Quaternion (Autonomous Unmanned Vehicle (AUV) Workbench Documentation)

java.lang.Object
- dynamics.utilities.Quaternion

```
public class Quaternion
extends Object
```
Author:

dtdavis

Constructor Summary

Constructors
Constructor and Description
`Quaternion()` Creates a new instance of Quaternion
`Quaternion(double phi, double theta, double psi)` Creates a new instance of Quaternion based on a set of Euler angles This quaternion is equivalent to the product of quaternions for individual Euler angle rotations.
`Quaternion(double w, double x, double y, double z)` Creates a new Quaternion with user specified values
`Quaternion(double scalar, Vector3D vector)` Creates a new Quaternion with user specified values
`Quaternion(Hmatrix hMatrix)` Creates a new Quaternion based on the rotations specified in a homogeneous transformation matrix
`Quaternion(Quaternion q2)` Creates a new instance of Quaternion that is a copy of an existing quaternion
`Quaternion(Vector3D v)` Creates a new Quaternion with user specified vector values and a scalar of 0
`Quaternion(Vector3D axis, double angle)` Creates a new Quaternion based on an axis and angle of rotation

Method Summary

All Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`Quaternion`	`add(Quaternion q2)` Adds two quaternions together and returns the result
`Quaternion`	`conjugate()` Computes the conjugate of the quaternion
`void`	`divideEquals(double divisor)` Divides the quaternion by a scalar value and resets the values of this quaternion
`double`	`dotProduct(Quaternion q2)` Computes the dot product of this quaternion and another.
`void`	`eulerStep(double p, double q, double r, double timeStep)` Rotates the quaternion based on angular velocities (p, q, r) over a specified time step using Euler integration NOTE: Changes the value of this Quaternion rather than returning a new Quaternion
`Quaternion`	`exponential()` Computes the exponential of the quaternion (notionally, e to the q power) Reference: An Introduction to Representing Rotations in Quaternion Arithmetic available at http://www.sjbrown.co.uk/quaternions.html
`Vector3D`	`getVector()` Returns the vector portion of the quaternion
`double`	`getW()` Returns the w value of the quaternion
`double`	`getX()` Returns the x value of the quaternion
`double`	`getY()` Returns the y value of the quaternion
`double`	`getZ()` Returns the z value of the quaternion
`Hmatrix`	`hMatrix()` Computes the homogeneous transformation matrix corresponding to this matrix
`Hmatrix`	`hMatrix(double x, double y, double z)` Computes a homogeneous transformation matrix associated with this quaternion and includes a specified translation
`Hmatrix`	`hMatrix(Vector3D translation)` Computes a homogeneous transformation matrix associated with this quaternion and includes a specified translation
`Quaternion`	`inverse()` Computes the inverse of a quaternion
`double`	`length()` Computes the Euclidian length of the quaternion
`void`	`minusEquals(Quaternion q2)` Subtracts value of a second quaternion to this one (over writes the values of this quaternion)
`void`	`normalize()` Normalizes the quaternion to a unit vector
`void`	`plusEquals(Quaternion q2)` Adds the value of a second quaternion to this one (over writes the values of this quaternion)
`void`	`postMultEquals(Quaternion q2)` Postmultiplies the value of this quaternion by another (over-writes the value of this quaternion)
`void`	`postMultEquals(Vector3D v)` Postmultiplies the value of this quaternion by the quaternion value of a 3D vector (0, x, y, z) (over-writes the value of this quaternion)
`Quaternion`	`postMultiply(Quaternion q2)` Multiplies two quaternions together and returns the result
`Quaternion`	`postMultiply(Vector3D v)` Postmultiplies the value of this quaternion by the quaternion value of a 3D vector (0, x, y, z) and returns the result
`Quaternion`	`preMultiply(Quaternion q2)` Multiplies two quaternions together and returns the result
`Quaternion`	`preMultiply(Vector3D v)` Premultiplies the value of this quaternion by the quaternion value of a 3D vector (0, x, y, z) and returns the result
`void`	`preMultTimesEquals(Quaternion q2)` Premultiplies the value of this quaternion by another (over-writes the value of this quaternion)
`void`	`preMultTimesEquals(Vector3D v)` Premultiplies the value of this quaternion by the quaternion value of a 3D vector (0, x, y, z) (over-writes the value of this quaternion)
`Quaternion`	`rotate(Quaternion q)` Use this quaternion to rotate another
`Quaternion`	`rotate(Vector3D v)` Use this quaternion to rotate a 3D vector
`double`	`rotationAngle()` Returns the angle of rotation represented by this quaternion
`Vector3D`	`rotationAxis()` Returns the axis of rotation (unit vector) of the rotation represented by this quaternion
`Quaternion`	`scalarDivide(double divisor)` Divides the quaternion by a scalar value
`Quaternion`	`scalarMultiply(double multiplier)` Multiplies the quaternion by a scalar value
`void`	`setValue(double newW, double newX, double newY, double newZ)` Resets the value of this Quaternion to new w, x, y, and z values
`void`	`setValue(double newW, Vector3D newVector)` Resets the value of this Quaternion based on a specified scalar and vector
`void`	`setValue(Quaternion q2)` Resets the value of this Quaternion to those of another
`void`	`setVector(Vector3D newVector)` Sets the vector portion of the quaternion
`void`	`setW(double newW)` Sets the w value of the quaternion
`void`	`setX(double newX)` Sets the x value of the quaternion
`void`	`setY(double newY)` Sets the y value of the quaternion
`void`	`setZ(double newZ)` Sets the z value of the quaternion
`Quaternion`	`slerp(Quaternion qEnd, double u)` Computes an interpolated quaternion between this one and a specified quaternion using spherical-linear interpolation (SLERP)
`Quaternion`	`subtract(Quaternion q2)` Subtracts one quaternion from this one and returns the result
`void`	`timesEquals(double multiplier)` Multiplies the quaternion by a scalar value and resets the values of this quaternion

