Package org.opensourcephysics.numerics

Class Quaternion

java.lang.Object

org.opensourcephysics.numerics.Quaternion

All Implemented Interfaces:

java.lang.Cloneable, MatrixTransformation, Transformation

public class Quaternion
extends java.lang.Object
implements MatrixTransformation

Quaternion models a unit quaternion and implements quaternion arithmetic.

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
protected static class	Quaternion.QuaternionLoader

Field Summary

Fields

Modifier and Type	Field	Description
protected double	ox
protected double	oy
protected double	oz
protected double	q0
protected double	q1
protected double	q2
protected double	q3

Constructor Summary

Constructors

Constructor	Description
Quaternion()	Constructs and initializes a unit quaternion (1,0,0,0).
Quaternion(double[] q)	Constructs and initializes a quaternion from the array of length 4.
Quaternion(double q0, double q1, double q2, double q3)	Constructs and initializes quaternion from the specified components.
Quaternion(double q0, Vec3D vector)	Constructs and initializes quaternion from the specified components.
Quaternion(Quaternion q)	Constructs and initializes a Quaternion with the same values as the given quaternion.

Method Summary

Modifier and Type	Method	Description
void	add(Quaternion q)	Adds this quaternion to the given quaternion.
double	angle(Quaternion q)	Returns the angle in radians between this quaternion and the given quaternion.
java.lang.Object	clone()	Instaniates a quaterion whose components are identical to this quaterion.
void	conjugate()	Conjugates this quaternion in place.
static Quaternion	createAlignmentTransformation(double[] v1, double[] v2)	Instantiates a quaternion that aligns the first vector with the second vector.
double[]	direct(double[] p)	Transforms (rotates) the coordinates of the given point.
double	dot(Quaternion q)	Returns the dot product of this quaternion and quaternion q.
double[]	getCoordinates()	Gets the Quaternion coordinates.
double[]	getFlatMatrix(double[] mat)	Gets the direct homogeneous affine transformation flattened into a 1-d array.
static XML.ObjectLoader	getLoader()
double[]	getOrigin()	Returns the origin for this rotation
double[][]	getRotationMatrix(double[][] mat)	Gets the direct rotation matrix of this quaternion rotation.
double[]	inverse(double[] p)	The inverse transformation (if it exists).
double	magnitude()	Returns the magnitude of this quaternion.
double	magnitudeSquared()	Returns the squared magnitude of this vector.
void	multiply(Quaternion q)	Multiplies this quaternion with the given quaternion.
void	normalize()	Normalizes this quaternion in place.
double[]	setCoordinates(double[] q)	Sets the quaternion coordinates from the array of length 4.
void	setCoordinates(double q0, double q1, double q2, double q3)	Sets the quaternion coordinates.
double[]	setOrigin(double[] origin)	Sets the origin for this rotation.
void	setOrigin(double ox, double oy, double oz)	Sets the origin for this rotation.
void	subtract(Quaternion q)	Subtracts this quaternion from the given quaternion.

Methods inherited from class java.lang.Object

equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail

q0

protected double q0

q1

protected double q1

q2

protected double q2

q3

protected double q3

ox

protected double ox

oy

protected double oy

oz

protected double oz

Constructor Detail

Quaternion

public Quaternion(double q0,
                  double q1,
                  double q2,
                  double q3)

Constructs and initializes quaternion from the specified components.

Parameters:

q0 - double

q1 - double

q2 - double

q3 - double

Quaternion

public Quaternion(double q0,
                  Vec3D vector)

Constructs and initializes quaternion from the specified components.

Parameters:

q0 - double

vector - sets with q1:vector.x, q2:vector.y, q3:vector.z

Quaternion

public Quaternion(double[] q)

Constructs and initializes a quaternion from the array of length 4.

Parameters:

q - the array of length 4 containing q0, q1, q2, q3

Quaternion

public Quaternion(Quaternion q)

Constructs and initializes a Quaternion with the same values as the given quaternion.

Parameters:

q - the Vector3d containing the initialization x y z data

Quaternion

public Quaternion()

Constructs and initializes a unit quaternion (1,0,0,0).

