org.apache.commons.math3.complex
Class Quaternion

java.lang.Object
  org.apache.commons.math3.complex.Quaternion

All Implemented Interfaces:

Serializable

public final class Quaternion
extends Object
implements Serializable

This class implements quaternions (Hamilton's hypercomplex numbers).
Instance of this class are guaranteed to be immutable.

Since:

3.1

Version:

$Id: Quaternion.java 7721 2013-02-14 14:07:13Z CardosoP $

See Also:

Serialized Form

Field Summary

static Quaternion	I i
static Quaternion	IDENTITY Identity quaternion.
static Quaternion	J j
static Quaternion	K k
static Quaternion	ZERO Zero quaternion.

Constructor Summary

Quaternion(double[] v)
Builds a pure quaternion from a vector (assuming that the scalar part is zero).

Quaternion(double scalar, double[] v)
Builds a quaternion from scalar and vector parts.

Quaternion(double a, double b, double c, double d)
Builds a quaternion from its components.

Method Summary

Quaternion	add(Quaternion q) Computes the sum of the instance and another quaternion.
static Quaternion	add(Quaternion q1, Quaternion q2) Computes the sum of two quaternions.
double	dotProduct(Quaternion q) Computes the dot-product of the instance by a quaternion.
static double	dotProduct(Quaternion q1, Quaternion q2) Computes the dot-product of two quaternions.
boolean	equals(Object other)
boolean	equals(Quaternion q, double eps) Checks whether this instance is equal to another quaternion within a given tolerance.
Quaternion	getConjugate() Returns the conjugate quaternion of the instance.
Quaternion	getInverse() Returns the inverse of this instance.
double	getNorm() Computes the norm of the quaternion.
Quaternion	getPositivePolarForm() Returns the polar form of the quaternion.
double	getQ0() Gets the first component of the quaternion (scalar part).
double	getQ1() Gets the second component of the quaternion (first component of the vector part).
double	getQ2() Gets the third component of the quaternion (second component of the vector part).
double	getQ3() Gets the fourth component of the quaternion (third component of the vector part).
double	getScalarPart() Gets the scalar part of the quaternion.
double[]	getVectorPart() Gets the three components of the vector part of the quaternion.
int	hashCode()
boolean	isPureQuaternion(double eps) Checks whether the instance is a pure quaternion within a given tolerance.
boolean	isUnitQuaternion(double eps) Checks whether the instance is a unit quaternion within a given tolerance.
Quaternion	multiply(double alpha) Multiplies the instance by a scalar.
Quaternion	multiply(Quaternion q) Returns the Hamilton product of the instance by a quaternion.
static Quaternion	multiply(Quaternion q1, Quaternion q2) Returns the Hamilton product of two quaternions.
Quaternion	normalize() Computes the normalized quaternion (the versor of the instance).
Quaternion	subtract(Quaternion q) Subtracts a quaternion from the instance.
static Quaternion	subtract(Quaternion q1, Quaternion q2) Subtracts two quaternions.
String	toString()

Methods inherited from class java.lang.Object

clone, finalize, getClass, notify, notifyAll, wait, wait, wait

Field Detail

IDENTITY

public static final Quaternion IDENTITY

Identity quaternion.

ZERO

public static final Quaternion ZERO

Zero quaternion.

I

public static final Quaternion I

i

J

public static final Quaternion J

j

K

public static final Quaternion K

k

Constructor Detail

Quaternion

public Quaternion(double a,
                  double b,
                  double c,
                  double d)

Builds a quaternion from its components.

Parameters:

a - Scalar component.

b - First vector component.

c - Second vector component.

d - Third vector component.

Quaternion

public Quaternion(double scalar,
                  double[] v)
           throws DimensionMismatchException

Builds a quaternion from scalar and vector parts.

Parameters:

scalar - Scalar part of the quaternion.

v - Components of the vector part of the quaternion.

Throws:

DimensionMismatchException - if the array length is not 3.

Quaternion

public Quaternion(double[] v)

Builds a pure quaternion from a vector (assuming that the scalar part is zero).

Parameters:

v - Components of the vector part of the pure quaternion.

Method Detail

getConjugate

public Quaternion getConjugate()

Returns the conjugate quaternion of the instance.

