Struct Quaternion

Structure defining quaternion number.

Implements

IEquatable<Quaternion>

IDotProduct<Quaternion, Double>

INorm<Quaternion>

IMetric<Quaternion>

IGroupAction<Quaternion, Double>

IGroupAction<Quaternion, Real>

IGroupAction<Quaternion, Complex>

Namespace: BRIDGES.Arithmetic.Numbers

Assembly: BRIDGES.dll

Syntax

public struct Quaternion : IDotProduct<Quaternion, double>, INorm<Quaternion>, IMetric<Quaternion>, IGroupAction<Quaternion, double>, IGroupAction<Quaternion, Real>, IGroupAction<Quaternion, Complex>

Constructors

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Quaternion(Quaternion)

Initialises a new instance of the Quaternion structure from another Quaternion number.

Declaration

public Quaternion(Quaternion quaternion)

Parameters

Type	Name	Description
Quaternion	quaternion	Quaternion number to deep copy.

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Quaternion(Double, Double, Double, Double)

Initialises a new instance of Quaternion structure by defining its real and imaginary components.

Declaration

public Quaternion(double r, double i, double j, double k)

Parameters

Type	Name	Description
Double	r	Value of the first component.
Double	i	Value of the second component.
Double	j	Value of the third component.
Double	k	Value of the fourth component.

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Quaternion(Double[])

Initialises a new instance of Quaternion structure by defining its components.

Declaration

public Quaternion(double[] components)

Parameters

Type	Name	Description
Double[]	components	Value of the components.

Properties

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I

Gets or sets the first component "i" of the vector part of this Quaternion number.

Declaration

public double I { get; set; }

Property Value

Type	Description
Double

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J

Gets or sets the second component "j" of the vector part of this Quaternion number.

Declaration

public double J { get; set; }

Property Value

Type	Description
Double

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K

Gets or sets the third component "k" of the vector part of this Quaternion number.

Declaration

public double K { get; set; }

Property Value

Type	Description
Double

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One

Gets a new instance of the Quaternion structure equal to the multiplicative neutral element : (1.0, 0.0, 0.0, 0.0).

Declaration

public static readonly Quaternion One { get; }

Property Value

Type	Description
Quaternion	The new Quaternion number equal to one.

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ScalarPart

Gets or sets the scalar part of this Quaternion number.

Declaration

public double ScalarPart { get; set; }

Property Value

Type	Description
Double

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VectorPart

Gets the vector part of this Quaternion number.

Declaration

public readonly double[] VectorPart { get; }

Property Value

Type	Description
Double[]

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Zero

Gets a new instance of the Quaternion structure equal to the additive neutral element : (0.0, 0.0, 0.0, 0.0).

Declaration

public static readonly Quaternion Zero { get; }

Property Value

Type	Description
Quaternion	The new Quaternion number equal to zero.

Methods

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Add(Complex, Quaternion)

Computes the left addition of a Complex number with a Quaternion number.

Declaration

public static Quaternion Add(Complex left, Quaternion right)

Parameters

Type	Name	Description
Complex	left	Complex number for the addition.
Quaternion	right	Quaternion number for the addition.

Returns

Type	Description
Quaternion	The new Quaternion number resulting from the addition.

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Add(Quaternion, Complex)

Computes the right addition of a Quaternion number with a Complex number.

Declaration

public static Quaternion Add(Quaternion left, Complex right)

Parameters

Type	Name	Description
Quaternion	left	Quaternion number for the addition.
Complex	right	Complex number for the addition.

Returns

Type	Description
Quaternion	The new Quaternion number resulting from the addition.

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Add(Quaternion, Quaternion)

Computes the addition of two Quaternion numbers.

Declaration

public static Quaternion Add(Quaternion left, Quaternion right)

Parameters

Type	Name	Description
Quaternion	left	Quaternion number for the addition.
Quaternion	right	Quaternion number for the addition.

Returns

Type	Description
Quaternion	The new Quaternion number resulting from the addition.

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Add(Quaternion, Real)

Computes the right addition of a Quaternion number with a Real number.

