Class Quaternion

Defines 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).

Inheritance

System.Object

Quaternion

Namespace: VRageMath

Assembly: VRage.Math.dll

Syntax

public sealed class Quaternion : ValueType, IEquatable<Quaternion>

Constructors

Quaternion(Single, Single, Single, Single)

Initializes a new instance of Quaternion.

Declaration

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

Parameters

Type	Name	Description
System.Single	x	The x-value of the quaternion.
System.Single	y	The y-value of the quaternion.
System.Single	z	The z-value of the quaternion.
System.Single	w	The w-value of the quaternion.

Quaternion(Vector3, Single)

Initializes a new instance of Quaternion.

Declaration

public Quaternion(Vector3 vectorPart, float scalarPart)

Parameters

Type	Name	Description
Vector3	vectorPart	The vector component of the quaternion.
System.Single	scalarPart	The rotation component of the quaternion.

Fields

Identity

Declaration

public static Quaternion Identity

Field Value

Type	Description
Quaternion

W

Specifies the rotation component of the quaternion.

Declaration

public float W

Field Value

Type	Description
System.Single

X

Specifies the x-value of the vector component of the quaternion.

Declaration

public float X

Field Value

Type	Description
System.Single

Y

Specifies the y-value of the vector component of the quaternion.

Declaration

public float Y

Field Value

Type	Description
System.Single

Z

Specifies the z-value of the vector component of the quaternion.

Declaration

public float Z

Field Value

Type	Description
System.Single

Zero

Declaration

public static Quaternion Zero

Field Value

Type	Description
Quaternion

Properties

Forward

Declaration

public Vector3 Forward { get; }

Property Value

Type	Description
Vector3

Right

Declaration

public Vector3 Right { get; }

Property Value

Type	Description
Vector3

Up

Declaration

public Vector3 Up { get; }

Property Value

Type	Description
Vector3

Methods

Add(Quaternion, Quaternion)

Adds two Quaternions.

Declaration

public static Quaternion Add(Quaternion quaternion1, Quaternion quaternion2)

Parameters

Type	Name	Description
Quaternion	quaternion1	Quaternion to add.
Quaternion	quaternion2	Quaternion to add.

Returns

Type	Description
Quaternion

Add(ref Quaternion, ref Quaternion, out Quaternion)

Adds two Quaternions.

Declaration

public static void Add(ref Quaternion quaternion1, ref Quaternion quaternion2, out Quaternion result)

Parameters

Type	Name	Description
Quaternion	quaternion1	Quaternion to add.
Quaternion	quaternion2	Quaternion to add.
Quaternion	result	[OutAttribute] 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

Concatenate(ref Quaternion, ref Quaternion, out Quaternion)

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

Declaration

public static void Concatenate(ref Quaternion value1, ref Quaternion value2, out Quaternion result)

Parameters

Type	Name	Description
Quaternion	value1	The first Quaternion rotation in the series.
Quaternion	value2	The second Quaternion rotation in the series.
Quaternion	result	[OutAttribute] The Quaternion rotation representing the concatenation of value1 followed by value2.

Conjugate()

Transforms this Quaternion into its conjugate.

Declaration

public void Conjugate()

Conjugate(Quaternion)

Returns 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

Conjugate(ref Quaternion, out Quaternion)

Returns the conjugate of a specified Quaternion.

Declaration

public static void Conjugate(ref Quaternion value, out Quaternion result)

Parameters

Type	Name	Description
Quaternion	value	The Quaternion of which to return the conjugate.
Quaternion	result	[OutAttribute] An existing Quaternion filled in to be the conjugate of the specified one.

CreateFromAxisAngle(Vector3, Single)

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

Declaration

public static Quaternion CreateFromAxisAngle(Vector3 axis, float angle)

Parameters

Type	Name	Description
Vector3	axis	The vector to rotate around.
System.Single	angle	The angle to rotate around the vector.

Returns

Type	Description
Quaternion

CreateFromAxisAngle(ref Vector3, Single, out Quaternion)

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

Declaration

public static void CreateFromAxisAngle(ref Vector3 axis, float angle, out Quaternion result)

Parameters

Type	Name	Description
Vector3	axis	The vector to rotate around.
System.Single	angle	The angle to rotate around the vector.
Quaternion	result	[OutAttribute] The created Quaternion.

