Struct Quaternion

Represents a Quaternion.

Implements

IEquatable<Quaternion>

IFormattable

Inherited Members

object.Equals(object, object)

object.GetType()

object.ReferenceEquals(object, object)

Namespace: OpenTK.Mathematics

Assembly: OpenTK.Mathematics.dll

Syntax

[Serializable]
public struct Quaternion : IEquatable<Quaternion>, IFormattable

Constructors

Quaternion(Vector3, float)

Initializes a new instance of the Quaternion struct.

Declaration

public Quaternion(Vector3 v, float w)

Parameters

Type	Name	Description
Vector3	v	The vector part.
float	w	The w part.

Quaternion(Vector3)

Initializes a new instance of the Quaternion struct from given Euler angles in radians. The rotations will get applied in following order:

1. Around X, 2. Around Y, 3. Around Z.

Declaration

public Quaternion(Vector3 eulerAngles)

Parameters

Type	Name	Description
Vector3	eulerAngles	The counterclockwise euler angles as a Vector3.

Quaternion(float, float, float, float)

Initializes a new instance of the Quaternion struct.

Declaration

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

Parameters

Type	Name	Description
float	x	The x component.
float	y	The y component.
float	z	The z component.
float	w	The w component.

Quaternion(float, float, float)

Initializes a new instance of the Quaternion struct from given Euler angles in radians. The rotations will get applied in following order:

1. around X axis, 2. around Y axis, 3. around Z axis.

Declaration

public Quaternion(float rotationX, float rotationY, float rotationZ)

Parameters

Type	Name	Description
float	rotationX	Counterclockwise rotation around X axis in radian.
float	rotationY	Counterclockwise rotation around Y axis in radian.
float	rotationZ	Counterclockwise rotation around Z axis in radian.

Fields

Identity

Defines the identity quaternion.

Declaration

public static readonly Quaternion Identity

Field Value

Type	Description
Quaternion

W

The W component of this instance.

Declaration

public float W

Field Value

Type	Description
float

Xyz

The X, Y and Z components of this instance.

Declaration

public Vector3 Xyz

Field Value

Type	Description
Vector3

Properties

Length

Gets the length (magnitude) of the quaternion.

Declaration

public readonly float Length { get; }

Property Value

Type	Description
float

See Also

LengthSquared

LengthSquared

Gets the square of the quaternion length (magnitude).

Declaration

public readonly float LengthSquared { get; }

Property Value

Type	Description
float

X

Gets or sets the X component of this instance.

Declaration

public float X { readonly get; set; }

Property Value

Type	Description
float

Y

Gets or sets the Y component of this instance.

Declaration

public float Y { readonly get; set; }

Property Value

Type	Description
float

Z

Gets or sets the Z component of this instance.

Declaration

public float Z { readonly get; set; }

Property Value

Type	Description
float

Methods

Add(Quaternion, Quaternion)

Add two quaternions.

Declaration

[Pure]
public static Quaternion Add(Quaternion left, Quaternion right)

Parameters

Type	Name	Description
Quaternion	left	The first operand.
Quaternion	right	The second operand.

Returns

Type	Description
Quaternion	The result of the addition.

Add(in Quaternion, in Quaternion, out Quaternion)

Add two quaternions.

Declaration

public static void Add(in Quaternion left, in Quaternion right, out Quaternion result)

Parameters

Type	Name	Description
Quaternion	left	The first operand.
Quaternion	right	The second operand.
Quaternion	result	The result of the addition.

Conjugate()

Inverts the Vector3 component of this Quaternion.

Declaration

public void Conjugate()

Conjugate(Quaternion)

Get the conjugate of the given quaternion.

Declaration

[Pure]
public static Quaternion Conjugate(Quaternion q)

Parameters

Type	Name	Description
Quaternion	q	The quaternion.

Returns

Type	Description
Quaternion	The conjugate of the given quaternion.

Conjugate(in Quaternion, out Quaternion)

Get the conjugate of the given quaternion.