Declaration

public static Quaternion Add(Quaternion left, Real right)

Parameters

Type	Name	Description
Quaternion	left	Quaternion number for the addition.
Real	right	Real number for the addition.

Returns

Type	Description
Quaternion	The new Quaternion number resulting from the addition.

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Add(Real, Quaternion)

Computes the left addition of a Real number with a Quaternion number.

Declaration

public static Quaternion Add(Real left, Quaternion right)

Parameters

Type	Name	Description
Real	left	Real number for the addition.
Quaternion	right	Quaternion number for the addition.

Returns

Type	Description
Quaternion	The new Quaternion number resulting from the addition.

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Conjugate(Quaternion)

Gets the conjugate value of a Quaternion number.

Declaration

public static Quaternion Conjugate(Quaternion quaternion)

Parameters

Type	Name	Description
Quaternion	quaternion	Quaternion number from which the conjugate is computed.

Returns

Type	Description
Quaternion	The new Quaternion number, conjugate of the initial one.

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DistanceTo(Quaternion)

Computes the norm of this element.

Declaration

public double DistanceTo(Quaternion other)

Parameters

Type	Name	Description
Quaternion	other

Returns

Type	Description
Double	The value of the norm.

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Divide(Complex, Quaternion)

Computes the division of a Complex number with a Quaternion number.

Declaration

public static Quaternion Divide(Complex left, Quaternion right)

Parameters

Type	Name	Description
Complex	left	Complex number to divide.
Quaternion	right	Quaternion number to divide with.

Returns

Type	Description
Quaternion	The new Quaternion number resulting from the division.

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Divide(Quaternion, Complex)

Computes the division of a Quaternion number with a Complex number.

Declaration

public static Quaternion Divide(Quaternion left, Complex right)

Parameters

Type	Name	Description
Quaternion	left	Quaternion number to divide.
Complex	right	Complex number to divide with.

Returns

Type	Description
Quaternion	The new Quaternion number resulting from the division.

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Divide(Quaternion, Quaternion)

Computes the division of two Quaternion numbers.

Declaration

public static Quaternion Divide(Quaternion left, Quaternion right)

Parameters

Type	Name	Description
Quaternion	left	Quaternion number to divide.
Quaternion	right	Quaternion number to divide with.

Returns

Type	Description
Quaternion	The new Quaternion number resulting from the division.

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Divide(Quaternion, Real)

Computes the division of a Quaternion number with a Real number.

Declaration

public static Quaternion Divide(Quaternion left, Real right)

Parameters

Type	Name	Description
Quaternion	left	Quaternion number to divide.
Real	right	Real number to divide with.

Returns

Type	Description
Quaternion	The new Quaternion number resulting from the division.

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Divide(Quaternion, Double)

Computes the scalar division of a Quaternion number with a -precision real number.

Declaration

public static Quaternion Divide(Quaternion operand, double divisor)

Parameters

Type	Name	Description
Quaternion	operand	Quaternion number to divide.
Double	divisor	-precision real number to divide with.

Returns

Type	Description
Quaternion	The new Quaternion number resulting from the scalar division.

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Divide(Real, Quaternion)

Computes the division of a Real number with a Quaternion number.

Declaration

public static Quaternion Divide(Real left, Quaternion right)

Parameters

Type	Name	Description
Real	left	Real number to divide.
Quaternion	right	Quaternion number to divide with.

Returns

Type	Description
Quaternion	The new Quaternion number resulting from the division.

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DotProduct(Quaternion)

Computes the euclidean dot product of this Quaternion number with another Quaternion number.

Declaration

public double DotProduct(Quaternion other)

Parameters

Type	Name	Description
Quaternion	other	Right Quaternion number for the dot product.

Returns

Type	Description
Double	The value of the dot product of the two elements.

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Equals(Quaternion)

Structure defining quaternion number.

Declaration

public bool Equals(Quaternion other)

Parameters

Type	Name	Description
Quaternion	other

Returns

Type	Description
Boolean

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Equals(Object)

Structure defining quaternion number.

Declaration

public override bool Equals(object obj)

Parameters

Type	Name	Description
Object	obj

Returns

Type	Description
Boolean

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GetHashCode()

Structure defining quaternion number.

