Class Quaternion
- java.lang.Object
-
- org.apache.commons.numbers.quaternion.Quaternion
-
- All Implemented Interfaces:
Serializable
public final class Quaternion extends Object implements Serializable
This class implements quaternions (Hamilton's hypercomplex numbers).Wherever quaternion components are listed in sequence, this class follows the convention of placing the scalar (
w) component first, e.g. [w, x, y, z]. Other libraries and textbooks may place thewcomponent last.Instances of this class are guaranteed to be immutable.
- See Also:
- Serialized Form
-
-
Field Summary
Fields Modifier and Type Field Description static QuaternionIi.static QuaternionJj.static QuaternionKk.static QuaternionONEIdentity quaternion.static QuaternionZEROZero quaternion.
-
Method Summary
All Methods Static Methods Instance Methods Concrete Methods Modifier and Type Method Description Quaternionadd(Quaternion q)Computes the sum of the instance and another quaternion.static Quaternionadd(Quaternion q1, Quaternion q2)Computes the sum of two quaternions.Quaternionconjugate()Returns the conjugate of this quaternion number.Quaterniondivide(double alpha)Divides the instance by a scalar.doubledot(Quaternion q)Computes the dot-product of the instance by a quaternion.static doubledot(Quaternion q1, Quaternion q2)Computes the dot-product of two quaternions.booleanequals(Object other)booleanequals(Quaternion q, double eps)Checks whether this instance is equal to another quaternion within a given tolerance.doublegetScalarPart()Gets the scalar part of the quaternion.double[]getVectorPart()Gets the three components of the vector part of the quaternion.doublegetW()Gets the first component of the quaternion (scalar part).doublegetX()Gets the second component of the quaternion (first component of the vector part).doublegetY()Gets the third component of the quaternion (second component of the vector part).doublegetZ()Gets the fourth component of the quaternion (third component of the vector part).inthashCode()Quaternioninverse()Returns the inverse of this instance.booleanisPure(double eps)Checks whether the instance is a pure quaternion within a given tolerance.booleanisUnit(double eps)Checks whether the instance is a unit quaternion within a given tolerance.Quaternionmultiply(double alpha)Multiplies the instance by a scalar.Quaternionmultiply(Quaternion q)Returns the Hamilton product of the instance by a quaternion.static Quaternionmultiply(Quaternion q1, Quaternion q2)Returns the Hamilton product of two quaternions.Quaternionnegate()Returns the opposite of this instance.doublenorm()Computes the norm of the quaternion.Quaternionnormalize()Computes the normalized quaternion (the versor of the instance).doublenormSq()Computes the square of the norm of the quaternion.static Quaternionof(double[] v)Builds a pure quaternion from a vector (assuming that the scalar part is zero).static Quaternionof(double scalar, double[] v)Builds a quaternion from scalar and vector parts.static Quaternionof(double w, double x, double y, double z)Builds a quaternion from its components.static Quaternionparse(String s)Parses a string that would be produced bytoString()and instantiates the corresponding object.QuaternionpositivePolarForm()Returns the polar form of the quaternion.Quaternionsubtract(Quaternion q)Subtracts a quaternion from the instance.static Quaternionsubtract(Quaternion q1, Quaternion q2)Subtracts two quaternions.StringtoString()
-
-
-
Field Detail
-
ZERO
public static final Quaternion ZERO
Zero quaternion.
-
ONE
public static final Quaternion ONE
Identity quaternion.
-
I
public static final Quaternion I
i.
-
J
public static final Quaternion J
j.
-
K
public static final Quaternion K
k.
-
-
Method Detail
-
of
public static Quaternion of(double w, double x, double y, double z)
Builds a quaternion from its components.- Parameters:
w- Scalar component.x- First vector component.y- Second vector component.z- Third vector component.- Returns:
- a quaternion instance.
-
of
public static Quaternion of(double scalar, double[] v)
Builds a quaternion from scalar and vector parts.- Parameters:
scalar- Scalar part of the quaternion.v- Components of the vector part of the quaternion.- Returns:
- a quaternion instance.
- Throws:
IllegalArgumentException- if the array length is not 3.
-
of
public static Quaternion of(double[] v)
Builds a pure quaternion from a vector (assuming that the scalar part is zero).- Parameters:
v- Components of the vector part of the pure quaternion.- Returns:
- a quaternion instance.
-
conjugate
public Quaternion conjugate()
Returns the conjugate of this quaternion number. The conjugate ofa + bi + cj + dkisa - bi -cj -dk.- Returns:
- the conjugate of this quaternion object.
