Quaternion

java.lang.Object
- etomica.math.Quaternion

```
public class Quaternion
extends java.lang.Object
```
Quaternion object , its properties and associated operations

Field Summary

Fields
Modifier and Type	Field	Description
`protected double`	`norm`
`protected double`	`q0`
`protected double`	`q1`
`protected double`	`q2`
`protected double`	`q3`
`protected static Space`	`space`
`protected Vector`	`vec`

Constructor Summary

Constructors
Constructor	Description
`Quaternion(double[] p)`	Constructs the Quaternion q = p[0] + p[1]i + p[2]j + p[3]*k
`Quaternion(double a, double[] b)`	Constructs the Quaternion q = a + b[0]i + b[1]j + b[2]*k
`Quaternion(double a, double b, double c, double d)`	Constructs the Quaternion q = a + bi + cj + d*k
`Quaternion(double a, Vector b)`	Constructs the Quaternion q = a + b
`Quaternion(Vector[] basisVec)`	Constructs the Quaternion q for an input basis vector array.
`Quaternion(Vector axis, double angle)`	Constructs the unit Quaternion q = cos(angle/2) + axis*sin(angle/2)
`Quaternion(OrientationFull3D or)`	Constructs the Quaternion q for an input OrientationFull3D with two vectors.
`Quaternion(Jama.Matrix rotMatrix)`	Constructs the Quaternion q given an input rotation matrix.

Method Summary

All Methods Instance Methods Concrete Methods
Modifier and Type	Method	Description
`Quaternion`	`conjugate()`	Returns the complex conjugate of the Quaternion q.
`double`	`getAngle()`	Returns the angle associated with the quaternion
`Vector`	`getAxis()`	Returns the axis associated with the Quaternion.
`double[]`	`getDoubleArray()`	Returns the Quaternion as a double array
`double`	`getNorm()`	Returns the norm of the Quaternion q defined as N = sqrt(q*q)
`OrientationFull3D`	`getOrientation()`	Returns an orientation corresponding to the rotation of cartesian coordinate frame {i,j,k} by the axis and angle associated with the Quaternion q.
`double`	`getQ0()`	Returns the q0 component of the Quaternion
`double`	`getQ1()`	Returns the q1 component of the Quaternion
`double`	`getQ2()`	Returns the q2 component of the Quaternion
`double`	`getQ3()`	Returns the q3 component of the Quaternion
`Jama.Matrix`	`getRotationMatrix()`	Returns the rotation matrix associated with the Quaternion q as a Jama.Matrix
`double`	`getScalar()`	Returns the scalar part of the Quaternion
`Vector`	`getVector()`	Returns the vector part of the Quaternion as Vector
`double[]`	`getVectorAsDoubleArray()`	Returns the vector associated with the Quaternion as a double array
`double`	`getVectorMagnitude()`	Returns the magnitude of the vector associated with the Quaternion
`Quaternion`	`inverse()`	Returns the inverse of the Quaternion q given by q^-1 = 1/(norm^2) * q*
`boolean`	`isEqualTo(Quaternion p)`	Returns whether the Quaternion is equal to another given Quaternion p
`boolean`	`isIllegal()`	Returns true if even a single component of the quaternion is either infinite or NaN
`boolean`	`isPureQuaternion()`	Returns whether the Quaternion is pure or not
`boolean`	`isUnitQuaternion()`	Returns whether the norm of the Quaternion is 1 or not
`void`	`normalize()`	Normalizes the Quaternion q i.e.
`void`	`PE(Quaternion p)`	Adds the input Quaternion components to its components.
`Quaternion`	`preMultiply(Quaternion preMultiplier)`	Returns the Quaternion r resulting from multiplying the input Quaternion preMultiplier to the current Quaternion q.
`void`	`rotateOrientation(OrientationFull3D or)`	Rotates the input orientation by using the Quaternion rotation operator L(v) = qvq*.
`void`	`rotateVector(Vector v)`	Rotates the input vector by using the Quaternion rotation operator L(v) = qvq*.
`void`	`TE(double a)`	Multiplies all the components of the Quaternion q by the given scalar
`java.lang.String`	`toString()`	Returns the string representation of the Quaternion q
`protected void`	`updateQuaternion()`	First checks if all the components are numbers.

