dynamics.utilities

Class Quaternion

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

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 -