-
multiply
public static Quaternion multiply(Quaternion q1, Quaternion q2)
Returns the Hamilton product of two quaternions.- Parameters:
q1- First quaternion.q2- Second quaternion.- Returns:
- the product
q1andq2, in that order.
-
multiply
public Quaternion multiply(Quaternion q)
Returns the Hamilton product of the instance by a quaternion.- Parameters:
q- Quaternion.- Returns:
- the product of this instance with
q, in that order.
-
add
public static Quaternion add(Quaternion q1, Quaternion q2)
Computes the sum of two quaternions.- Parameters:
q1- Quaternion.q2- Quaternion.- Returns:
- the sum of
q1andq2.
-
add
public Quaternion add(Quaternion q)
Computes the sum of the instance and another quaternion.- Parameters:
q- Quaternion.- Returns:
- the sum of this instance and
q.
-
subtract
public static Quaternion subtract(Quaternion q1, Quaternion q2)
Subtracts two quaternions.- Parameters:
q1- First Quaternion.q2- Second quaternion.- Returns:
- the difference between
q1andq2.
-
subtract
public Quaternion subtract(Quaternion q)
Subtracts a quaternion from the instance.- Parameters:
q- Quaternion.- Returns:
- the difference between this instance and
q.
-
dot
public static double dot(Quaternion q1, Quaternion q2)
Computes the dot-product of two quaternions.- Parameters:
q1- Quaternion.q2- Quaternion.- Returns:
- the dot product of
q1andq2.
-
dot
public double dot(Quaternion q)
Computes the dot-product of the instance by a quaternion.- Parameters:
q- Quaternion.- Returns:
- the dot product of this instance and
q.
-
norm
public double norm()
Computes the norm of the quaternion.- Returns:
- the norm.
-
normSq
public double normSq()
Computes the square of the norm of the quaternion.- Returns:
- the square of the norm.
-
normalize
public Quaternion normalize()
Computes the normalized quaternion (the versor of the instance). The norm of the quaternion must not be near zero.- Returns:
- a normalized quaternion.
- Throws:
IllegalStateException- if the norm of the quaternion is NaN, infinite, or near zero.
-
equals
public boolean equals(Quaternion q, double eps)
Checks whether this instance is equal to another quaternion within a given tolerance.- Parameters:
q- Quaternion with which to compare the current quaternion.eps- Tolerance.- Returns:
trueif the each of the components are equal within the allowed absolute error.
-
isUnit
public boolean isUnit(double eps)
Checks whether the instance is a unit quaternion within a given tolerance.- Parameters:
eps- Tolerance (absolute error).- Returns:
trueif the norm is 1 within the given tolerance,falseotherwise
-
isPure
public boolean isPure(double eps)
Checks whether the instance is a pure quaternion within a given tolerance.- Parameters:
eps- Tolerance (absolute error).- Returns:
trueif the scalar part of the quaternion is zero.
-
positivePolarForm
public Quaternion positivePolarForm()
Returns the polar form of the quaternion.- Returns:
- the unit quaternion with positive scalar part.
-
negate
public Quaternion negate()
Returns the opposite of this instance.- Returns:
- the quaternion for which all components have an opposite sign to this one.
-
inverse
public Quaternion inverse()
Returns the inverse of this instance. The norm of the quaternion must not be zero.- Returns:
- the inverse.
- Throws:
IllegalStateException- if the norm (squared) of the quaternion is NaN, infinite, or near zero.
-
getW
public double getW()
Gets the first component of the quaternion (scalar part).- Returns:
- the scalar part.
-
getX
public double getX()
Gets the second component of the quaternion (first component of the vector part).- Returns:
- the first component of the vector part.
-
getY
public double getY()
Gets the third component of the quaternion (second component of the vector part).- Returns:
- the second component of the vector part.
-
getZ
public double getZ()
Gets the fourth component of the quaternion (third component of the vector part).- Returns:
- the third component of the vector part.
-
getScalarPart
public double getScalarPart()
Gets the scalar part of the quaternion.- Returns:
- the scalar part.
- See Also:
getW()
-
getVectorPart
public double[] getVectorPart()
Gets the three components of the vector part of the quaternion.
-
multiply
public Quaternion multiply(double alpha)
Multiplies the instance by a scalar.- Parameters:
alpha- Scalar factor.- Returns:
- a scaled quaternion.
-
divide
public Quaternion divide(double alpha)
Divides the instance by a scalar.- Parameters:
alpha- Scalar factor.- Returns:
- a scaled quaternion.
-
parse
public static Quaternion parse(String s)
Parses a string that would be produced bytoString()and instantiates the corresponding object.- Parameters:
s- String representation.- Returns:
- an instance.
- Throws:
NumberFormatException- if the string does not conform to the specification.
-
-