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

- Field Detail
  - q0
```
protected double q0
```
  - q1
```
protected double q1
```
  - q2
```
protected double q2
```
  - q3
```
protected double q3
```
  - space
```
protected static final Space space
```
  - vec
```
protected final Vector vec
```
  - norm
```
protected double norm
```
- Constructor Detail
  - Quaternion
```
public Quaternion(double[] p)
```
    Constructs the Quaternion q = p[0] + p[1]*i + p[2]*j + p[3]*k
  - Quaternion
```
public Quaternion(double a,
                  Vector b)
```
    Constructs the Quaternion q = a + b
  - Quaternion
```
public Quaternion(Vector axis,
                  double angle)
```
    Constructs the unit Quaternion q = cos(angle/2) + axis*sin(angle/2)
    
    Parameters:
    
    axis -
    
    angle -
  - Quaternion
```
public Quaternion(double a,
                  double b,
                  double c,
                  double d)
```
    Constructs the Quaternion q = a + b*i + c*j + d*k
  - Quaternion
```
public Quaternion(double a,
                  double[] b)
```
    Constructs the Quaternion q = a + b[0]*i + b[1]*j + b[2]*k
  - Quaternion
```
public Quaternion(OrientationFull3D or)
```
    Constructs the Quaternion q for an input OrientationFull3D with two vectors. First creates the three basis vectors from the orientation. Then converts that into a rotation matrix and finally into a Quaternion. This Quaternion represents the rotation of the {i,j,k} coordinate frame to the orthonormal coordinate frame formed by the the basis vectors.
    
    Parameters:
    
    or -
  - Quaternion
```
public Quaternion(Vector[] basisVec)
```
    Constructs the Quaternion q for an input basis vector array. Converts the basis vector array into a rotation matrix and finally into a Quaternion. This Quaternion represents the rotation of the {i,j,k} coordinate frame to the orthonormal coordinate frame formed by the basis vectors.
    
    Parameters:
    
    basisVec -
  - Quaternion
```
public Quaternion(Jama.Matrix rotMatrix)
```
    Constructs the Quaternion q given an input rotation matrix. Note that the determinant of the input matrix should be +1. Otherwise it doesn't represent a rotation
    
    Parameters:
    
    rotMatrix -
- Method Detail
  - updateQuaternion
```
protected void updateQuaternion()
```
    First checks if all the components are numbers. Then recomputes the norm and the vector of the Quaternion that has been operated upon.
  - isIllegal
```
public boolean isIllegal()
```
    Returns true if even a single component of the quaternion is either infinite or NaN
    
    Returns:
    
    boolean true/false
  - getQ0
```
public double getQ0()
```
    Returns the q0 component of the Quaternion
    
    Returns:
    
    double q0
  - getQ1
```
public double getQ1()
```
    Returns the q1 component of the Quaternion
    
    Returns:
    
    double q1
  - getQ2
```
public double getQ2()
```
    Returns the q2 component of the Quaternion
    
    Returns:
    
    double q2
  - getQ3
```
public double getQ3()
```
    Returns the q3 component of the Quaternion
    
    Returns:
    
    double q3
  - getScalar
```
public double getScalar()
```
    Returns the scalar part of the Quaternion
    
    Returns:
    
    double q0
  - getVector
```
public Vector getVector()
```
    Returns the vector part of the Quaternion as Vector
    
    Returns:
    
    Vector v = q1*i + q2*j + q3*k
  - getAxis
```
public Vector getAxis()
```
    Returns the axis associated with the Quaternion. Note, axis is a unit vector
  - getAngle
```
public double getAngle()
```
    Returns the angle associated with the quaternion
    
    Returns:
  - getVectorAsDoubleArray
```
public double[] getVectorAsDoubleArray()
```
    Returns the vector associated with the Quaternion as a double array
    
    Returns:
    
    double [] v
  - getVectorMagnitude
```
public double getVectorMagnitude()
```
    Returns the magnitude of the vector associated with the Quaternion
    
    Returns:
    
    double magnitude = |vec|
  - getDoubleArray
```
public double[] getDoubleArray()
```
    Returns the Quaternion as a double array
    
    Returns:
    
    double [] q
  - getRotationMatrix
```
public Jama.Matrix getRotationMatrix()
```
    Returns the rotation matrix associated with the Quaternion q as a Jama.Matrix
    
    Returns:
    
    Jama.Matrix A
  - getOrientation
```
public OrientationFull3D getOrientation()
```
    Returns an orientation corresponding to the rotation of cartesian coordinate frame {i,j,k} by the axis and angle associated with the Quaternion q.
    