CreateFromForwardUp(Vector3, Vector3)

Works for normalized vectors only

Declaration

public static Quaternion CreateFromForwardUp(Vector3 forward, Vector3 up)

Parameters

Type	Name	Description
Vector3	forward
Vector3	up

Returns

Type	Description
Quaternion

CreateFromRotationMatrix(Matrix)

Creates a Quaternion from a rotation Matrix.

Declaration

public static Quaternion CreateFromRotationMatrix(Matrix matrix)

Parameters

Type	Name	Description
Matrix	matrix	The rotation Matrix to create the Quaternion from.

Returns

Type	Description
Quaternion

CreateFromRotationMatrix(ref Matrix, out Quaternion)

Creates a Quaternion from a rotation Matrix.

Declaration

public static void CreateFromRotationMatrix(ref Matrix matrix, out Quaternion result)

Parameters

Type	Name	Description
Matrix	matrix	The rotation Matrix to create the Quaternion from.
Quaternion	result	[OutAttribute] The created Quaternion.

CreateFromRotationMatrix(ref Matrix3x3, out Quaternion)

Creates a Quaternion from a rotation Matrix.

Declaration

public static void CreateFromRotationMatrix(ref Matrix3x3 matrix, out Quaternion result)

Parameters

Type	Name	Description
Matrix3x3	matrix	The rotation Matrix to create the Quaternion from.
Quaternion	result	[OutAttribute] The created Quaternion.

CreateFromRotationMatrix(in MatrixD)

Declaration

public static Quaternion CreateFromRotationMatrix(in MatrixD matrix)

Parameters

Type	Name	Description
MatrixD	matrix

Returns

Type	Description
Quaternion

CreateFromRotationMatrix(ref MatrixD, out Quaternion)

Declaration

public static void CreateFromRotationMatrix(ref MatrixD matrix, out Quaternion result)

Parameters

Type	Name	Description
MatrixD	matrix
Quaternion	result

CreateFromTwoVectors(Vector3, Vector3)

Declaration

public static Quaternion CreateFromTwoVectors(Vector3 firstVector, Vector3 secondVector)

Parameters

Type	Name	Description
Vector3	firstVector
Vector3	secondVector

Returns

Type	Description
Quaternion

CreateFromTwoVectors(ref Vector3, ref Vector3, out Quaternion)

Declaration

public static void CreateFromTwoVectors(ref Vector3 firstVector, ref Vector3 secondVector, out Quaternion result)

Parameters

Type	Name	Description
Vector3	firstVector
Vector3	secondVector
Quaternion	result

CreateFromYawPitchRoll(Single, Single, Single)

Creates a new Quaternion from specified yaw, pitch, and roll angles.

Declaration

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

Parameters

Type	Name	Description
System.Single	yaw	The yaw angle, in radians, around the y-axis.
System.Single	pitch	The pitch angle, in radians, around the x-axis.
System.Single	roll	The roll angle, in radians, around the z-axis.

Returns

Type	Description
Quaternion

CreateFromYawPitchRoll(Single, Single, Single, out Quaternion)

Creates a new Quaternion from specified yaw, pitch, and roll angles.

Declaration

public static void CreateFromYawPitchRoll(float yaw, float pitch, float roll, out Quaternion result)

Parameters

Type	Name	Description
System.Single	yaw	The yaw angle, in radians, around the y-axis.
System.Single	pitch	The pitch angle, in radians, around the x-axis.
System.Single	roll	The roll angle, in radians, around the z-axis.
Quaternion	result	[OutAttribute] An existing Quaternion filled in to express the specified yaw, pitch, and roll angles.

Divide(Quaternion, Quaternion)

Divides a Quaternion by another Quaternion.

Declaration

public static Quaternion Divide(Quaternion quaternion1, Quaternion quaternion2)

Parameters

Type	Name	Description
Quaternion	quaternion1	Source Quaternion.
Quaternion	quaternion2	The divisor.

Returns

Type	Description
Quaternion

Divide(ref Quaternion, ref Quaternion, out Quaternion)

Divides a Quaternion by another Quaternion.

Declaration

public static void Divide(ref Quaternion quaternion1, ref Quaternion quaternion2, out Quaternion result)

Parameters

Type	Name	Description
Quaternion	quaternion1	Source Quaternion.
Quaternion	quaternion2	The divisor.
Quaternion	result	[OutAttribute] Result of the division.

Dot(Quaternion, Quaternion)

Calculates the dot product of two Quaternions.

Declaration

public static float Dot(Quaternion quaternion1, Quaternion quaternion2)

Parameters

Type	Name	Description
Quaternion	quaternion1	Source Quaternion.
Quaternion	quaternion2	Source Quaternion.