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

- Constructor Detail
  - Quaternion
```
public Quaternion()
```
    Creates a new instance of Quaternion
  - Quaternion
```
public Quaternion(Quaternion q2)
```
    Creates a new instance of Quaternion that is a copy of an existing quaternion
    
    Parameters:
    
    q2 - quaternion to be copied
  - Quaternion
```
public Quaternion(double phi,
                  double theta,
                  double psi)
```
    Creates a new instance of Quaternion based on a set of Euler angles This quaternion is equivalent to the product of quaternions for individual Euler angle rotations. That is q = qPsi * qTheta * qPhi where, for instance qPsi is the quaternion for rotation about the z axis by Psi radians ( cos(psi/2), 0, 0, sin(psi/2) )
    
    Parameters:
    
    phi -
    
    theta -
    
    psi -
  - Quaternion
```
public Quaternion(double scalar,
                  Vector3D vector)
```
    Creates a new Quaternion with user specified values
    
    Parameters:
    
    scalar - portion of the quaternion (w)
    
    vector - 3D vector portion of the quaternion (x, y, z)
  - Quaternion
```
public Quaternion(double w,
                  double x,
                  double y,
                  double z)
```
    Creates a new Quaternion with user specified values
    
    Parameters:
    
    w - scalar element quaternion
    
    x - first element of the 3D vector portion of the quaternion
    
    y - second element of the 3D vector portion of the quaternion
    
    z - third element of the 3D vector portion of the quaternion
  - Quaternion
```
public Quaternion(Vector3D v)
```
    Creates a new Quaternion with user specified vector values and a scalar of 0
    
    Parameters:
    
    v - vector value for new quaternion
  - Quaternion
```
public Quaternion(Vector3D axis,
                  double angle)
```
    Creates a new Quaternion based on an axis and angle of rotation
    
    Parameters:
    
    axis - vector representation of the axis of rotation
    
    angle - of rotation specified in radians
  - Quaternion
```
public Quaternion(Hmatrix hMatrix)
```
    Creates a new Quaternion based on the rotations specified in a homogeneous transformation matrix
    
    Parameters:
    
    hMatrix - homogeneous transformation matrix
- Method Detail
  - setValue
```
public void setValue(Quaternion q2)
```
    Resets the value of this Quaternion to those of another
    
    Parameters:
    
    q2 - new Quaternion values
  - setValue
```
public void setValue(double newW,
                     double newX,
                     double newY,
                     double newZ)
```
    Resets the value of this Quaternion to new w, x, y, and z values
    
    Parameters:
    
    newW -
    
    newX -
    
    newY -
    
    newZ -
  - setValue
```
public void setValue(double newW,
                     Vector3D newVector)
```
    Resets the value of this Quaternion based on a specified scalar and vector
    