    Returns:
    
    OrientationFull3D or
  - isPureQuaternion
```
public boolean isPureQuaternion()
```
    Returns whether the Quaternion is pure or not
    
    Returns:
    
    boolean true/false
  - isEqualTo
```
public boolean isEqualTo(Quaternion p)
```
    Returns whether the Quaternion is equal to another given Quaternion p
    
    Parameters:
    
    p -
    
    Returns:
    
    boolean true/false
  - isUnitQuaternion
```
public boolean isUnitQuaternion()
```
    Returns whether the norm of the Quaternion is 1 or not
    
    Returns:
    
    boolean true/false
  - PE
```
public void PE(Quaternion p)
```
    Adds the input Quaternion components to its components. Addition is done component wise
    
    Parameters:
    
    p -
  - TE
```
public void TE(double a)
```
    Multiplies all the components of the Quaternion q by the given scalar
    
    Parameters:
    
    a -
  - preMultiply
```
public Quaternion preMultiply(Quaternion preMultiplier)
```
    Returns the Quaternion r resulting from multiplying the input Quaternion preMultiplier to the current Quaternion q. Can be thought of as a pre-multiplication with the current Quaternion. Mulitplication is done based on Hamilton's rules and result in (r = preMultiplier*q): r = p0*q0 - pVec.dot(qVec) + p0*qVec + q0*pVec + pVec X qVec
    
    Parameters:
    
    preMultiplier -
    
    Returns:
    
    Quaternion r = pq
  - conjugate
```
public Quaternion conjugate()
```
    Returns the complex conjugate of the Quaternion q.
    
    Returns:
    
    Quaternion q* = q0 - qVec
  - getNorm
```
public double getNorm()
```
    Returns the norm of the Quaternion q defined as N = sqrt(q*q)
    
    Returns:
    
    double N = sart(q0^2 + q1^2 + q2^2 + q3^2)
  - normalize
```
public void normalize()
```
    Normalizes the Quaternion q i.e. divides all components by the norm
  - inverse
```
public Quaternion inverse()
```
    Returns the inverse of the Quaternion q given by q^-1 = 1/(norm^2) * q*
    
    Returns:
    
    Quaternion q^-1
  - rotateVector
```
public void rotateVector(Vector v)
```
    Rotates the input vector by using the Quaternion rotation operator L(v) = qvq*. w = L(v) = qvq* = (2*q0^2 -1)v + 2*(qVec.dot(v))*qVec + 2*q0*(qVec X v)
    
    Parameters:
    
    v -
  - rotateOrientation
```
public void rotateOrientation(OrientationFull3D or)
```
    Rotates the input orientation by using the Quaternion rotation operator L(v) = qvq*. Rotates the two vectors that form the orientation.
    
    Parameters:
    
    or -
  - toString
```
public java.lang.String toString()
```
    Returns the string representation of the Quaternion q
    
    Overrides:
    
    toString in class java.lang.Object
    
    Returns:
    
    String

Class Quaternion

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

q0

q1

q2

q3

space

vec

norm

Constructor Detail

Quaternion

Quaternion

Quaternion

Quaternion

Quaternion

Quaternion

Quaternion

Quaternion

Method Detail

updateQuaternion

isIllegal

getQ0

getQ1

getQ2

getQ3

getScalar

getVector

getAxis

getAngle

getVectorAsDoubleArray

getVectorMagnitude

getDoubleArray

getRotationMatrix

getOrientation

isPureQuaternion

isEqualTo

isUnitQuaternion

PE

TE

preMultiply

conjugate

getNorm

normalize

inverse

rotateVector

rotateOrientation

toString