Returns

Type	Description
System.Single

Dot(ref Quaternion, ref Quaternion, out Single)

Calculates the dot product of two Quaternions.

Declaration

public static void Dot(ref Quaternion quaternion1, ref Quaternion quaternion2, out float result)

Parameters

Type	Name	Description
Quaternion	quaternion1	Source Quaternion.
Quaternion	quaternion2	Source Quaternion.
System.Single	result	[OutAttribute] Dot product of the Quaternions.

Equals(Object)

Returns a value that indicates whether the current instance is equal to a specified object.

Declaration

public override bool Equals(object obj)

Parameters

Type	Name	Description
System.Object	obj	Object to make the comparison with.

Returns

Type	Description
System.Boolean

Equals(Quaternion)

Determines whether the specified Object is equal to the Quaternion.

Declaration

public bool Equals(Quaternion other)

Parameters

Type	Name	Description
Quaternion	other	The Quaternion to compare with the current Quaternion.

Returns

Type	Description
System.Boolean

Equals(Quaternion, Single)

Declaration

public bool Equals(Quaternion value, float epsilon)

Parameters

Type	Name	Description
Quaternion	value
System.Single	epsilon

Returns

Type	Description
System.Boolean

FindLargestIndex()

Declaration

public int FindLargestIndex()

Returns

Type	Description
System.Int32

FromVector4(Vector4)

Declaration

public static Quaternion FromVector4(Vector4 v)

Parameters

Type	Name	Description
Vector4	v

Returns

Type	Description
Quaternion

GetAxisAngle(out Vector3, out Single)

Declaration

public void GetAxisAngle(out Vector3 axis, out float angle)

Parameters

Type	Name	Description
Vector3	axis
System.Single	angle

GetComponent(Int32)

Declaration

public float GetComponent(int index)

Parameters

Type	Name	Description
System.Int32	index

Returns

Type	Description
System.Single

GetForward(ref Quaternion, out Vector3)

Gets forward vector (0,0,-1) transformed by quaternion.

Declaration

public static void GetForward(ref Quaternion q, out Vector3 result)

Parameters

Type	Name	Description
Quaternion	q
Vector3	result

GetHashCode()

Get the hash code of this object.

Declaration

public override int GetHashCode()

Returns

Type	Description
System.Int32

GetRight(ref Quaternion, out Vector3)

Gets right vector (1,0,0) transformed by quaternion.

Declaration

public static void GetRight(ref Quaternion q, out Vector3 result)

Parameters

Type	Name	Description
Quaternion	q
Vector3	result

GetUp(ref Quaternion, out Vector3)

Gets up vector (0,1,0) transformed by quaternion.

Declaration

public static void GetUp(ref Quaternion q, out Vector3 result)

Parameters

Type	Name	Description
Quaternion	q
Vector3	result

Inverse(Quaternion)

Returns the inverse of a Quaternion.

Declaration

public static Quaternion Inverse(Quaternion quaternion)

Parameters

Type	Name	Description
Quaternion	quaternion	Source Quaternion.

Returns

Type	Description
Quaternion

Inverse(ref Quaternion, out Quaternion)

Returns the inverse of a Quaternion.

Declaration

public static void Inverse(ref Quaternion quaternion, out Quaternion result)

Parameters

Type	Name	Description
Quaternion	quaternion	Source Quaternion.
Quaternion	result	[OutAttribute] The inverse of the Quaternion.

IsZero(Quaternion)

Declaration

public static bool IsZero(Quaternion value)

Parameters

Type	Name	Description
Quaternion	value

Returns

Type	Description
System.Boolean

IsZero(Quaternion, Single)

Declaration

public static bool IsZero(Quaternion value, float epsilon)

Parameters

Type	Name	Description
Quaternion	value
System.Single	epsilon

Returns

Type	Description
System.Boolean

Length()

Calculates the length of a Quaternion.

Declaration

public float Length()

Returns

Type	Description
System.Single

LengthSquared()

Calculates the length squared of a Quaternion.

Declaration

public float LengthSquared()

Returns

Type	Description
System.Single

Lerp(Quaternion, Quaternion, Single)

Linearly interpolates between two quaternions.

Declaration

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

Parameters

Type	Name	Description
Quaternion	quaternion1	Source quaternion.
Quaternion	quaternion2	Source quaternion.
System.Single	amount	Value indicating how far to interpolate between the quaternions.

