JSci.maths
Class Quaternion

java.lang.Object
  JSci.maths.Quaternion

All Implemented Interfaces:

AbelianGroup.Member, Algebra.Member, BanachSpace.Member, CStarAlgebra.Member, Field.Member, Member, Module.Member, Ring.Member, java.io.Serializable, VectorSpace.Member

public final class Quaternion

extends java.lang.Object

implements Field.Member, CStarAlgebra.Member

The Quaternion class encapsulates quaternions.

See Also:

Serialized Form

PlanetMath references:

Quaternions

Field Summary

static Quaternion	I
static Quaternion	J
static Quaternion	K
static Quaternion	ONE

Constructor Summary

Quaternion(double real, Double3Vector imag)
Constructs a quaternion.

Quaternion(double q0, double q1, double q2, double q3)
Constructs the quaternion q₀+iq₁+jq₂+kq₃.

Method Summary

AbelianGroup.Member	add(AbelianGroup.Member x) Returns the addition of this number and another.
Quaternion	add(Quaternion q) Returns the addition of this quaternion and another.
Quaternion	addImag(Double3Vector imag) Returns the addition of this quaternion with an imaginary part.
Quaternion	addReal(double real) Returns the addition of this quaternion with a real part.
Quaternion	conjugate() Returns the conjugate of this quaternion.
static Quaternion	cos(Quaternion q)
static Quaternion	cosh(Quaternion q)
Quaternion	divide(double x) Returns the division of this quaternion by a scalar.
Field.Member	divide(Field.Member x) Returns the division of this number and another.
Quaternion	divide(Quaternion q) Returns the division of this quaternion by another.
boolean	equals(java.lang.Object obj) Compares two quaternions for equality.
static Quaternion	exp(Quaternion q)
int	hashCode() Returns a hashcode for this quaternion.
Double3Vector	imag() Returns the imaginary part of this quaternion.
Field.Member	inverse() Returns the inverse of this quaternion.
CStarAlgebra.Member	involution() Returns the involution of this quaternion.
boolean	isInfinite() Returns true if either the real or imaginary part is infinite.
boolean	isNaN() Returns true if either the real or imaginary part is NaN.
static Quaternion	log(Quaternion q)
Quaternion	multiply(double x) Returns the multiplication of this quaternion by a scalar.
Quaternion	multiply(Quaternion q) Returns the multiplication of this quaternion and another.
Ring.Member	multiply(Ring.Member x) Returns the multiplication of this number and another.
AbelianGroup.Member	negate() Returns the negative of this quaternion.
double	norm() Returns the l2-norm (magnitude), which is also the C* norm.
Quaternion	normalize()
double	real() Returns the real part of this quaternion.
static Quaternion	rotation(AbstractDoubleSquareMatrix m) Constructs a quaternion representing a rotation matrix.
VectorSpace.Member	scalarDivide(Field.Member x) Returns the division of this number by a real scalar.
Module.Member	scalarMultiply(Ring.Member x) Returns the multiplication of this number by a real scalar.
static Quaternion	sin(Quaternion q)
static Quaternion	sinh(Quaternion q)
AbelianGroup.Member	subtract(AbelianGroup.Member x) Returns the subtraction of this number and another.
Quaternion	subtract(Quaternion q) Returns the subtraction of this quaternion by another.
Quaternion	subtractImag(Double3Vector imag) Returns the subtraction of this quaternion by an imaginary part.
Quaternion	subtractReal(double real) Returns the subtraction of this quaternion by a real part.
double	sumSquares() Returns the sum of the squares of the components.
static Quaternion	tan(Quaternion q)
static Quaternion	tanh(Quaternion q)
AbstractDoubleSquareMatrix	toRotationMatrix() Returns a 3D rotation matrix representing this quaternion.
java.lang.String	toString() Returns a string representing the value of this quaternion.

Methods inherited from class java.lang.Object

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

Field Detail

ONE

public static final Quaternion ONE

I

public static final Quaternion I

J

public static final Quaternion J

K

public static final Quaternion K

Constructor Detail

Quaternion

public Quaternion(double real,
                  Double3Vector imag)

Constructs a quaternion.

Quaternion

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

Constructs the quaternion q₀+iq₁+jq₂+kq₃.

Method Detail

rotation

public static Quaternion rotation(AbstractDoubleSquareMatrix m)

Constructs a quaternion representing a rotation matrix. Note: if the matrix is not orthogonal then the quaternion will not have unit norm. Note: unit quaternions are a double cover of SO(3).