    Parameters:
    
    newW -
    
    newVector -
  - length
```
public double length()
```
    Computes the Euclidian length of the quaternion
  - conjugate
```
public Quaternion conjugate()
```
    Computes the conjugate of the quaternion
  - inverse
```
public Quaternion inverse()
```
    Computes the inverse of a quaternion
  - normalize
```
public void normalize()
```
    Normalizes the quaternion to a unit vector
  - postMultiply
```
public Quaternion postMultiply(Quaternion q2)
```
    Multiplies two quaternions together and returns the result
    
    Parameters:
    
    q2 - quaternion to be multiplied by this one. The multiplication will occur in the order this x q2
  - postMultEquals
```
public void postMultEquals(Quaternion q2)
```
    Postmultiplies the value of this quaternion by another (over-writes the value of this quaternion)
    
    Parameters:
    
    q2 - quaternion to be multiplied by this one. The multiplication will occur in the order this x q2
  - postMultiply
```
public Quaternion postMultiply(Vector3D v)
```
    Postmultiplies the value of this quaternion by the quaternion value of a 3D vector (0, x, y, z) and returns the result
    
    Parameters:
    
    v - vector to be multiplied by this quaternion. The multiplication will occur in the order this x v
  - postMultEquals
```
public void postMultEquals(Vector3D v)
```
    Postmultiplies the value of this quaternion by the quaternion value of a 3D vector (0, x, y, z) (over-writes the value of this quaternion)
    
    Parameters:
    
    v - vector to be multiplied by this one. The multiplication will occur in the order this x v
  - preMultiply
```
public Quaternion preMultiply(Quaternion q2)
```
    Multiplies two quaternions together and returns the result
    
    Parameters:
    
    q2 - quaternion to be multiplied by this one. The multiplication will occur in the order q2 x this
  - preMultTimesEquals
```
public void preMultTimesEquals(Quaternion q2)
```
    Premultiplies the value of this quaternion by another (over-writes the value of this quaternion)
    
    Parameters:
    
    q2 - quaternion to be mmultiplied by this one
  - preMultiply
```
public Quaternion preMultiply(Vector3D v)
```
    Premultiplies the value of this quaternion by the quaternion value of a 3D vector (0, x, y, z) and returns the result
    
    Parameters:
    
    v - vector to be multiplied by this quaternion. The multiplication will occur in the order v x this
  - preMultTimesEquals
```
public void preMultTimesEquals(Vector3D v)
```
    Premultiplies the value of this quaternion by the quaternion value of a 3D vector (0, x, y, z) (over-writes the value of this quaternion)
    
    Parameters:
    
    v - vector to be mmultiplied by this one multiplication will occur in the order v x this
  - dotProduct
```
public double dotProduct(Quaternion q2)
```
    Computes the dot product of this quaternion and another. Dot product is defined as w1*w2 + vector1.vector2
    
    Parameters:
    
    q2 - quaternion to be multiplied times this one
  - add
```
public Quaternion add(Quaternion q2)
```
    Adds two quaternions together and returns the result
    
    Parameters:
    
    q2 - quaternion to be added
  - plusEquals
```
public void plusEquals(Quaternion q2)
```
    Adds the value of a second quaternion to this one (over writes the values of this quaternion)
    
    Parameters:
    
    q2 - quaternion to be added to this one
  - subtract
```
public Quaternion subtract(Quaternion q2)
```
    Subtracts one quaternion from this one and returns the result
    
    Parameters:
    
    q2 - quaternion to be added
  - minusEquals
```
public void minusEquals(Quaternion q2)
```
    Subtracts value of a second quaternion to this one (over writes the values of this quaternion)
    
    Parameters:
    
    q2 - quaternion to be added to this one
  - scalarMultiply
```
public Quaternion scalarMultiply(double multiplier)
```
    Multiplies the quaternion by a scalar value
    
    Parameters:
    
    multiplier - scalar multiple
  - timesEquals
```
public void timesEquals(double multiplier)
```
    Multiplies the quaternion by a scalar value and resets the values of this quaternion
    
    Parameters:
    
    multiplier - scalar multiple
  - scalarDivide
```
public Quaternion scalarDivide(double divisor)
```
    Divides the quaternion by a scalar value
    
    Parameters:
    
    divisor - scalar divisor
  - divideEquals
```
public void divideEquals(double divisor)
```
    Divides the quaternion by a scalar value and resets the values of this quaternion
    
