Apache Commons Math 3.6.1 · org.apache.commons.math3.complex.Quaternion

Modifier and Type	Field and Description
public static final Quaternion	I i
public static final Quaternion	IDENTITY Identity quaternion.
public static final Quaternion	J j
public static final Quaternion	K k
private final double	q0 First component (scalar part).
private final double	q1 Second component (first vector part).
private final double	q2 Third component (second vector part).
private final double	q3 Fourth component (third vector part).
private static final long	serialVersionUID Serializable version identifier.
public static final Quaternion	ZERO Zero quaternion.

Access	Constructor and Description
public	Quaternion(final double Scalar component. a, final double First vector component. b, final double Second vector component. c, final double Third vector component. d) Builds a quaternion from its components.
public	Quaternion(final double Scalar part of the quaternion. scalar, final double[] Components of the vector part of the quaternion. v) Builds a quaternion from scalar and vector parts.
public	Quaternion(final double[] Components of the vector part of the pure quaternion. v) Builds a pure quaternion from a vector (assuming that the scalar part is zero).

Method Summary

Modifier and Type	Method and Description
public static Quaternion	Returns: the sum of `q1` and `q2`. add(final Quaternion Quaternion. q1, final Quaternion Quaternion. q2) Computes the sum of two quaternions.
public Quaternion	Returns: the sum of this instance and `q` add(final Quaternion Quaternion. q) Computes the sum of the instance and another quaternion.
public static double	Returns: the dot product of `q1` and `q2`. dotProduct(final Quaternion Quaternion. q1, final Quaternion Quaternion. q2) Computes the dot-product of two quaternions.
public double	Returns: the dot product of this instance and `q`. dotProduct(final Quaternion Quaternion. q) Computes the dot-product of the instance by a quaternion.
public boolean	equals(Object the reference object with which to compare. other) Overrides java.lang.Object.equals. Indicates whether some other object is "equal to" this one.
public boolean	Returns: `true` if the each of the components are equal within the allowed absolute error. equals(final Quaternion Quaternion with which to compare the current quaternion. q, final double Tolerance. eps) Checks whether this instance is equal to another quaternion within a given tolerance.
public Quaternion	Returns: the conjugate quaternion getConjugate() Returns the conjugate quaternion of the instance.
public Quaternion	Returns: the inverse. getInverse() Returns the inverse of this instance.
public double	Returns: the norm. getNorm() Computes the norm of the quaternion.
public Quaternion	Returns: the unit quaternion with positive scalar part. getPositivePolarForm() Returns the polar form of the quaternion.
public double	Returns: the scalar part. getQ0() Gets the first component of the quaternion (scalar part).
public double	Returns: the first component of the vector part. getQ1() Gets the second component of the quaternion (first component of the vector part).
public double	Returns: the second component of the vector part. getQ2() Gets the third component of the quaternion (second component of the vector part).
public double	Returns: the third component of the vector part. getQ3() Gets the fourth component of the quaternion (third component of the vector part).
public double	Returns: the scalar part. getScalarPart() Gets the scalar part of the quaternion.
public double[]	Returns: the vector part. getVectorPart() Gets the three components of the vector part of the quaternion.
public int	hashCode() Overrides java.lang.Object.hashCode. Returns a hash code value for this object.
public boolean	Returns: `true` if the scalar part of the quaternion is zero. isPureQuaternion(double Tolerance (absolute error). eps) Checks whether the instance is a pure quaternion within a given tolerance.
public boolean	Returns: `true` if the norm is 1 within the given tolerance, `false` otherwise isUnitQuaternion(double Tolerance (absolute error). eps) Checks whether the instance is a unit quaternion within a given tolerance.
public static Quaternion	Returns: the product `q1` and `q2`, in that order. multiply(final Quaternion First quaternion. q1, final Quaternion Second quaternion. q2) Returns the Hamilton product of two quaternions.
public Quaternion	Returns: the product of this instance with `q`, in that order. multiply(final Quaternion Quaternion. q) Returns the Hamilton product of the instance by a quaternion.
public Quaternion	Returns: a scaled quaternion. multiply(final double Scalar factor. alpha) Multiplies the instance by a scalar.
public Quaternion	Returns: a normalized quaternion. normalize() Computes the normalized quaternion (the versor of the instance).
public static Quaternion	Returns: the difference between `q1` and `q2`. subtract(final Quaternion First Quaternion. q1, final Quaternion Second quaternion. q2) Subtracts two quaternions.
public Quaternion	Returns: the difference between this instance and `q`. subtract(final Quaternion Quaternion. q) Subtracts a quaternion from the instance.
public String	toString() Overrides java.lang.Object.toString. Returns a string representation of the object.