Declaration

public override int GetHashCode()

Returns

Type	Description
Int32

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Inverse(Quaternion)

Computes the inverse of this Quaternion number.

Declaration

public static Quaternion Inverse(Quaternion operand)

Parameters

Type	Name	Description
Quaternion	operand	Quaternion from which the inverse is computed.

Returns

Type	Description
Quaternion	The new Quaternion number, inverse of the initial one.

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Multiply(Complex, Quaternion)

Computes the left multiplication of a Complex number with a Quaternion number.

Declaration

public static Quaternion Multiply(Complex left, Quaternion right)

Parameters

Type	Name	Description
Complex	left	Complex number for the multiplicaion.
Quaternion	right	Quaternion number for the multiplicaion.

Returns

Type	Description
Quaternion	The new Quaternion number resulting from the multiplication.

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Multiply(Quaternion, Complex)

Computes the right multiplication of a Quaternion number with a Complex number.

Declaration

public static Quaternion Multiply(Quaternion left, Complex right)

Parameters

Type	Name	Description
Quaternion	left	Quaternion number for the multiplicaion.
Complex	right	Complex number for the multiplicaion.

Returns

Type	Description
Quaternion	The new Quaternion number resulting from the multiplication.

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Multiply(Quaternion, Quaternion)

Computes the multiplication of two Quaternion numbers.

Declaration

public static Quaternion Multiply(Quaternion left, Quaternion right)

Parameters

Type	Name	Description
Quaternion	left	Quaternion number for the multiplication.
Quaternion	right	Quaternion number for the multiplication.

Returns

Type	Description
Quaternion	The new Quaternion number resulting from the multiplication.

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Multiply(Quaternion, Real)

Computes the right multiplication of a Quaternion number with a Real number.

Declaration

public static Quaternion Multiply(Quaternion left, Real right)

Parameters

Type	Name	Description
Quaternion	left	Quaternion number for the multiplicaion.
Real	right	Real number for the multiplicaion.

Returns

Type	Description
Quaternion	The new Quaternion number resulting from the multiplication.

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Multiply(Quaternion, Double)

Computes the left scalar multiplication of a Quaternion number with a -precision real number.

Declaration

public static Quaternion Multiply(Quaternion operand, double factor)

Parameters

Type	Name	Description
Quaternion	operand	Quaternion number to multiply.
Double	factor	-precision real number.

Returns

Type	Description
Quaternion	The new Quaternion number resulting from the scalar multiplication.

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Multiply(Real, Quaternion)

Computes the left multiplication of a Real number with a Quaternion number.

Declaration

public static Quaternion Multiply(Real left, Quaternion right)

Parameters

Type	Name	Description
Real	left	Real number for the multiplicaion.
Quaternion	right	Quaternion number for the multiplicaion.

Returns

Type	Description
Quaternion	The new Quaternion number resulting from the multiplication.

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Multiply(Double, Quaternion)

Computes the right scalar multiplication of a Quaternion number with a -precision real number.

Declaration

public static Quaternion Multiply(double factor, Quaternion operand)

Parameters

Type	Name	Description
Double	factor	-precision real number.
Quaternion	operand	Quaternion number to multiply.

Returns

Type	Description
Quaternion	The new Quaternion number resulting from the scalar multiplication.

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Norm()

Computes the euclidean norm of this Quaternion number.

Declaration

public double Norm()

Returns

Type	Description
Double	The value of the norm.

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Opposite(Quaternion)

Computes the opposite of the given Quaternion number.

Declaration

public static Quaternion Opposite(Quaternion operand)

Parameters

Type	Name	Description
Quaternion	operand	Quaternion number from which the opposite is computed.

Returns

Type	Description
Quaternion	The new Quaternion number, opposite of the initial one.

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Subtract(Complex, Quaternion)

Computes the subtraction of a Complex number with a Quaternion number.

Declaration

public static Quaternion Subtract(Complex left, Quaternion right)

Parameters

Type	Name	Description
Complex	left	Complex number to subtract.
Quaternion	right	Quaternion number to subtract with.