Returns

Type	Description
Quaternion

Lerp(ref Quaternion, ref Quaternion, Single, out Quaternion)

Linearly interpolates between two quaternions.

Declaration

public static void Lerp(ref Quaternion quaternion1, ref Quaternion quaternion2, float amount, out Quaternion result)

Parameters

Type	Name	Description
Quaternion	quaternion1	Source quaternion.
Quaternion	quaternion2	Source quaternion.
System.Single	amount	Value indicating how far to interpolate between the quaternions.
Quaternion	result	[OutAttribute] The resulting quaternion.

Multiply(Quaternion, Single)

Multiplies a quaternion by a scalar value.

Declaration

public static Quaternion Multiply(Quaternion quaternion1, float scaleFactor)

Parameters

Type	Name	Description
Quaternion	quaternion1	Source quaternion.
System.Single	scaleFactor	Scalar value.

Returns

Type	Description
Quaternion

Multiply(Quaternion, Quaternion)

Multiplies two quaternions.

Declaration

public static Quaternion Multiply(Quaternion quaternion1, Quaternion quaternion2)

Parameters

Type	Name	Description
Quaternion	quaternion1	The quaternion on the left of the multiplication.
Quaternion	quaternion2	The quaternion on the right of the multiplication.

Returns

Type	Description
Quaternion

Multiply(ref Quaternion, Single, out Quaternion)

Multiplies a quaternion by a scalar value.

Declaration

public static void Multiply(ref Quaternion quaternion1, float scaleFactor, out Quaternion result)

Parameters

Type	Name	Description
Quaternion	quaternion1	Source quaternion.
System.Single	scaleFactor	Scalar value.
Quaternion	result	[OutAttribute] The result of the multiplication.

Multiply(ref Quaternion, ref Quaternion, out Quaternion)

Multiplies two quaternions.

Declaration

public static void Multiply(ref Quaternion quaternion1, ref Quaternion quaternion2, out Quaternion result)

Parameters

Type	Name	Description
Quaternion	quaternion1	The quaternion on the left of the multiplication.
Quaternion	quaternion2	The quaternion on the right of the multiplication.
Quaternion	result	[OutAttribute] The result of the multiplication.

Negate(Quaternion)

Flips the sign of each component of the quaternion.

Declaration

public static Quaternion Negate(Quaternion quaternion)

Parameters

Type	Name	Description
Quaternion	quaternion	Source quaternion.

Returns

Type	Description
Quaternion

Negate(ref Quaternion, out Quaternion)

Flips the sign of each component of the quaternion.

Declaration

public static void Negate(ref Quaternion quaternion, out Quaternion result)

Parameters

Type	Name	Description
Quaternion	quaternion	Source quaternion.
Quaternion	result	[OutAttribute] Negated quaternion.

Normalize()

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

Declaration

public void Normalize()

Normalize(Quaternion)

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

Declaration

public static Quaternion Normalize(Quaternion quaternion)

Parameters

Type	Name	Description
Quaternion	quaternion	Source quaternion.

Returns

Type	Description
Quaternion

Normalize(ref Quaternion, out Quaternion)

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

Declaration

public static void Normalize(ref Quaternion quaternion, out Quaternion result)

Parameters

Type	Name	Description
Quaternion	quaternion	Source quaternion.
Quaternion	result	[OutAttribute] Normalized quaternion.

SetComponent(Int32, Single)

Declaration

public void SetComponent(int index, float value)

Parameters

Type	Name	Description
System.Int32	index
System.Single	value

Slerp(Quaternion, Quaternion, Single)

Interpolates between two quaternions, using spherical linear interpolation.

Declaration

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

Parameters

Type	Name	Description
Quaternion	quaternion1	Source quaternion.
Quaternion	quaternion2	Source quaternion.
System.Single	amount	Value that indicates how far to interpolate between the quaternions.

Returns

Type	Description
Quaternion

Slerp(ref Quaternion, ref Quaternion, Single, out Quaternion)

Interpolates between two quaternions, using spherical linear interpolation.

Declaration

public static void Slerp(ref Quaternion quaternion1, ref Quaternion quaternion2, float amount, out Quaternion result)

Parameters

Type	Name	Description
Quaternion	quaternion1	Source quaternion.
Quaternion	quaternion2	Source quaternion.
System.Single	amount	Value that indicates how far to interpolate between the quaternions.
Quaternion	result	[OutAttribute] Result of the interpolation.

