaternion`	`add()`	Unary plus.
`Quaternion`	`add(Quaternion v)`	Addition of two quaternions
`Quaternion`	`addAssign(Quaternion r)`	Add-to operator
`void`	`copy(EigenQuaterniond r)`	copy a boost quaternion to this Quaternion
`Quaternion`	`copy(SWIGTYPE_p_rw__math__Rotation3DT_t rhs)`	copyfrom rotaion matrix, same as setRotation.
`void`	`delete()`
`Quaternion`	`divide(double s)`	Scalar Devision.
`EigenQuaterniond`	`e()`	Convert to an Eigen Quaternion.
`Quaternion`	`elemDivide(double lhs)`	element whise division
`boolean`	`equals(Quaternion r)`	Comparison (equals) operator
`Quaternion`	`exp()`
`double`	`get(long i)`
`static long`	`getCPtr(Quaternion obj)`
`double`	`getLength()`	get length of quaternion \sqrt{q_x^2+q_y^2+q_z^2+q_w^2}
`double`	`getLengthSquared()`	get squared length of quaternion q_x^2+q_y^2+q_z^2+q_w^2
`double`	`getQw()`	get method for the w component
`double`	`getQx()`	get method for the x component
`double`	`getQy()`	get method for the y component
`double`	`getQz()`	get method for the z component
`Quaternion`	`inverse()`	Calculate the inverse Quaternion
`Quaternion`	`ln()`	calculates the natural logerithm of this quaternion
`Quaternion`	`multiply(double s)`	Scalar multiplication.
`Quaternion`	`multiply(Quaternion r)`	Multiply-from operator
`Quaternion`	`multiplyAssign(double s)`	Scalar multiplication.
`Quaternion`	`multiplyAssign(Quaternion r)`	Multiply with operator
`Quaternion`	`negate()`	Unary minus.
`void`	`normalize()`	normalizes this quaternion so that normalze(Q)=\frac{Q}{\sqrt{q_x^2+q_y^2+q_z^2+q_w^2}}
`boolean`	`notEqual(Quaternion r)`	Comparison (not equals) operator
`Quaternion`	`pow(double power)`	calculates the quaternion lifted to the power of power
`void`	`set(long i, double d)`
`long`	`size()`	The dimension of the quaternion (i.e.
`Quaternion`	`slerp(Quaternion v, double t)`	Calculates a slerp interpolation between this and v. The slerp interpolation ensures a constant velocity across the interpolation. For t=0 the result is this and for t=1 it is v. Note: Algorithm and implementation is thanks to euclideanspace.com
`Quaternion`	`subtract(Quaternion v)`	Subtraction.
`Quaternion`	`subtractAssign(Quaternion r)`	Subtract-from operator
`SWIGTYPE_p_Eigen__MatrixT_double_4_1_t`	`toEigenVector()`	convert to Eigen Vector
`Rotation3D`	`toRotation3D()`	Returns the corresponding 3\times 3 Rotation matrix
`java.lang.String`	`toString()`

Methods inherited from class org.robwork.sdurw_math.Rotation3DVector
getCPtr

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

- Constructor Detail
  - Quaternion
```
public Quaternion(long cPtr,
                  boolean cMemoryOwn)
```
  - Quaternion
```
public Quaternion()
```
    constuct Quaterinion of {0,0,0,1}
  - Quaternion
```
public Quaternion(double qx,
                  double qy,
                  double qz,
                  double qw)
```
    Creates a Quaternion
    
    Parameters:
    
    qx - [in] q_x
    
    qy - [in] q_y
    
    qz - [in] q_z
    
    qw - [in] q_w
  - Quaternion
```
public Quaternion(Quaternion quat)
```
    Creates a Quaternion from another Quaternion
    
    Parameters:
    
    quat - [in] Quaternion
  - Quaternion
```
public Quaternion(Rotation3DVector rot)
```
    Creates a Quaternion from another Rotation3DVector type
    
    Parameters:
    
    rot - [in] The Rotation3DVector type
  - Quaternion
```
public Quaternion(Rotation3D rot)
```
    Extracts a Quaternion from Rotation matrix using
    setRotation(const Rotation3D<R>& rot)
    
    Parameters:
    
    rot - [in] A 3x3 rotation matrix \mathbf{rot}
  - Quaternion
```
public Quaternion(EigenQuaterniond r)
```
    Creates a Quaternion from a Eigen quaternion
    
    Parameters:
    
    r - [in] a boost quaternion
- Method Detail
  - getCPtr
```
public static long getCPtr(Quaternion obj)
```
  - delete
```
public void delete()
```
    Overrides:
    
    delete in class Rotation3DVector
  - getQx
```
public double getQx()
```
    get method for the x component
    
    Returns:
    
    the x component of the quaternion
  - getQy
```
public double getQy()
```
    get method for the y component
    
    Returns:
    
    the y component of the quaternion
  - getQz
```
public double getQz()
```
    get method for the z component
    
    Returns:
    
    the z component of the quaternion
  - getQw
```
public double getQw()
```
    get method for the w component
    
    Returns:
    
    the w component of the quaternion
  - get
```
public double get(long i)
```
  - set
```
public void set(long i,
                double d)
```
  - toRotation3D
```
public Rotation3D toRotation3D()
```
    Description copied from class: Rotation3DVector
    
    Returns the corresponding 3\times 3 Rotation matrix
    
    Overrides:
    
    toRotation3D in class Rotation3DVector
    
    Returns:
    
    The rotation matrix
  - size
```
public long size()
```
    The dimension of the quaternion (i.e. 4).
    This method is provided to help support generic algorithms using
    size() and operator[].
  - e
```
public EigenQuaterniond e()
```
    Convert to an Eigen Quaternion.
    