Method Detail

createAlignmentTransformation

public static Quaternion createAlignmentTransformation(double[] v1,
                                                       double[] v2)

Instantiates a quaternion that aligns the first vector with the second vector.

Parameters:

v1 - double[]

v2 - double[]

Returns:

Quaternion

setOrigin

public void setOrigin(double ox,
                      double oy,
                      double oz)

Sets the origin for this rotation.

Parameters:

ox - double

oy - double

oz - double

setOrigin

public double[] setOrigin(double[] origin)

Sets the origin for this rotation.

Parameters:

origin - double[] the new origin

Returns:

double[]

getOrigin

public double[] getOrigin()

Returns the origin for this rotation

Returns:

getRotationMatrix

public final double[][] getRotationMatrix(double[][] mat)

Gets the direct rotation matrix of this quaternion rotation. Assumes that the quaternion has been normalized. If the mat parameter is null a double[3][3] array is created; otherwise the given array is used.

Parameters:

mat - double[][] optional matrix

Returns:

double[][] the matrix

getFlatMatrix

public final double[] getFlatMatrix(double[] mat)

Gets the direct homogeneous affine transformation flattened into a 1-d array. If the mat parameter is null a double[16] array is created; otherwise the given array is used.

Specified by:

getFlatMatrix in interface MatrixTransformation

Parameters:

mat - double[] optional matrix

Returns:

double[] the matrix

getCoordinates

public double[] getCoordinates()

Gets the Quaternion coordinates.

Returns:

double[]

setCoordinates

public void setCoordinates(double q0,
                           double q1,
                           double q2,
                           double q3)

Sets the quaternion coordinates.

Parameters:

q0 - double

q1 - double

q2 - double

q3 - double

setCoordinates

public double[] setCoordinates(double[] q)

Sets the quaternion coordinates from the array of length 4.

Parameters:

q - the array of length 4 containing q0, q1, q2, q3

normalize

public final void normalize()

Normalizes this quaternion in place.

conjugate

public final void conjugate()

Conjugates this quaternion in place.

add

public final void add(Quaternion q)

Adds this quaternion to the given quaternion.

Parameters:

q - Quaternion

subtract

public final void subtract(Quaternion q)

Subtracts this quaternion from the given quaternion.

Parameters:

q - Quaternion

multiply

public final void multiply(Quaternion q)

Multiplies this quaternion with the given quaternion.

Parameters:

q - Quaternion

dot

public final double dot(Quaternion q)

Returns the dot product of this quaternion and quaternion q.

Parameters:

q - the other quaternion

Returns:

the dot product of this and q

magnitudeSquared

public final double magnitudeSquared()

Returns the squared magnitude of this vector.

Returns:

the squared magnitude

magnitude

public final double magnitude()

Returns the magnitude of this quaternion.

Returns:

the magnitude

angle

public final double angle(Quaternion q)

Returns the angle in radians between this quaternion and the given quaternion.

Parameters:

q - the other quaternion

Returns:

the angle in radians in the range [0,PI]

clone

public java.lang.Object clone()

Instaniates a quaterion whose components are identical to this quaterion.

Specified by:

clone in interface Transformation

Overrides:

clone in class java.lang.Object

Returns:

Object

direct

public double[] direct(double[] p)

Transforms (rotates) the coordinates of the given point.

Specified by:

direct in interface Transformation

Parameters:

p - double[]

Returns:

double[]

inverse

public double[] inverse(double[] p)
                 throws java.lang.UnsupportedOperationException

Description copied from interface: Transformation

The inverse transformation (if it exists). If the transformation is not invertible, then a call to this method must throw a UnsupportedOperationException exception.

Specified by:

inverse in interface Transformation

Parameters:

p - double[] the coordinates to be transformed (the array's contents will be changed accordingly)

Returns:

double[] the transformed vector (i.e. point)

Throws:

java.lang.UnsupportedOperationException - If the transformation is not invertible

getLoader

public static XML.ObjectLoader getLoader()