Returns:

the conjugate quaternion

multiply

public static Quaternion multiply(Quaternion q1,
                                  Quaternion q2)

Returns the Hamilton product of two quaternions.

Parameters:

q1 - First quaternion.

q2 - Second quaternion.

Returns:

the product q1 and q2, in that order.

multiply

public Quaternion multiply(Quaternion q)

Returns the Hamilton product of the instance by a quaternion.

Parameters:

q - Quaternion.

Returns:

the product of this instance with q, in that order.

add

public static Quaternion add(Quaternion q1,
                             Quaternion q2)

Computes the sum of two quaternions.

Parameters:

q1 - Quaternion.

q2 - Quaternion.

Returns:

the sum of q1 and q2.

add

public Quaternion add(Quaternion q)

Computes the sum of the instance and another quaternion.

Parameters:

q - Quaternion.

Returns:

the sum of this instance and q

subtract

public static Quaternion subtract(Quaternion q1,
                                  Quaternion q2)

Subtracts two quaternions.

Parameters:

q1 - First Quaternion.

q2 - Second quaternion.

Returns:

the difference between q1 and q2.

subtract

public Quaternion subtract(Quaternion q)

Subtracts a quaternion from the instance.

Parameters:

q - Quaternion.

Returns:

the difference between this instance and q.

dotProduct

public static double dotProduct(Quaternion q1,
                                Quaternion q2)

Computes the dot-product of two quaternions.

Parameters:

q1 - Quaternion.

q2 - Quaternion.

Returns:

the dot product of q1 and q2.

dotProduct

public double dotProduct(Quaternion q)

Computes the dot-product of the instance by a quaternion.

Parameters:

q - Quaternion.

Returns:

the dot product of this instance and q.

getNorm

public double getNorm()

Computes the norm of the quaternion.

Returns:

the norm.

normalize

public Quaternion normalize()

Computes the normalized quaternion (the versor of the instance). The norm of the quaternion must not be zero.

Returns:

a normalized quaternion.

Throws:

ZeroException - if the norm of the quaternion is zero.

equals

public boolean equals(Object other)

Overrides:

equals in class Object

hashCode

public int hashCode()

Overrides:

hashCode in class Object

equals

public boolean equals(Quaternion q,
                      double eps)

Checks whether this instance is equal to another quaternion within a given tolerance.

Parameters:

q - Quaternion with which to compare the current quaternion.

eps - Tolerance.

Returns:

true if the each of the components are equal within the allowed absolute error.

isUnitQuaternion

public boolean isUnitQuaternion(double eps)

Checks whether the instance is a unit quaternion within a given tolerance.

Parameters:

eps - Tolerance (absolute error).

Returns:

true if the norm is 1 within the given tolerance, false otherwise

isPureQuaternion

public boolean isPureQuaternion(double eps)

Checks whether the instance is a pure quaternion within a given tolerance.

Parameters:

eps - Tolerance (absolute error).

Returns:

true if the scalar part of the quaternion is zero.

getPositivePolarForm

public Quaternion getPositivePolarForm()

Returns the polar form of the quaternion.

Returns:

the unit quaternion with positive scalar part.

getInverse

public Quaternion getInverse()

Returns the inverse of this instance. The norm of the quaternion must not be zero.

Returns:

the inverse.

Throws:

ZeroException - if the norm (squared) of the quaternion is zero.

getQ0

public double getQ0()

Gets the first component of the quaternion (scalar part).

Returns:

the scalar part.

getQ1

public double getQ1()

Gets the second component of the quaternion (first component of the vector part).

Returns:

the first component of the vector part.

getQ2

public double getQ2()

Gets the third component of the quaternion (second component of the vector part).

Returns:

the second component of the vector part.

getQ3

public double getQ3()

Gets the fourth component of the quaternion (third component of the vector part).

Returns:

the third component of the vector part.

getScalarPart

public double getScalarPart()

Gets the scalar part of the quaternion.

Returns:

the scalar part.

See Also:

getQ0()

getVectorPart

public double[] getVectorPart()

Gets the three components of the vector part of the quaternion.

Returns:

the vector part.

See Also:

getQ1(), getQ2(), getQ3()

multiply

public Quaternion multiply(double alpha)

Multiplies the instance by a scalar.

Parameters:

alpha - Scalar factor.

Returns:

a scaled quaternion.

toString

public String toString()

Overrides:

toString in class Object