Inherited from java.lang.Object:: clone finalize getClass notify notifyAll wait wait wait

I	back to summary
public static final Quaternion I i

IDENTITY	back to summary
public static final Quaternion IDENTITY Identity quaternion.

J	back to summary
public static final Quaternion J j

K	back to summary
public static final Quaternion K k

q0	back to summary
private final double q0 First component (scalar part).

q1	back to summary
private final double q1 Second component (first vector part).

q2	back to summary
private final double q2 Third component (second vector part).

q3	back to summary
private final double q3 Fourth component (third vector part).

serialVersionUID	back to summary
private static final long serialVersionUID Serializable version identifier.

ZERO	back to summary
public static final Quaternion ZERO Zero quaternion.

Quaternion	back to summary
public Quaternion(final double a, final double b, final double c, final double d) Builds a quaternion from its components. Parameters a:double Scalar component. b:double First vector component. c:double Second vector component. d:double Third vector component.

Quaternion	back to summary
public Quaternion(final double scalar, final double[] v) throws DimensionMismatchException Builds a quaternion from scalar and vector parts. Parameters scalar:double Scalar part of the quaternion. v:double[] Components of the vector part of the quaternion. Exceptions DimensionMismatchException: if the array length is not 3.

Quaternion	back to summary
public Quaternion(final double[] v) Builds a pure quaternion from a vector (assuming that the scalar part is zero). Parameters v:double[] Components of the vector part of the pure quaternion.

Method Detail

add back to summary

add	back to summary
public static Quaternion add(final Quaternion q1, final Quaternion q2) Computes the sum of two quaternions. Parameters q1:Quaternion Quaternion. q2:Quaternion Quaternion. Returns:Quaternion the sum of `q1` and `q2`.

public static Quaternion add(final Quaternion q1, final Quaternion q2)

Computes the sum of two quaternions.

Parameters

q1:Quaternion: Quaternion.
q2:Quaternion: Quaternion.

Returns:Quaternion

the sum of q1 and q2.

add back to summary

add	back to summary
public Quaternion add(final Quaternion q) Computes the sum of the instance and another quaternion. Parameters q:Quaternion Quaternion. Returns:Quaternion the sum of this instance and `q`

public Quaternion add(final Quaternion q)

Computes the sum of the instance and another quaternion.

Parameters

q:Quaternion: Quaternion.

Returns:Quaternion

the sum of this instance and q

dotProduct back to summary

dotProduct	back to summary
public static double dotProduct(final Quaternion q1, final Quaternion q2) Computes the dot-product of two quaternions. Parameters q1:Quaternion Quaternion. q2:Quaternion Quaternion. Returns:double the dot product of `q1` and `q2`.

public static double dotProduct(final Quaternion q1, final Quaternion q2)

Computes the dot-product of two quaternions.

Parameters

q1:Quaternion: Quaternion.
q2:Quaternion: Quaternion.

Returns:double

the dot product of q1 and q2.

dotProduct back to summary

dotProduct	back to summary
public double dotProduct(final Quaternion q) Computes the dot-product of the instance by a quaternion. Parameters q:Quaternion Quaternion. Returns:double the dot product of this instance and `q`.

public double dotProduct(final Quaternion q)

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

Parameters

q:Quaternion: Quaternion.