Returns

Type	Description
Quaternion	The new Quaternion number resulting from the subtraction.

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Subtract(Quaternion, Complex)

Computes the subtraction of a Quaternion number with a Complex number.

Declaration

public static Quaternion Subtract(Quaternion left, Complex right)

Parameters

Type	Name	Description
Quaternion	left	Quaternion number to subtract.
Complex	right	Complex number to subtract with.

Returns

Type	Description
Quaternion	The new Quaternion number resulting from the subtraction.

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Subtract(Quaternion, Quaternion)

Computes the subtraction of two Quaternion numbers.

Declaration

public static Quaternion Subtract(Quaternion left, Quaternion right)

Parameters

Type	Name	Description
Quaternion	left	Quaternion number to subtract.
Quaternion	right	Quaternion number to subtract with.

Returns

Type	Description
Quaternion	The new Quaternion number resulting from the subtraction.

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Subtract(Quaternion, Real)

Computes the subtraction of a Quaternion number with a Real number.

Declaration

public static Quaternion Subtract(Quaternion left, Real right)

Parameters

Type	Name	Description
Quaternion	left	Quaternion number to subtract.
Real	right	Real number to subtract with.

Returns

Type	Description
Quaternion	The new Quaternion number resulting from the subtraction.

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Subtract(Real, Quaternion)

Computes the subtraction of a Real number with a Quaternion number.

Declaration

public static Quaternion Subtract(Real left, Quaternion right)

Parameters

Type	Name	Description
Real	left	Real number to subtract.
Quaternion	right	Quaternion number to subtract with.

Returns

Type	Description
Quaternion	The new Quaternion number resulting from the subtraction.

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ToString()

Structure defining quaternion number.

Declaration

public override string ToString()

Returns

Type	Description
String

Operators

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Addition(Complex, Quaternion)

Computes the left addition of a Complex number with a Quaternion number.

Declaration

public static Quaternion operator +(Complex left, Quaternion right)

Parameters

Type	Name	Description
Complex	left	Complex number for the addition.
Quaternion	right	Quaternion number for the addition.

Returns

Type	Description
Quaternion	The new Quaternion number resulting from the addition.

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Addition(Quaternion, Complex)

Computes the right addition of a Quaternion number with a Complex number.

Declaration

public static Quaternion operator +(Quaternion left, Complex right)

Parameters

Type	Name	Description
Quaternion	left	Quaternion number for the addition.
Complex	right	Complex number for the addition.

Returns

Type	Description
Quaternion	The new Quaternion number resulting from the addition.

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Addition(Quaternion, Quaternion)

Computes the addition of two Quaternion numbers.

Declaration

public static Quaternion operator +(Quaternion left, Quaternion right)

Parameters

Type	Name	Description
Quaternion	left	Quaternion number for the addition.
Quaternion	right	Quaternion number for the addition.

Returns

Type	Description
Quaternion	The new Quaternion number resulting from the addition.

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Addition(Quaternion, Real)

Computes the right addition of a Quaternion number with a Real number.

Declaration

public static Quaternion operator +(Quaternion left, Real right)

Parameters

Type	Name	Description
Quaternion	left	Quaternion number for the addition.
Real	right	Real number for the addition.

Returns

Type	Description
Quaternion	The new Quaternion number resulting from the addition.

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Addition(Quaternion, Double)

Computes the right addition of a Quaternion number with a -precision real number.

Declaration

public static Quaternion operator +(Quaternion left, double right)

Parameters

Type	Name	Description
Quaternion	left	Quaternion number for the addition.
Double	right	-precision real number for the addition.

Returns

Type	Description
Quaternion	The new Quaternion number resulting from the addition.

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Addition(Real, Quaternion)

Computes the left addition of a Real number with a Quaternion number.

Declaration

public static Quaternion operator +(Real left, Quaternion right)

Parameters

Type	Name	Description
Real	left	Real number for the addition.
Quaternion	right	Quaternion number for the addition.

Returns

Type	Description
Quaternion	The new Quaternion number resulting from the addition.

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Addition(Double, Quaternion)

Computes the left addition of a -precision real number with a Quaternion number.

