Struct Quaternion

A structure encapsulating a four-dimensional vector (x,y,z,w), which is used to efficiently rotate an object about the (x,y,z) vector by the angle theta, where w = cos(theta/2).

Inherited Members

Object.Equals(Object, Object)

Object.ReferenceEquals(Object, Object)

Object.GetType()

Namespace: System.Numerics

Assembly: System.Numerics.dll

Syntax

public struct Quaternion

Constructors

Quaternion(Double, Double, Double, Double)

Constructs a Quaternion from the given components.

Declaration

public Quaternion(double x, double y, double z, double w)

Parameters

Type	Name	Description
Double	x	The X component of the Quaternion.
Double	y	The Y component of the Quaternion.
Double	z	The Z component of the Quaternion.
Double	w	The W component of the Quaternion.

Quaternion(Vector3, Double)

Constructs a Quaternion from the given vector and rotation parts.

Declaration

public Quaternion(Vector3 vectorPart, double scalarPart)

Parameters

Type	Name	Description
Vector3	vectorPart	The vector part of the Quaternion.
Double	scalarPart	The rotation part of the Quaternion.

Fields

W

Specifies the rotation component of the Quaternion.

Declaration

public double W

Field Value

Type	Description
Double

X

Specifies the X-value of the vector component of the Quaternion.

Declaration

public double X

Field Value

Type	Description
Double

Y

Specifies the Y-value of the vector component of the Quaternion.

Declaration

public double Y

Field Value

Type	Description
Double

Z

Specifies the Z-value of the vector component of the Quaternion.

Declaration

public double Z

Field Value

Type	Description
Double

Properties

Identity

Returns a Quaternion representing no rotation.

Declaration

public static readonly Quaternion Identity { get; }

Property Value

Type	Description
Quaternion

IsIdentity

Returns whether the Quaternion is the identity Quaternion.

Declaration

public readonly bool IsIdentity { get; }

Property Value

Type	Description
Boolean

Methods

Add(Quaternion, Quaternion)

Adds two Quaternions element-by-element.

Declaration

public static Quaternion Add(Quaternion value1, Quaternion value2)

Parameters

Type	Name	Description
Quaternion	value1	The first source Quaternion.
Quaternion	value2	The second source Quaternion.

Returns

Type	Description
Quaternion	The result of adding the Quaternions.

Concatenate(Quaternion, Quaternion)

Concatenates two Quaternions; the result represents the value1 rotation followed by the value2 rotation.

Declaration

public static Quaternion Concatenate(Quaternion value1, Quaternion value2)

Parameters

Type	Name	Description
Quaternion	value1	The first Quaternion rotation in the series.
Quaternion	value2	The second Quaternion rotation in the series.

Returns

Type	Description
Quaternion	A new Quaternion representing the concatenation of the value1 rotation followed by the value2 rotation.

Conjugate(Quaternion)

Creates the conjugate of a specified Quaternion.

Declaration

public static Quaternion Conjugate(Quaternion value)

Parameters

Type	Name	Description
Quaternion	value	The Quaternion of which to return the conjugate.

Returns

Type	Description
Quaternion	A new Quaternion that is the conjugate of the specified one.

CreateFromAxisAngle(Vector3, Double)

Creates a Quaternion from a vector and an angle to rotate about the vector.

Declaration

public static Quaternion CreateFromAxisAngle(Vector3 axis, double angle)

Parameters

Type	Name	Description
Vector3	axis	The vector to rotate around.
Double	angle	The angle, in radians, to rotate around the vector.

Returns

Type	Description
Quaternion	The created Quaternion.

CreateFromYawPitchRoll(Double, Double, Double)

Creates a new Quaternion from the given yaw, pitch, and roll, in radians.

Declaration

public static Quaternion CreateFromYawPitchRoll(double yaw, double pitch, double roll)

Parameters

Type	Name	Description
Double	yaw	The yaw angle, in radians, around the Y-axis.
Double	pitch	The pitch angle, in radians, around the X-axis.
Double	roll	The roll angle, in radians, around the Z-axis.