    Returns:
    
    Eigen Quaternion representation.
  - toEigenVector
```
public SWIGTYPE_p_Eigen__MatrixT_double_4_1_t toEigenVector()
```
    convert to Eigen Vector
    
    Returns:
    
    eigen Vector of quaternion
  - negate
```
public Quaternion negate()
```
    Unary minus.
  - add
```
public Quaternion add()
```
    Unary plus.
  - subtract
```
public Quaternion subtract(Quaternion v)
```
    Subtraction.
  - multiply
```
public Quaternion multiply(Quaternion r)
```
    Multiply-from operator
  - add
```
public Quaternion add(Quaternion v)
```
    Addition of two quaternions
  - multiply
```
public Quaternion multiply(double s)
```
    Scalar multiplication.
  - divide
```
public Quaternion divide(double s)
```
    Scalar Devision.
  - elemDivide
```
public Quaternion elemDivide(double lhs)
```
    element whise division
    
    Parameters:
    
    lhs - [in] the scalar to devide with
    
    Returns:
    
    the result of elementwise devision
  - getLength
```
public double getLength()
```
    get length of quaternion
    \sqrt{q_x^2+q_y^2+q_z^2+q_w^2}
    
    Returns:
    
    the length og this quaternion
  - getLengthSquared
```
public double getLengthSquared()
```
    get squared length of quaternion
    q_x^2+q_y^2+q_z^2+q_w^2
    
    Returns:
    
    the length og this quaternion
  - normalize
```
public void normalize()
```
    normalizes this quaternion so that
    normalze(Q)=\frac{Q}{\sqrt{q_x^2+q_y^2+q_z^2+q_w^2}}
  - slerp
```
public Quaternion slerp(Quaternion v,
                        double t)
```
    Calculates a slerp interpolation between this and v.
    
    The slerp interpolation ensures a constant velocity across the interpolation.
    For t=0 the result is this and for t=1 it is v.
    
    Note: Algorithm and implementation is thanks to euclideanspace.com
  - exp
```
public Quaternion exp()
```
  - inverse
```
public Quaternion inverse()
```
    Calculate the inverse Quaternion
    
    Returns:
    
    the inverse quaternion
  - ln
```
public Quaternion ln()
```
    calculates the natural logerithm of this quaternion
    
    Returns:
    
    natural logetihm
  - pow
```
public Quaternion pow(double power)
```
    calculates the quaternion lifted to the power of power
    
    Parameters:
    
    power - [in] the power the quaternion is lifted to
    
    Returns:
    
    Quaternion^power
  - copy
```
public void copy(EigenQuaterniond r)
```
    copy a boost quaternion to this Quaternion
    
    Parameters:
    
    r - [in] - boost quaternion
  - multiplyAssign
```
public Quaternion multiplyAssign(double s)
```
    Scalar multiplication.
  - multiplyAssign
```
public Quaternion multiplyAssign(Quaternion r)
```
    Multiply with operator
  - addAssign
```
public Quaternion addAssign(Quaternion r)
```
    Add-to operator
  - subtractAssign
```
public Quaternion subtractAssign(Quaternion r)
```
    Subtract-from operator
  - copy
```
public Quaternion copy(SWIGTYPE_p_rw__math__Rotation3DT_t rhs)
```
    copyfrom rotaion matrix, same as setRotation.
    
    Parameters:
    
    rhs - [in] the rotation that will be copyed
  - equals
```
public boolean equals(Quaternion r)
```
    Comparison (equals) operator
  - notEqual
```
public boolean notEqual(Quaternion r)
```
    Comparison (not equals) operator
  - toString
```
public java.lang.String toString()
```
    Overrides:
    
    toString in class java.lang.Object

Class Quaternion

Constructor Summary

Method Summary

Methods inherited from class org.robwork.sdurw_math.Rotation3DVector

Methods inherited from class java.lang.Object

Constructor Detail

Quaternion

Quaternion

Quaternion

Quaternion

Quaternion

Quaternion

Quaternion

Method Detail

getCPtr

delete

getQx

getQy

getQz

getQw

get

set

toRotation3D

size

e

toEigenVector

negate

add

subtract

multiply

add

multiply

divide

elemDivide

getLength

getLengthSquared

normalize

slerp

exp

inverse

ln

pow

copy

multiplyAssign

multiplyAssign

addAssign

subtractAssign

copy

equals

notEqual

toString