Subtract(Quaternion, Quaternion)

Subtracts a quaternion from another quaternion.

Declaration

public static Quaternion Subtract(Quaternion quaternion1, Quaternion quaternion2)

Parameters

Type	Name	Description
Quaternion	quaternion1	Source quaternion.
Quaternion	quaternion2	Source quaternion.

Returns

Type	Description
Quaternion

Subtract(ref Quaternion, ref Quaternion, out Quaternion)

Subtracts a quaternion from another quaternion.

Declaration

public static void Subtract(ref Quaternion quaternion1, ref Quaternion quaternion2, out Quaternion result)

Parameters

Type	Name	Description
Quaternion	quaternion1	Source quaternion.
Quaternion	quaternion2	Source quaternion.
Quaternion	result	[OutAttribute] Result of the subtraction.

ToString()

Retireves a string representation of the current object.

Declaration

public override string ToString()

Returns

Type	Description
System.String

ToString(String)

Declaration

public string ToString(string format)

Parameters

Type	Name	Description
System.String	format

Returns

Type	Description
System.String

ToStringAxisAngle(String)

Declaration

public string ToStringAxisAngle(string format = "G")

Parameters

Type	Name	Description
System.String	format

Returns

Type	Description
System.String

ToVector4()

Declaration

public Vector4 ToVector4()

Returns

Type	Description
Vector4

Operators

Addition(Quaternion, Quaternion)

Adds two Quaternions.

Declaration

public static Quaternion operator +(Quaternion quaternion1, Quaternion quaternion2)

Parameters

Type	Name	Description
Quaternion	quaternion1	Quaternion to add.
Quaternion	quaternion2	Quaternion to add.

Returns

Type	Description
Quaternion

Division(Quaternion, Quaternion)

Divides a Quaternion by another Quaternion.

Declaration

public static Quaternion operator /(Quaternion quaternion1, Quaternion quaternion2)

Parameters

Type	Name	Description
Quaternion	quaternion1	Source Quaternion.
Quaternion	quaternion2	The divisor.

Returns

Type	Description
Quaternion

Equality(Quaternion, Quaternion)

Compares two Quaternions for equality.

Declaration

public static bool operator ==(Quaternion quaternion1, Quaternion quaternion2)

Parameters

Type	Name	Description
Quaternion	quaternion1	Source Quaternion.
Quaternion	quaternion2	Source Quaternion.

Returns

Type	Description
System.Boolean

Inequality(Quaternion, Quaternion)

Compare two Quaternions for inequality.

Declaration

public static bool operator !=(Quaternion quaternion1, Quaternion quaternion2)

Parameters

Type	Name	Description
Quaternion	quaternion1	Source Quaternion.
Quaternion	quaternion2	Source Quaternion.

Returns

Type	Description
System.Boolean

Multiply(Quaternion, Single)

Multiplies a quaternion by a scalar value.

Declaration

public static Quaternion operator *(Quaternion quaternion1, float scaleFactor)

Parameters

Type	Name	Description
Quaternion	quaternion1	Source quaternion.
System.Single	scaleFactor	Scalar value.

Returns

Type	Description
Quaternion

Multiply(Quaternion, Quaternion)

Multiplies two quaternions.

Declaration

public static Quaternion operator *(Quaternion quaternion1, Quaternion quaternion2)

Parameters

Type	Name	Description
Quaternion	quaternion1	Source quaternion.
Quaternion	quaternion2	Source quaternion.

Returns

Type	Description
Quaternion

Multiply(Quaternion, Vector3)

Multiplies a vector by a quaternion. Resulting vector rotated by quaternion

Declaration

public static Vector3 operator *(Quaternion quaternion, Vector3 vector)

Parameters

Type	Name	Description
Quaternion	quaternion	Source quaternion.
Vector3	vector	Vector to be rotated.

Returns

Type	Description
Vector3

Subtraction(Quaternion, Quaternion)

Subtracts a quaternion from another quaternion.

Declaration

public static Quaternion operator -(Quaternion quaternion1, Quaternion quaternion2)

Parameters

Type	Name	Description
Quaternion	quaternion1	Source quaternion.
Quaternion	quaternion2	Source quaternion.

Returns

Type	Description
Quaternion

UnaryNegation(Quaternion)

Flips the sign of each component of the quaternion.

Declaration

public static Quaternion operator -(Quaternion quaternion)

Parameters

Type	Name	Description
Quaternion	quaternion	Source quaternion.

Returns

Type	Description
Quaternion