Returns

Type	Description
Quaternion

Divide(Quaternion, Quaternion)

Divides a Quaternion by another Quaternion.

Declaration

public static Quaternion Divide(Quaternion value1, Quaternion value2)

Parameters

Type	Name	Description
Quaternion	value1	The source Quaternion.
Quaternion	value2	The divisor.

Returns

Type	Description
Quaternion	The result of the division.

Dot(Quaternion, Quaternion)

Calculates the dot product of two Quaternions.

Declaration

public static double Dot(Quaternion quaternion1, Quaternion quaternion2)

Parameters

Type	Name	Description
Quaternion	quaternion1	The first source Quaternion.
Quaternion	quaternion2	The second source Quaternion.

Returns

Type	Description
Double	The dot product of the Quaternions.

Equals(Quaternion)

Returns a boolean indicating whether the given Quaternion is equal to this Quaternion instance.

Declaration

public bool Equals(Quaternion other)

Parameters

Type	Name	Description
Quaternion	other	The Quaternion to compare this instance to.

Returns

Type	Description
Boolean	True if the other Quaternion is equal to this instance; False otherwise.

Equals(Object)

Returns a boolean indicating whether the given Object is equal to this Quaternion instance.

Declaration

public override bool Equals(object obj)

Parameters

Type	Name	Description
Object	obj	The Object to compare against.

Returns

Type	Description
Boolean	True if the Object is equal to this Quaternion; False otherwise.

Overrides

ValueType.Equals(Object)

GetHashCode()

Returns the hash code for this instance.

Declaration

public override int GetHashCode()

Returns

Type	Description
Int32	The hash code.

Overrides

Object.GetHashCode()

Inverse(Quaternion)

Returns the inverse of a Quaternion.

Declaration

public static Quaternion Inverse(Quaternion value)

Parameters

Type	Name	Description
Quaternion	value	The source Quaternion.

Returns

Type	Description
Quaternion	The inverted Quaternion.

Length()

Calculates the length of the Quaternion.

Declaration

public double Length()

Returns

Type	Description
Double	The computed length of the Quaternion.

LengthSquared()

Calculates the length squared of the Quaternion. This operation is cheaper than Length().

Declaration

public double LengthSquared()

Returns

Type	Description
Double	The length squared of the Quaternion.

Lerp(Quaternion, Quaternion, Double)

Linearly interpolates between two quaternions.

Declaration

public static Quaternion Lerp(Quaternion quaternion1, Quaternion quaternion2, double amount)

Parameters

Type	Name	Description
Quaternion	quaternion1	The first source Quaternion.
Quaternion	quaternion2	The second source Quaternion.
Double	amount	The relative weight of the second source Quaternion in the interpolation.

Returns

Type	Description
Quaternion	The interpolated Quaternion.

Multiply(Quaternion, Double)

Multiplies a Quaternion by a scalar value.

Declaration

public static Quaternion Multiply(Quaternion value1, double value2)

Parameters

Type	Name	Description
Quaternion	value1	The source Quaternion.
Double	value2	The scalar value.

Returns

Type	Description
Quaternion	The result of the multiplication.

Multiply(Quaternion, Quaternion)

Multiplies two Quaternions together.

Declaration

public static Quaternion Multiply(Quaternion value1, Quaternion value2)

Parameters

Type	Name	Description
Quaternion	value1	The Quaternion on the left side of the multiplication.
Quaternion	value2	The Quaternion on the right side of the multiplication.

Returns

Type	Description
Quaternion	The result of the multiplication.

Negate(Quaternion)

Flips the sign of each component of the quaternion.

Declaration

public static Quaternion Negate(Quaternion value)

Parameters

Type	Name	Description
Quaternion	value	The source Quaternion.

Returns

Type	Description
Quaternion	The negated Quaternion.

Normalize(Quaternion)

Divides each component of the Quaternion by the length of the Quaternion.

Declaration

public static Quaternion Normalize(Quaternion value)

Parameters

Type	Name	Description
Quaternion	value	The source Quaternion.

Returns

Type	Description
Quaternion	The normalized Quaternion.