Declaration

public static void Conjugate(in Quaternion q, out Quaternion result)

Parameters

Type	Name	Description
Quaternion	q	The quaternion.
Quaternion	result	The conjugate of the given quaternion.

Equals(Quaternion)

Declaration

public readonly bool Equals(Quaternion other)

Parameters

Type	Name	Description
Quaternion	other

Returns

Type	Description
bool

Equals(object)

Declaration

public override readonly bool Equals(object obj)

Parameters

Type	Name	Description
object	obj

Returns

Type	Description
bool

Overrides

ValueType.Equals(object)

FromAxisAngle(Vector3, float)

Build a quaternion from the given axis and angle in radians.

Declaration

[Pure]
public static Quaternion FromAxisAngle(Vector3 axis, float angle)

Parameters

Type	Name	Description
Vector3	axis	The axis to rotate about.
float	angle	The rotation angle in radians.

Returns

Type	Description
Quaternion	The equivalent quaternion.

FromEulerAngles(Vector3)

Builds a Quaternion from the given euler angles in radians. The rotations will get applied in following order:

1. X axis, 2. Y axis, 3. Z axis.

Declaration

[Pure]
public static Quaternion FromEulerAngles(Vector3 eulerAngles)

Parameters

Type	Name	Description
Vector3	eulerAngles	The counterclockwise euler angles as a vector.

Returns

Type	Description
Quaternion	The equivalent Quaternion.

FromEulerAngles(in Vector3, out Quaternion)

Builds a Quaternion from the given euler angles in radians. The rotations will get applied in following order:

1. Around X, 2. Around Y, 3. Around Z.

Declaration

public static void FromEulerAngles(in Vector3 eulerAngles, out Quaternion result)

Parameters

Type	Name	Description
Vector3	eulerAngles	The counterclockwise euler angles a vector.
Quaternion	result	The equivalent Quaternion.

FromEulerAngles(float, float, float)

Builds a Quaternion from the given euler angles in radians The rotations will get applied in following order:

1. pitch (X axis), 2. yaw (Y axis), 3. roll (Z axis).

Declaration

[Pure]
public static Quaternion FromEulerAngles(float pitch, float yaw, float roll)

Parameters

Type	Name	Description
float	pitch	The pitch (attitude), counterclockwise rotation around X axis.
float	yaw	The yaw (heading), counterclockwise rotation around Y axis.
float	roll	The roll (bank), counterclockwise rotation around Z axis.

Returns

Type	Description
Quaternion	The quaternion.

FromMatrix(Matrix3)

Builds a quaternion from the given rotation matrix.

Declaration

[Pure]
public static Quaternion FromMatrix(Matrix3 matrix)

Parameters

Type	Name	Description
Matrix3	matrix	A rotation matrix.

Returns

Type	Description
Quaternion	The equivalent quaternion.

FromMatrix(in Matrix3, out Quaternion)

Builds a quaternion from the given rotation matrix.

Declaration

public static void FromMatrix(in Matrix3 matrix, out Quaternion result)

Parameters

Type	Name	Description
Matrix3	matrix	A rotation matrix.
Quaternion	result	The equivalent quaternion.

GetHashCode()

Declaration

public override readonly int GetHashCode()

Returns

Type	Description
int

Overrides

ValueType.GetHashCode()

Invert()

Inverts this Quaternion.

Declaration

public void Invert()

Invert(Quaternion)

Get the inverse of the given quaternion.

Declaration

[Pure]
public static Quaternion Invert(Quaternion q)

Parameters

Type	Name	Description
Quaternion	q	The quaternion to invert.

Returns

Type	Description
Quaternion	The inverse of the given quaternion.

Invert(in Quaternion, out Quaternion)

Get the inverse of the given quaternion.

Declaration

public static void Invert(in Quaternion q, out Quaternion result)

Parameters

Type	Name	Description
Quaternion	q	The quaternion to invert.
Quaternion	result	The inverse of the given quaternion.

Inverted()

Returns the inverse of this Quaternion.

