Package de.tilman_neumann.jml.quaternion

Class RationalQuaternion

java.lang.Object

de.tilman_neumann.jml.quaternion.RationalQuaternion

public class RationalQuaternion
extends java.lang.Object

Quaternions are an extension of complex numbers to four dimensions defined as Q(i,j,k) = {x + y*i + z*j + w*k : x,y,z,w ∈ R and i^2 = j^2 = k^2 = ijk = -1}.

Constructor Summary

Constructors

Constructor	Description
RationalQuaternion(BigRational x, BigRational y, BigRational z, BigRational w)

Method Summary

Modifier and Type	Method	Description
RationalQuaternion	add(RationalQuaternion b)
RationalQuaternion	conjugate()
boolean	equals(java.lang.Object o)
BigRational	getW()
BigRational	getX()
BigRational	getY()
BigRational	getZ()
int	hashCode()
RationalQuaternion	inverse()	The inverse of a quaternion q is the conjugate of q divided coefficient-wise by the norm of q.
boolean	isUnit()
boolean	isZero()
RationalQuaternion	leftDivide(RationalQuaternion b)	"left-divide" this by b.
RationalQuaternion	multiply(BigRational b)
RationalQuaternion	multiply(RationalQuaternion b)
RationalQuaternion	multiply(java.math.BigInteger b)
RationalQuaternion	negate()
BigRational	norm()
RationalQuaternion	normalize()
RationalQuaternion	rightDivide(RationalQuaternion b)	"right-divide" this by b.
RationalQuaternion	square()
RationalQuaternion	subtract(RationalQuaternion b)
java.lang.String	toString()

Methods inherited from class java.lang.Object

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

Constructor Details

RationalQuaternion

public RationalQuaternion(BigRational x,
BigRational y,
BigRational z,
BigRational w)

Method Details

getX

public BigRational getX()

getY

public BigRational getY()

getZ

public BigRational getZ()

getW

public BigRational getW()

conjugate

public RationalQuaternion conjugate()

negate

public RationalQuaternion negate()

normalize

public RationalQuaternion normalize()

norm

public BigRational norm()

Returns:

the norm of this

isZero

public boolean isZero()

isUnit

public boolean isUnit()

Returns:

true if this is a unit

add

public RationalQuaternion add(RationalQuaternion b)

subtract

public RationalQuaternion subtract(RationalQuaternion b)

multiply

public RationalQuaternion multiply(java.math.BigInteger b)

multiply

public RationalQuaternion multiply(BigRational b)

multiply

public RationalQuaternion multiply(RationalQuaternion b)

square

public RationalQuaternion square()

inverse

public RationalQuaternion inverse()

The inverse of a quaternion q is the conjugate of q divided coefficient-wise by the norm of q.

Returns:

the inverse of this

leftDivide

public RationalQuaternion leftDivide(RationalQuaternion b)

"left-divide" this by b. In quaternions, there are two division algorithms, because multiplication is not commutative. The left-division variant computes a/b = inverse(b)*a = conjugate(b)*a / N(b). Its resulting quotient is apt for the right term in a complementary test multiplication. The division in rational coefficients is exact, i.e. there is no remainder.

Parameters:

b -

Returns:

left division quotient

rightDivide

public RationalQuaternion rightDivide(RationalQuaternion b)

"right-divide" this by b. In quaternions, there are two division algorithms, because multiplication is not commutative. The right-division variant computes a/b = a*inverse(b) = a*conjugate(b) / N(b). Its resulting quotient is apt for the left> term in a complementary test multiplication. The division in rational coefficients is exact, i.e. there is no remainder.

Parameters:

b -

Returns:

right division quotient

equals

public boolean equals(java.lang.Object o)

Overrides:

equals in class java.lang.Object

hashCode

public int hashCode()

Overrides:

hashCode in class java.lang.Object

toString

public java.lang.String toString()

Overrides:

toString in class java.lang.Object