vmm3d.core

Class Quaternion

java.lang.Object

vmm3d.core.Quaternion

public class Quaternion
extends java.lang.Object

Represents an element of the set of quaternions.

Field Summary

Fields

Modifier and Type	Field and Description
double	a
double	b
double	c
double	d
static Quaternion	q1
static Quaternion	qI
static Quaternion	qJ
static Quaternion	qK
static Quaternion	ZERO

Constructor Summary

Constructors

Constructor and Description
Quaternion() Create a quaternion with all coordinates intially equal to zero.
Quaternion(double a, double b, double c, double d) Create a quaternion from initial values for each coordinate.
Quaternion(Quaternion source) Create a copy of an exiting non-null Quaternion object

Method Summary

Modifier and Type	Method and Description
Quaternion	conj() p.conj() returns the conjugate to p
Quaternion	dividedBy(Quaternion q) Compute the quotient of this quaternaion by another quaternion.
double	dot(Quaternion q) p.dot(q) returns the scalar product
boolean	equals(java.lang.Object obj)
Quaternion	inverse() Compute the multiplicative inverser of this quaternion.
Quaternion	minus(Quaternion q) Compute the difference of this quaternaion and another quaternion
double	norm() Returns the norm of this quaternion.
Quaternion	plus(Quaternion q) Compute the sum of this quaternaion and another quaternion
Quaternion	rotateAroundHopfFibre(double phi) Returns rotation by phi around standard Hopf fiber through (1,0,0,0)
Quaternion	rotateAroundHopfFibre(double phi, Quaternion q0) Returns rotation by phi around standard Hopf fiber through q0
Vector3D	StereographicProjection() Returns stereographic projection from (-1,0,0,0)
Quaternion	times(double x) Compute the product of this quaternaion and a real number
Quaternion	times(Quaternion q) Compute the product of this quaternaion and another quaternion
java.lang.String	toString()

Methods inherited from class java.lang.Object

getClass, hashCode, notify, notifyAll, wait, wait, wait

Field Detail

ZERO

public static final Quaternion ZERO

q1

public static final Quaternion q1

qI

public static final Quaternion qI

qJ

public static final Quaternion qJ

qK

public static final Quaternion qK

a

public double a

b

public double b

c

public double c

d

public double d

Constructor Detail

Quaternion

public Quaternion()

Create a quaternion with all coordinates intially equal to zero.

Quaternion

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

Create a quaternion from initial values for each coordinate.

Quaternion

public Quaternion(Quaternion source)

Create a copy of an exiting non-null Quaternion object

Parameters:

source - the object to be copied. A NullPointerException is thrown if this is null.

Method Detail

equals

public boolean equals(java.lang.Object obj)

Overrides:

equals in class java.lang.Object

toString

public java.lang.String toString()

Overrides:

toString in class java.lang.Object

dot

public double dot(Quaternion q)

p.dot(q) returns the scalar product

norm

public double norm()

Returns the norm of this quaternion.

conj

public Quaternion conj()

p.conj() returns the conjugate to p

plus

public Quaternion plus(Quaternion q)

Compute the sum of this quaternaion and another quaternion

Parameters:

q - the non-null quaternion to be added to this one. If this is null, a NullPointerException is thrown.

minus

public Quaternion minus(Quaternion q)

Compute the difference of this quaternaion and another quaternion

Parameters:

q - the non-null quaternion to be subtracted from this one. If this is null, a NullPointerException is thrown.

times

public Quaternion times(Quaternion q)

Compute the product of this quaternaion and another quaternion

Parameters:

q - the non-null quaternion to be ultiplied by this one. If this is null, a NullPointerException is thrown.

times

public Quaternion times(double x)

Compute the product of this quaternaion and a real number

inverse

public Quaternion inverse()

Compute the multiplicative inverser of this quaternion. Note that the inverse of zero will not generate an error; instead, the inverse of zero is a quaternion object in which every coordinate is Double.NaN.

dividedBy

public Quaternion dividedBy(Quaternion q)

Compute the quotient of this quaternaion by another quaternion. Note that division by zero does not generate an error. Instead, the the result is a vector in which each coordinate is Double.NaN.

Parameters:

q - the non-null quaternion that this quaternion is to be multiplied by. If this is null, a NullPointerException is thrown.

rotateAroundHopfFibre

public Quaternion rotateAroundHopfFibre(double phi)

Returns rotation by phi around standard Hopf fiber through (1,0,0,0)

rotateAroundHopfFibre

public Quaternion rotateAroundHopfFibre(double phi,
                                        Quaternion q0)

Returns rotation by phi around standard Hopf fiber through q0

StereographicProjection

public Vector3D StereographicProjection()

Returns stereographic projection from (-1,0,0,0)