Returns:double

the dot product of this instance and q.

equals back to summary

equals	back to summary
public boolean equals(Object other) Overrides java.lang.Object.equals. Doc from java.lang.Object.equals. Indicates whether some other object is "equal to" this one. The `equals` method implements an equivalence relation on non-null object references: It is reflexive: for any non-null reference value `x`, `x.equals(x)` should return `true`. It is symmetric: for any non-null reference values `x` and `y`, `x.equals(y)` should return `true` if and only if `y.equals(x)` returns `true`. It is transitive: for any non-null reference values `x`, `y`, and `z`, if `x.equals(y)` returns `true` and `y.equals(z)` returns `true`, then `x.equals(z)` should return `true`. It is consistent: for any non-null reference values `x` and `y`, multiple invocations of `x.equals(y)` consistently return `true` or consistently return `false`, provided no information used in `equals` comparisons on the objects is modified. For any non-null reference value `x`, `x.equals(null)` should return `false`. An equivalence relation partitions the elements it operates on into equivalence classes; all the members of an equivalence class are equal to each other. Members of an equivalence class are substitutable for each other, at least for some purposes. Parameters other:Object the reference object with which to compare. Returns:boolean `true` if this object is the same as the obj argument; `false` otherwise. Annotations @Override

public boolean equals(Object other)

Overrides java.lang.Object.equals.

Doc from java.lang.Object.equals.

Indicates whether some other object is "equal to" this one.

The equals method implements an equivalence relation on non-null object references:

It is reflexive: for any non-null reference value x, x.equals(x) should return true.
It is symmetric: for any non-null reference values x and y, x.equals(y) should return true if and only if y.equals(x) returns true.
It is transitive: for any non-null reference values x, y, and z, if x.equals(y) returns true and y.equals(z) returns true, then x.equals(z) should return true.
It is consistent: for any non-null reference values x and y, multiple invocations of x.equals(y) consistently return true or consistently return false, provided no information used in equals comparisons on the objects is modified.
For any non-null reference value x, x.equals(null) should return false.

An equivalence relation partitions the elements it operates on into equivalence classes; all the members of an equivalence class are equal to each other. Members of an equivalence class are substitutable for each other, at least for some purposes.

Parameters

other:Object: the reference object with which to compare.

Returns:boolean

true if this object is the same as the obj argument; false otherwise.

Annotations

@Override

equals back to summary

equals	back to summary
public boolean equals(final Quaternion q, final double eps) Checks whether this instance is equal to another quaternion within a given tolerance. Parameters q:Quaternion Quaternion with which to compare the current quaternion. eps:double Tolerance. Returns:boolean `true` if the each of the components are equal within the allowed absolute error.

public boolean equals(final Quaternion q, final double eps)

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

Parameters

q:Quaternion: Quaternion with which to compare the current quaternion.
eps:double: Tolerance.

Returns:boolean

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

getConjugate	back to summary
public Quaternion getConjugate() Returns the conjugate quaternion of the instance. Returns:Quaternion the conjugate quaternion

getConjugate

back to summary

public Quaternion getConjugate()

Returns the conjugate quaternion of the instance.

Returns:Quaternion: the conjugate quaternion

getInverse	back to summary
public Quaternion getInverse() Returns the inverse of this instance. The norm of the quaternion must not be zero. Returns:Quaternion the inverse. Exceptions ZeroException: if the norm (squared) of the quaternion is zero.

getInverse

back to summary

public Quaternion getInverse()

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

Returns:Quaternion

the inverse.

Exceptions

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

getNorm	back to summary
public double getNorm() Computes the norm of the quaternion. Returns:double the norm.

getNorm

back to summary

public double getNorm()

Computes the norm of the quaternion.