    Parameters:
    
    divisor - scalar multiple
  - eulerStep
```
public void eulerStep(double p,
                      double q,
                      double r,
                      double timeStep)
```
    Rotates the quaternion based on angular velocities (p, q, r) over a specified time step using Euler integration NOTE: Changes the value of this Quaternion rather than returning a new Quaternion
    
    Parameters:
    
    p - rotation rate (radians / second) about the body x axis
    
    q - rotation rate (radians / second) about the body y axis
    
    r - rotation rate (radians / second) about the body z axis
    
    timeStep - amount of time for incremental rotation
  - rotate
```
public Quaternion rotate(Quaternion q)
```
    Use this quaternion to rotate another
    
    Parameters:
    
    q - quaternion to be rotated (most likely in pure vector form, i.e. w = 0)
  - rotate
```
public Quaternion rotate(Vector3D v)
```
    Use this quaternion to rotate a 3D vector
    
    Parameters:
    
    v - vector to be rotated
  - rotationAxis
```
public Vector3D rotationAxis()
```
    Returns the axis of rotation (unit vector) of the rotation represented by this quaternion
  - rotationAngle
```
public double rotationAngle()
```
    Returns the angle of rotation represented by this quaternion
  - exponential
```
public Quaternion exponential()
```
    Computes the exponential of the quaternion (notionally, e to the q power) Reference: An Introduction to Representing Rotations in Quaternion Arithmetic available at http://www.sjbrown.co.uk/quaternions.html
  - slerp
```
public Quaternion slerp(Quaternion qEnd,
                        double u)
```
    Computes an interpolated quaternion between this one and a specified quaternion using spherical-linear interpolation (SLERP)
    
    Parameters:
    
    qEnd - quaternion at the end of the interpolation
    
    u - fraction of the distance between this quaternion and the ending quaternion (0 <= t <= 1) If t is outside of the range [0,1], the method should return a value corresponding to the quaternion of a rotation beyond qEnd (or before this) along the same trajectory
  - hMatrix
```
public Hmatrix hMatrix()
```
    Computes the homogeneous transformation matrix corresponding to this matrix
  - hMatrix
```
public Hmatrix hMatrix(Vector3D translation)
```
    Computes a homogeneous transformation matrix associated with this quaternion and includes a specified translation
    
    Parameters:
    
    translation -
  - hMatrix
```
public Hmatrix hMatrix(double x,
                       double y,
                       double z)
```
    Computes a homogeneous transformation matrix associated with this quaternion and includes a specified translation
    
    Parameters:
    
    x - position of the translation
    
    y - position of the translation
    
    z - position of the translation
  - getVector
```
public Vector3D getVector()
```
    Returns the vector portion of the quaternion
  - getX
```
public double getX()
```
    Returns the x value of the quaternion
  - getY
```
public double getY()
```
    Returns the y value of the quaternion
  - getZ
```
public double getZ()
```
    Returns the z value of the quaternion
  - getW
```
public double getW()
```
    Returns the w value of the quaternion
  - setVector
```
public void setVector(Vector3D newVector)
```
    Sets the vector portion of the quaternion
    
    Parameters:
    
    newVector -
  - setX
```
public void setX(double newX)
```
    Sets the x value of the quaternion
    
    Parameters:
    
    newX -
  - setY
```
public void setY(double newY)
```
    Sets the y value of the quaternion
    
    Parameters:
    
    newY -
  - setZ
```
public void setZ(double newZ)
```
    Sets the z value of the quaternion
    
    Parameters:
    
    newZ -
  - setW
```
public void setW(double newW)
```
    Sets the w value of the quaternion
    
    Parameters:
    
    newW -

Class Quaternion

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Constructor Detail

Quaternion

Quaternion

Quaternion

Quaternion

Quaternion

Quaternion

Quaternion

Quaternion

Method Detail

setValue

setValue

setValue

length

conjugate

inverse

normalize

postMultiply

postMultEquals

postMultiply

postMultEquals

preMultiply

preMultTimesEquals

preMultiply

preMultTimesEquals

dotProduct

add

plusEquals

subtract

minusEquals

scalarMultiply

timesEquals

scalarDivide

divideEquals

eulerStep

rotate

rotate

rotationAxis

rotationAngle

exponential

slerp

hMatrix

hMatrix

hMatrix

getVector

getX

getY

getZ

getW

setVector

setX

setY

setZ

setW