Declaration

public static Quaternion operator +(double left, Quaternion right)

Parameters

Type	Name	Description
Double	left	-precision real number for the addition.
Quaternion	right	Quaternion number for the addition.

Returns

Type	Description
Quaternion	The new Quaternion number resulting from the addition.

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Division(Complex, Quaternion)

Computes the division of a Complex number with a Quaternion number.

Declaration

public static Quaternion operator /(Complex left, Quaternion right)

Parameters

Type	Name	Description
Complex	left	Complex number to divide.
Quaternion	right	Quaternion number to divide with.

Returns

Type	Description
Quaternion	The new Quaternion number resulting from the division.

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Division(Quaternion, Complex)

Computes the division of a Quaternion number with a Complex number.

Declaration

public static Quaternion operator /(Quaternion left, Complex right)

Parameters

Type	Name	Description
Quaternion	left	Quaternion number to divide.
Complex	right	Complex number to divide with.

Returns

Type	Description
Quaternion	The new Quaternion number resulting from the division.

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Division(Quaternion, Quaternion)

Computes the division of two Quaternion numbers.

Declaration

public static Quaternion operator /(Quaternion left, Quaternion right)

Parameters

Type	Name	Description
Quaternion	left	Quaternion number to divide.
Quaternion	right	Quaternion number to divide with.

Returns

Type	Description
Quaternion	The new Quaternion number resulting from the division.

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Division(Quaternion, Real)

Computes the division of a Quaternion number with a Real number.

Declaration

public static Quaternion operator /(Quaternion left, Real right)

Parameters

Type	Name	Description
Quaternion	left	Quaternion number to divide.
Real	right	Real number to divide with.

Returns

Type	Description
Quaternion	The new Quaternion number resulting from the division.

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Division(Quaternion, Double)

Computes the division of a Quaternion number with a -precision real number.

Declaration

public static Quaternion operator /(Quaternion left, double right)

Parameters

Type	Name	Description
Quaternion	left	Quaternion number to divide.
Double	right	-precision real number to divide with.

Returns

Type	Description
Quaternion	The new Quaternion number resulting from the division.

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Division(Real, Quaternion)

Computes the division of a Real number with a Quaternion number.

Declaration

public static Quaternion operator /(Real left, Quaternion right)

Parameters

Type	Name	Description
Real	left	Real number to divide.
Quaternion	right	Quaternion number to divide with.

Returns

Type	Description
Quaternion	The new Quaternion number resulting from the division.

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Division(Double, Quaternion)

Computes the division of a -precision real number with a Quaternion number.

Declaration

public static Quaternion operator /(double left, Quaternion right)

Parameters

Type	Name	Description
Double	left	-precision real number to divide.
Quaternion	right	Quaternion number to divide with.

Returns

Type	Description
Quaternion	The new Quaternion number resulting from the division.

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Explicit(Complex to Quaternion)

Converts a Complex number into a Quaternion number.

Declaration

public static explicit operator Quaternion(Complex complex)

Parameters

Type	Name	Description
Complex	complex	Complex number to convert.

Returns

Type	Description
Quaternion	The new Quaternion number resulting from the conversion.

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Explicit(Real to Quaternion)

Converts a Real number into a Quaternion number.

Declaration

public static explicit operator Quaternion(Real real)

Parameters

Type	Name	Description
Real	real	Real number to convert.

Returns

Type	Description
Quaternion	The new Quaternion number resulting from the conversion.

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Explicit(Double to Quaternion)

Converts a -precision real number into a Quaternion number.

Declaration

public static explicit operator Quaternion(double number)

Parameters

Type	Name	Description
Double	number	-precision real number to convert.

Returns

Type	Description
Quaternion	The new Quaternion number resulting from the conversion.

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Explicit(ValueTuple<Double, Double, Double, Double> to Quaternion)

Converts a into a Quaternion number.

Declaration

public static explicit operator Quaternion(ValueTuple<double, double, double, double> quadruple)

Parameters

Type	Name	Description
ValueTuple<Double, Double, Double, Double>	quadruple	to convert.