Returns:double: the norm.

getPositivePolarForm	back to summary
public Quaternion getPositivePolarForm() Returns the polar form of the quaternion. Returns:Quaternion the unit quaternion with positive scalar part.

getPositivePolarForm

back to summary

public Quaternion getPositivePolarForm()

Returns the polar form of the quaternion.

Returns:Quaternion: the unit quaternion with positive scalar part.

getQ0	back to summary
public double getQ0() Gets the first component of the quaternion (scalar part). Returns:double the scalar part.

getQ0

back to summary

public double getQ0()

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

Returns:double: the scalar part.

getQ1	back to summary
public double getQ1() Gets the second component of the quaternion (first component of the vector part). Returns:double the first component of the vector part.

getQ1

back to summary

public double getQ1()

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

Returns:double: the first component of the vector part.

getQ2	back to summary
public double getQ2() Gets the third component of the quaternion (second component of the vector part). Returns:double the second component of the vector part.

getQ2

back to summary

public double getQ2()

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

Returns:double: the second component of the vector part.

getQ3	back to summary
public double getQ3() Gets the fourth component of the quaternion (third component of the vector part). Returns:double the third component of the vector part.

getQ3

back to summary

public double getQ3()

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

Returns:double: the third component of the vector part.

getScalarPart back to summary

getScalarPart	back to summary
public double getScalarPart() Gets the scalar part of the quaternion. Returns:double the scalar part. See Also `getQ0()`

public double getScalarPart()

Gets the scalar part of the quaternion.

Returns:double: the scalar part.
See Also: getQ0()

getVectorPart back to summary

getVectorPart	back to summary
public double[] getVectorPart() Gets the three components of the vector part of the quaternion. Returns:double[] the vector part. See Also `getQ1()`, `getQ2()`, `getQ3()`

public double[] getVectorPart()

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

Returns:double[]: the vector part.
See Also: getQ1(), getQ2(), getQ3()

hashCode back to summary

hashCode	back to summary
public int hashCode() Overrides java.lang.Object.hashCode. Doc from java.lang.Object.hashCode. Returns a hash code value for this object. This method is supported for the benefit of hash tables such as those provided by `java.util.HashMap`. The general contract of `hashCode` is: Whenever it is invoked on the same object more than once during an execution of a Java application, the `hashCode` method must consistently return the same integer, provided no information used in `equals` comparisons on the object is modified. This integer need not remain consistent from one execution of an application to another execution of the same application. If two objects are equal according to the `equals` method, then calling the `hashCode` method on each of the two objects must produce the same integer result. It is not required that if two objects are unequal according to the `equals` method, then calling the `hashCode` method on each of the two objects must produce distinct integer results. However, the programmer should be aware that producing distinct integer results for unequal objects may improve the performance of hash tables. Returns:int a hash code value for this object Annotations @Override

public int hashCode()

Overrides java.lang.Object.hashCode.

Doc from java.lang.Object.hashCode.

Returns a hash code value for this object. This method is supported for the benefit of hash tables such as those provided by java.util.HashMap.

The general contract of hashCode is:

Whenever it is invoked on the same object more than once during an execution of a Java application, the hashCode method must consistently return the same integer, provided no information used in equals comparisons on the object is modified. This integer need not remain consistent from one execution of an application to another execution of the same application.
If two objects are equal according to the equals method, then calling the hashCode method on each of the two objects must produce the same integer result.
It is not required that if two objects are unequal according to the equals method, then calling the hashCode method on each of the two objects must produce distinct integer results. However, the programmer should be aware that producing distinct integer results for unequal objects may improve the performance of hash tables.

Returns:int

a hash code value for this object

Annotations

@Override

isPureQuaternion back to summary

isPureQuaternion	back to summary
public boolean isPureQuaternion(double eps) Checks whether the instance is a pure quaternion within a given tolerance. Parameters eps:double Tolerance (absolute error). Returns:boolean `true` if the scalar part of the quaternion is zero.

public boolean isPureQuaternion(double eps)

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

Parameters

eps:double: Tolerance (absolute error).