Parameters:

m - a rotation matrix

toRotationMatrix

public AbstractDoubleSquareMatrix toRotationMatrix()

Returns a 3D rotation matrix representing this quaternion. Note: if this quaternion does not have unit norm then the matrix will not be orthogonal.

equals

public boolean equals(java.lang.Object obj)

Compares two quaternions for equality.

Parameters:

obj - a quaternion

toString

public java.lang.String toString()

Returns a string representing the value of this quaternion.

hashCode

public int hashCode()

Returns a hashcode for this quaternion.

isNaN

public boolean isNaN()

Returns true if either the real or imaginary part is NaN.

isInfinite

public boolean isInfinite()

Returns true if either the real or imaginary part is infinite.

real

public double real()

Returns the real part of this quaternion.

imag

public Double3Vector imag()

Returns the imaginary part of this quaternion.

norm

public double norm()

Returns the l²-norm (magnitude), which is also the C^* norm.

Specified by:

norm in interface BanachSpace.Member

sumSquares

public double sumSquares()

Returns the sum of the squares of the components.

negate

public AbelianGroup.Member negate()

Returns the negative of this quaternion.

Specified by:

negate in interface AbelianGroup.Member

inverse

public Field.Member inverse()

Returns the inverse of this quaternion.

Specified by:

inverse in interface Field.Member

involution

public CStarAlgebra.Member involution()

Returns the involution of this quaternion.

Specified by:

involution in interface CStarAlgebra.Member

conjugate

public Quaternion conjugate()

Returns the conjugate of this quaternion.

add

public AbelianGroup.Member add(AbelianGroup.Member x)

Returns the addition of this number and another.

Specified by:

add in interface AbelianGroup.Member

Parameters:

x - a group member

add

public Quaternion add(Quaternion q)

Returns the addition of this quaternion and another.

Parameters:

q - a quaternion

addReal

public Quaternion addReal(double real)

Returns the addition of this quaternion with a real part.

Parameters:

real - a real part

addImag

public Quaternion addImag(Double3Vector imag)

Returns the addition of this quaternion with an imaginary part.

Parameters:

imag - an imaginary part

subtract

public AbelianGroup.Member subtract(AbelianGroup.Member x)

Returns the subtraction of this number and another.

Specified by:

subtract in interface AbelianGroup.Member

Parameters:

x - a group member

subtract

public Quaternion subtract(Quaternion q)

Returns the subtraction of this quaternion by another.

Parameters:

q - a quaternion

subtractReal

public Quaternion subtractReal(double real)

Returns the subtraction of this quaternion by a real part.

Parameters:

real - a real part

subtractImag

public Quaternion subtractImag(Double3Vector imag)

Returns the subtraction of this quaternion by an imaginary part.

Parameters:

imag - an imaginary part

scalarMultiply

public Module.Member scalarMultiply(Ring.Member x)

Returns the multiplication of this number by a real scalar.

Specified by:

scalarMultiply in interface Module.Member

Parameters:

x - a ring member

multiply

public Ring.Member multiply(Ring.Member x)

Returns the multiplication of this number and another.

Specified by:

multiply in interface Ring.Member

Parameters:

x - a ring member

multiply

public Quaternion multiply(Quaternion q)

Returns the multiplication of this quaternion and another.

Parameters:

q - a quaternion

multiply

public Quaternion multiply(double x)

Returns the multiplication of this quaternion by a scalar.

Parameters:

x - a real number

scalarDivide

public VectorSpace.Member scalarDivide(Field.Member x)

Returns the division of this number by a real scalar.

Specified by:

scalarDivide in interface VectorSpace.Member

Parameters:

x - a field member

divide

public Field.Member divide(Field.Member x)

Returns the division of this number and another.

Specified by:

divide in interface Field.Member

Parameters:

x - a field member

divide

public Quaternion divide(Quaternion q)

Returns the division of this quaternion by another.

Parameters:

q - a quaternion

Throws:

java.lang.ArithmeticException - If divide by zero.

divide

public Quaternion divide(double x)

Returns the division of this quaternion by a scalar.

Parameters:

x - a real number

Throws:

java.lang.ArithmeticException - If divide by zero.

normalize

public Quaternion normalize()

exp

public static Quaternion exp(Quaternion q)

log

public static Quaternion log(Quaternion q)

sin

public static Quaternion sin(Quaternion q)

cos

public static Quaternion cos(Quaternion q)

tan

public static Quaternion tan(Quaternion q)

sinh

public static Quaternion sinh(Quaternion q)

cosh

public static Quaternion cosh(Quaternion q)

tanh

public static Quaternion tanh(Quaternion q)