Returns

Type	Description
Quaternion	The new Quaternion number resulting from the conversion.

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Multiply(Complex, Quaternion)

Computes the left multiplication of a Complex number with a Quaternion number.

Declaration

public static Quaternion operator *(Complex left, Quaternion right)

Parameters

Type	Name	Description
Complex	left	Complex number for the multiplicaion.
Quaternion	right	Quaternion number for the multiplicaion.

Returns

Type	Description
Quaternion	The new Quaternion number resulting from the multiplication.

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Multiply(Quaternion, Complex)

Computes the right multiplication of a Quaternion number with a Complex number.

Declaration

public static Quaternion operator *(Quaternion left, Complex right)

Parameters

Type	Name	Description
Quaternion	left	Quaternion number for the multiplicaion.
Complex	right	Complex number for the multiplicaion.

Returns

Type	Description
Quaternion	The new Quaternion number resulting from the multiplication.

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Multiply(Quaternion, Quaternion)

Computes the multiplication of two Quaternion numbers.

Declaration

public static Quaternion operator *(Quaternion left, Quaternion right)

Parameters

Type	Name	Description
Quaternion	left	Quaternion number for the multiplication.
Quaternion	right	Quaternion number for the multiplication.

Returns

Type	Description
Quaternion	The new Quaternion number resulting from the multiplication.

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Multiply(Quaternion, Real)

Computes the right multiplication of a Quaternion number with a Real number.

Declaration

public static Quaternion operator *(Quaternion left, Real right)

Parameters

Type	Name	Description
Quaternion	left	Quaternion number for the multiplicaion.
Real	right	Real number for the multiplicaion.

Returns

Type	Description
Quaternion	The new Quaternion number resulting from the multiplication.

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Multiply(Quaternion, Double)

Computes the right multiplication of a Quaternion number with a -precision real number.

Declaration

public static Quaternion operator *(Quaternion left, double right)

Parameters

Type	Name	Description
Quaternion	left	Quaternion number for the multiplicaion.
Double	right	-precision real number for the multiplicaion.

Returns

Type	Description
Quaternion	The new Quaternion number resulting from the multiplication.

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Multiply(Real, Quaternion)

Computes the left multiplication of a Real number with a Quaternion number.

Declaration

public static Quaternion operator *(Real left, Quaternion right)

Parameters

Type	Name	Description
Real	left	Real number for the multiplicaion.
Quaternion	right	Quaternion number for the multiplicaion.

Returns

Type	Description
Quaternion	The new Quaternion number resulting from the multiplication.

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Multiply(Double, Quaternion)

Computes the left multiplication of a -precision real number with a Quaternion number.

Declaration

public static Quaternion operator *(double left, Quaternion right)

Parameters

Type	Name	Description
Double	left	-precision real number for the multiplicaion.
Quaternion	right	Quaternion number for the multiplicaion.

Returns

Type	Description
Quaternion	The new Quaternion number resulting from the multiplication.

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Subtraction(Complex, Quaternion)

Computes the subtraction of a Complex number with a Quaternion number.

Declaration

public static Quaternion operator -(Complex left, Quaternion right)

Parameters

Type	Name	Description
Complex	left	Complex number to subtract.
Quaternion	right	Quaternion number to subtract with.

Returns

Type	Description
Quaternion	The new Quaternion number resulting from the subtraction.

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Subtraction(Quaternion, Complex)

Computes the subtraction of a Quaternion number with a Complex number.

Declaration

public static Quaternion operator -(Quaternion left, Complex right)

Parameters

Type	Name	Description
Quaternion	left	Quaternion number to subtract.
Complex	right	Complex number to subtract with.

Returns

Type	Description
Quaternion	The new Quaternion number resulting from the subtraction.

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Subtraction(Quaternion, Quaternion)

Computes the subtraction of two Quaternion numbers.

Declaration

public static Quaternion operator -(Quaternion left, Quaternion right)

Parameters

Type	Name	Description
Quaternion	left	Quaternion number to subtract.
Quaternion	right	Quaternion number to subtract with.

Returns

Type	Description
Quaternion	The new Quaternion number resulting from the subtraction.

