Class Quaternion

java.lang.Object
  Quaternion

public class Quaternion
extends java.lang.Object

Quaternions. Basic operations.

Constructor Summary

Quaternion(double a, double b, double c, double d)
Constructor from four double values.

Method Summary

java.lang.Object	clone() Clone of the quaternion.
Quaternion	conjugate() Conjugate of the quaternion.
Quaternion	divideByLeft(Quaternion q) Left quotient of quaternions.
Quaternion	divideByRight(Quaternion q) Right quotient of quaternions.
Quaternion	dotMult(Quaternion q) Dot product of quaternions.
boolean	equals(java.lang.Object qo) Equality test of quaternions.
double	getIpart() Imaginary part i of the quaternion.
double	getJpart() Imaginary part j of the quaternion.
double	getKpart() Imaginary part k of the quaternion.
double	getRpart() Real part of the quaternion.
int	hashCode() Integer hashCode has to be the same for equal objects.
Quaternion	inverse() Inverse of the quaternion.
boolean	isZero() Test whether the quaternion is zero.
Quaternion	minus(Quaternion q) Difference of quaternions.
double	norm() Norm of the quaternion.
Quaternion	opposite() Opposite of the quaternion.
Quaternion	plus(Quaternion q) Sum of quaternions.
Quaternion	times(double r) Multiplication by a coefficient.
Quaternion	times(Quaternion q) Product of quaternions.
java.lang.String	toString() Conversion of the quaternion to the string.
static Quaternion	valueOf(java.lang.String s) Conversion from the string to the quaternion.

Methods inherited from class java.lang.Object

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

Constructor Detail

Quaternion

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

Constructor from four double values.

Parameters:

a - real part

b - imaginary part i

c - imaginary part j

d - imaginary part k

Method Detail

getRpart

public double getRpart()

Real part of the quaternion.

Returns:

real part

getIpart

public double getIpart()

Imaginary part i of the quaternion.

Returns:

imaginary part i

getJpart

public double getJpart()

Imaginary part j of the quaternion.

Returns:

imaginary part j

getKpart

public double getKpart()

Imaginary part k of the quaternion.

Returns:

imaginary part k

toString

public java.lang.String toString()

Conversion of the quaternion to the string.

Overrides:

toString in class java.lang.Object

Returns:

a string form of this quaternion: "a+bi+cj+dk" (without any brackets)

valueOf

public static Quaternion valueOf(java.lang.String s)

Conversion from the string to the quaternion. Reverse to toString method.

Parameters:

s - string of form produced by the toString method

Returns:

a quaternion represented by string s

Throws:

java.lang.IllegalArgumentException - if string s does not represent a quaternion (defined by the toString method)

clone

public java.lang.Object clone()
                       throws java.lang.CloneNotSupportedException

Clone of the quaternion.

Overrides:

clone in class java.lang.Object

Returns:

independent clone of this

Throws:

java.lang.CloneNotSupportedException

isZero

public boolean isZero()

Test whether the quaternion is zero.

Returns:

true, if the real part and all the imaginary parts are (close to) zero

conjugate

public Quaternion conjugate()

Conjugate of the quaternion. Expressed by the formula conjugate(a+bi+cj+dk) = a-bi-cj-dk

Returns:

conjugate of this

opposite

public Quaternion opposite()

Opposite of the quaternion. Expressed by the formula opposite(a+bi+cj+dk) = -a-bi-cj-dk

Returns:

quaternion -this

plus

public Quaternion plus(Quaternion q)

Sum of quaternions. Expressed by the formula (a1+b1i+c1j+d1k) + (a2+b2i+c2j+d2k) = (a1+a2) + (b1+b2)i + (c1+c2)j + (d1+d2)k

Parameters:

q - addend

Returns:

quaternion this+q

times

public Quaternion times(Quaternion q)

Product of quaternions. Expressed by the formula (a1+b1i+c1j+d1k) * (a2+b2i+c2j+d2k) = (a1a2-b1b2-c1c2-d1d2) + (a1b2+b1a2+c1d2-d1c2)i + (a1c2-b1d2+c1a2+d1b2)j + (a1d2+b1c2-c1b2+d1a2)k

Parameters:

q - factor

Returns:

quaternion this*q

times

public Quaternion times(double r)

Multiplication by a coefficient.

Parameters:

r - coefficient

Returns:

quaternion this*r

inverse

public Quaternion inverse()

Inverse of the quaternion. Expressed by the formula 1/(a+bi+cj+dk) = a/(a*a+b*b+c*c+d*d) + ((-b)/(a*a+b*b+c*c+d*d))i + ((-c)/(a*a+b*b+c*c+d*d))j + ((-d)/(a*a+b*b+c*c+d*d))k

Returns:

quaternion 1/this

minus

public Quaternion minus(Quaternion q)

Difference of quaternions. Expressed as addition to the opposite.

Parameters:

q - subtrahend

Returns:

quaternion this-q

divideByRight

public Quaternion divideByRight(Quaternion q)

Right quotient of quaternions. Expressed as multiplication to the inverse.

Parameters:

q - (right) divisor

Returns:

quaternion this*inverse(q)

divideByLeft

public Quaternion divideByLeft(Quaternion q)

Left quotient of quaternions.

Parameters:

q - (left) divisor

Returns:

quaternion inverse(q)*this

equals

public boolean equals(java.lang.Object qo)

Equality test of quaternions. Difference of equal numbers is (close to) zero.

Overrides:

equals in class java.lang.Object

Parameters:

qo - second quaternion

Returns:

logical value of the expression this.equals(qo)

dotMult

public Quaternion dotMult(Quaternion q)

Dot product of quaternions. (p*conjugate(q) + q*conjugate(p))/2

Parameters:

q - factor

Returns:

dot product of this and q

hashCode

public int hashCode()

Integer hashCode has to be the same for equal objects.

Overrides:

hashCode in class java.lang.Object

Returns:

hashcode

norm

public double norm()

Norm of the quaternion. Expressed by the formula norm(a+bi+cj+dk) = Math.sqrt(a*a+b*b+c*c+d*d)

Returns:

norm of this (norm is a real number)