Returns:boolean

true if the scalar part of the quaternion is zero.

isUnitQuaternion back to summary

isUnitQuaternion	back to summary
public boolean isUnitQuaternion(double eps) Checks whether the instance is a unit quaternion within a given tolerance. Parameters eps:double Tolerance (absolute error). Returns:boolean `true` if the norm is 1 within the given tolerance, `false` otherwise

public boolean isUnitQuaternion(double eps)

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

Parameters

eps:double: Tolerance (absolute error).

Returns:boolean

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

multiply back to summary

multiply	back to summary
public static Quaternion multiply(final Quaternion q1, final Quaternion q2) Returns the Hamilton product of two quaternions. Parameters q1:Quaternion First quaternion. q2:Quaternion Second quaternion. Returns:Quaternion the product `q1` and `q2`, in that order.

public static Quaternion multiply(final Quaternion q1, final Quaternion q2)

Returns the Hamilton product of two quaternions.

Parameters

q1:Quaternion: First quaternion.
q2:Quaternion: Second quaternion.

Returns:Quaternion

the product q1 and q2, in that order.

multiply back to summary

multiply	back to summary
public Quaternion multiply(final Quaternion q) Returns the Hamilton product of the instance by a quaternion. Parameters q:Quaternion Quaternion. Returns:Quaternion the product of this instance with `q`, in that order.

public Quaternion multiply(final Quaternion q)

Returns the Hamilton product of the instance by a quaternion.

Parameters

q:Quaternion: Quaternion.

Returns:Quaternion

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

multiply	back to summary
public Quaternion multiply(final double alpha) Multiplies the instance by a scalar. Parameters alpha:double Scalar factor. Returns:Quaternion a scaled quaternion.

multiply

back to summary

public Quaternion multiply(final double alpha)

Multiplies the instance by a scalar.

Parameters

alpha:double: Scalar factor.

Returns:Quaternion

a scaled quaternion.

normalize	back to summary
public Quaternion normalize() Computes the normalized quaternion (the versor of the instance). The norm of the quaternion must not be zero. Returns:Quaternion a normalized quaternion. Exceptions ZeroException: if the norm of the quaternion is zero.

normalize

back to summary

public Quaternion normalize()

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

Returns:Quaternion

a normalized quaternion.

Exceptions

ZeroException:: if the norm of the quaternion is zero.

subtract back to summary

subtract	back to summary
public static Quaternion subtract(final Quaternion q1, final Quaternion q2) Subtracts two quaternions. Parameters q1:Quaternion First Quaternion. q2:Quaternion Second quaternion. Returns:Quaternion the difference between `q1` and `q2`.

public static Quaternion subtract(final Quaternion q1, final Quaternion q2)

Subtracts two quaternions.

Parameters

q1:Quaternion: First Quaternion.
q2:Quaternion: Second quaternion.

Returns:Quaternion

the difference between q1 and q2.

subtract back to summary

subtract	back to summary
public Quaternion subtract(final Quaternion q) Subtracts a quaternion from the instance. Parameters q:Quaternion Quaternion. Returns:Quaternion the difference between this instance and `q`.

public Quaternion subtract(final Quaternion q)

Subtracts a quaternion from the instance.

Parameters

q:Quaternion: Quaternion.

Returns:Quaternion

the difference between this instance and q.

toString back to summary

toString	back to summary
public String toString() Overrides java.lang.Object.toString. Doc from java.lang.Object.toString. Returns a string representation of the object. Satisfying this method's contract implies a non-`null` result must be returned. Returns:String a string representation of the object Annotations @Override

public String toString()

Overrides java.lang.Object.toString.

Doc from java.lang.Object.toString.

Returns a string representation of the object. Satisfying this method's contract implies a non-null result must be returned.

Returns:String

a string representation of the object

Annotations

@Override

public final Class Quaternion

Field Summary

Constructor Summary

Method Summary

Field Detail

Constructor Detail

Method Detail