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Subtraction(Quaternion, Real)

Computes the subtraction of a Quaternion number with a Real number.

Declaration

public static Quaternion operator -(Quaternion left, Real right)

Parameters

Type	Name	Description
Quaternion	left	Quaternion number to subtract.
Real	right	Real number to subtract with.

Returns

Type	Description
Quaternion	The new Quaternion number resulting from the subtraction.

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Subtraction(Quaternion, Double)

Computes the subtraction of a Quaternion number with a -precision real number.

Declaration

public static Quaternion operator -(Quaternion left, double right)

Parameters

Type	Name	Description
Quaternion	left	Quaternion number to subtract.
Double	right	-precision real number to subtract with.

Returns

Type	Description
Quaternion	The new Quaternion number resulting from the subtraction.

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Subtraction(Real, Quaternion)

Computes the subtraction of a Real number with a Quaternion number.

Declaration

public static Quaternion operator -(Real left, Quaternion right)

Parameters

Type	Name	Description
Real	left	Real number to subtract.
Quaternion	right	Quaternion number to subtract with.

Returns

Type	Description
Quaternion	The new Quaternion number resulting from the subtraction.

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Subtraction(Double, Quaternion)

Computes the subtraction of a Real number with a -precision real number.

Declaration

public static Quaternion operator -(double left, Quaternion right)

Parameters

Type	Name	Description
Double	left	-precision real number to subtract.
Quaternion	right	Quaternion number to subtract with.

Returns

Type	Description
Quaternion	The new Quaternion number resulting from the subtraction.

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UnaryNegation(Quaternion)

Computes the opposite of the given Quaternion number.

Declaration

public static Quaternion operator -(Quaternion operand)

Parameters

Type	Name	Description
Quaternion	operand	Quaternion number from which the opposite is computed.

Returns

Type	Description
Quaternion	The new Quaternion number, opposite of the initial one.

Explicit Interface Implementations

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IGroupAction<Quaternion, Complex>.Divide(Complex)

Computes the right scalar division of the current element.

Declaration

Quaternion IGroupAction<Quaternion, Complex>.Divide(Complex divisor)

Parameters

Type	Name	Description
Complex	divisor

Returns

Type	Description
Quaternion	The new element resulting from the scalar dividion.

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IGroupAction<Quaternion, Complex>.Multiply(Complex)

Computes the right scalar multiplication of the current element.

Declaration

Quaternion IGroupAction<Quaternion, Complex>.Multiply(Complex factor)

Parameters

Type	Name	Description
Complex	factor

Returns

Type	Description
Quaternion	The new element resulting from the scalar multiplication.

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IGroupAction<Quaternion, Real>.Divide(Real)

Computes the right scalar division of the current element.

Declaration

Quaternion IGroupAction<Quaternion, Real>.Divide(Real divisor)

Parameters

Type	Name	Description
Real	divisor

Returns

Type	Description
Quaternion	The new element resulting from the scalar dividion.

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IGroupAction<Quaternion, Real>.Multiply(Real)

Computes the right scalar multiplication of the current element.

Declaration

Quaternion IGroupAction<Quaternion, Real>.Multiply(Real factor)

Parameters

Type	Name	Description
Real	factor

Returns

Type	Description
Quaternion	The new element resulting from the scalar multiplication.

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IGroupAction<Quaternion, Double>.Divide(Double)

Computes the right scalar division of the current element.

Declaration

Quaternion IGroupAction<Quaternion, double>.Divide(double divisor)

Parameters

Type	Name	Description
Double	divisor

Returns

Type	Description
Quaternion	The new element resulting from the scalar dividion.

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IGroupAction<Quaternion, Double>.Multiply(Double)

Computes the right scalar multiplication of the current element.

Declaration

Quaternion IGroupAction<Quaternion, double>.Multiply(double factor)

Parameters

Type	Name	Description
Double	factor

Returns

Type	Description
Quaternion	The new element resulting from the scalar multiplication.

Implements

IEquatable<>

IDotProduct<TSelf, TValue>

INorm<TSelf>

IMetric<TSelf>

IGroupAction<TSelf, TValue>