Slerp(Quaternion, Quaternion, Double)

Interpolates between two quaternions, using spherical linear interpolation.

Declaration

public static Quaternion Slerp(Quaternion quaternion1, Quaternion quaternion2, double amount)

Parameters

Type	Name	Description
Quaternion	quaternion1	The first source Quaternion.
Quaternion	quaternion2	The second source Quaternion.
Double	amount	The relative weight of the second source Quaternion in the interpolation.

Returns

Type	Description
Quaternion	The interpolated Quaternion.

Subtract(Quaternion, Quaternion)

Subtracts one Quaternion from another.

Declaration

public static Quaternion Subtract(Quaternion value1, Quaternion value2)

Parameters

Type	Name	Description
Quaternion	value1	The first source Quaternion.
Quaternion	value2	The second Quaternion, to be subtracted from the first.

Returns

Type	Description
Quaternion	The result of the subtraction.

ToString()

Returns a String representing this Quaternion instance.

Declaration

public override string ToString()

Returns

Type	Description
String	The string representation.

Overrides

Object.ToString()

Operators

Addition(Quaternion, Quaternion)

Adds two Quaternions element-by-element.

Declaration

public static Quaternion operator +(Quaternion value1, Quaternion value2)

Parameters

Type	Name	Description
Quaternion	value1	The first source Quaternion.
Quaternion	value2	The second source Quaternion.

Returns

Type	Description
Quaternion	The result of adding the Quaternions.

Division(Quaternion, Quaternion)

Divides a Quaternion by another Quaternion.

Declaration

public static Quaternion operator /(Quaternion value1, Quaternion value2)

Parameters

Type	Name	Description
Quaternion	value1	The source Quaternion.
Quaternion	value2	The divisor.

Returns

Type	Description
Quaternion	The result of the division.

Equality(Quaternion, Quaternion)

Returns a boolean indicating whether the two given Quaternions are equal.

Declaration

public static bool operator ==(Quaternion value1, Quaternion value2)

Parameters

Type	Name	Description
Quaternion	value1	The first Quaternion to compare.
Quaternion	value2	The second Quaternion to compare.

Returns

Type	Description
Boolean	True if the Quaternions are equal; False otherwise.

Inequality(Quaternion, Quaternion)

Returns a boolean indicating whether the two given Quaternions are not equal.

Declaration

public static bool operator !=(Quaternion value1, Quaternion value2)

Parameters

Type	Name	Description
Quaternion	value1	The first Quaternion to compare.
Quaternion	value2	The second Quaternion to compare.

Returns

Type	Description
Boolean	True if the Quaternions are not equal; False if they are equal.

Multiply(Quaternion, Double)

Multiplies a Quaternion by a scalar value.

Declaration

public static Quaternion operator *(Quaternion value1, double value2)

Parameters

Type	Name	Description
Quaternion	value1	The source Quaternion.
Double	value2	The scalar value.

Returns

Type	Description
Quaternion	The result of the multiplication.

Multiply(Quaternion, Quaternion)

Multiplies two Quaternions together.

Declaration

public static Quaternion operator *(Quaternion value1, Quaternion value2)

Parameters

Type	Name	Description
Quaternion	value1	The Quaternion on the left side of the multiplication.
Quaternion	value2	The Quaternion on the right side of the multiplication.

Returns

Type	Description
Quaternion	The result of the multiplication.

Subtraction(Quaternion, Quaternion)

Subtracts one Quaternion from another.

Declaration

public static Quaternion operator -(Quaternion value1, Quaternion value2)

Parameters

Type	Name	Description
Quaternion	value1	The first source Quaternion.
Quaternion	value2	The second Quaternion, to be subtracted from the first.

Returns

Type	Description
Quaternion	The result of the subtraction.

UnaryNegation(Quaternion)

Flips the sign of each component of the quaternion.

Declaration

public static Quaternion operator -(Quaternion value)

Parameters

Type	Name	Description
Quaternion	value	The source Quaternion.

Returns

Type	Description
Quaternion	The negated Quaternion.