Declaration

public readonly Quaternion Inverted()

Returns

Type	Description
Quaternion	The inverted copy.

Multiply(Quaternion, Quaternion)

Multiplies two instances.

Declaration

[Pure]
public static Quaternion Multiply(Quaternion left, Quaternion right)

Parameters

Type	Name	Description
Quaternion	left	The first instance.
Quaternion	right	The second instance.

Returns

Type	Description
Quaternion	A new instance containing the result of the calculation.

Multiply(Quaternion, float)

Multiplies an instance by a scalar.

Declaration

[Pure]
public static Quaternion Multiply(Quaternion quaternion, float scale)

Parameters

Type	Name	Description
Quaternion	quaternion	The instance.
float	scale	The scalar.

Returns

Type	Description
Quaternion	A new instance containing the result of the calculation.

Multiply(in Quaternion, in Quaternion, out Quaternion)

Multiplies two instances.

Declaration

public static void Multiply(in Quaternion left, in Quaternion right, out Quaternion result)

Parameters

Type	Name	Description
Quaternion	left	The first instance.
Quaternion	right	The second instance.
Quaternion	result	A new instance containing the result of the calculation.

Multiply(in Quaternion, float, out Quaternion)

Multiplies an instance by a scalar.

Declaration

public static void Multiply(in Quaternion quaternion, float scale, out Quaternion result)

Parameters

Type	Name	Description
Quaternion	quaternion	The instance.
float	scale	The scalar.
Quaternion	result	A new instance containing the result of the calculation.

Normalize()

Scales the Quaternion to unit length.

Declaration

public void Normalize()

Normalize(Quaternion)

Scale the given quaternion to unit length.

Declaration

[Pure]
public static Quaternion Normalize(Quaternion q)

Parameters

Type	Name	Description
Quaternion	q	The quaternion to normalize.

Returns

Type	Description
Quaternion	The normalized copy.

Normalize(in Quaternion, out Quaternion)

Scale the given quaternion to unit length.

Declaration

public static void Normalize(in Quaternion q, out Quaternion result)

Parameters

Type	Name	Description
Quaternion	q	The quaternion to normalize.
Quaternion	result	The normalized quaternion.

Normalized()

Returns a copy of the Quaternion scaled to unit length.

Declaration

public readonly Quaternion Normalized()

Returns

Type	Description
Quaternion	The normalized copy.

Slerp(Quaternion, Quaternion, float)

Do Spherical linear interpolation between two quaternions.

Declaration

[Pure]
public static Quaternion Slerp(Quaternion q1, Quaternion q2, float blend)

Parameters

Type	Name	Description
Quaternion	q1	The first quaternion.
Quaternion	q2	The second quaternion.
float	blend	The blend factor.

Returns

Type	Description
Quaternion	A smooth blend between the given quaternions.

Sub(Quaternion, Quaternion)

Subtracts two instances.

Declaration

[Pure]
public static Quaternion Sub(Quaternion left, Quaternion right)

Parameters

Type	Name	Description
Quaternion	left	The left instance.
Quaternion	right	The right instance.

Returns

Type	Description
Quaternion	The result of the operation.

Sub(in Quaternion, in Quaternion, out Quaternion)

Subtracts two instances.

Declaration

public static void Sub(in Quaternion left, in Quaternion right, out Quaternion result)

Parameters

Type	Name	Description
Quaternion	left	The left instance.
Quaternion	right	The right instance.
Quaternion	result	The result of the operation.

ToAxisAngle()

Convert this instance to an axis-angle representation.

Declaration

public Vector4 ToAxisAngle()

Returns

Type	Description
Vector4	A Vector4 that is the axis-angle representation of this quaternion.

ToAxisAngle(out Vector3, out float)

Convert the current quaternion to axis angle representation.

Declaration

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

Parameters

Type	Name	Description
Vector3	axis	The resultant axis.
float	angle	The resultant angle.

ToEulerAngles()

Convert this instance to an Euler angle representation.

Declaration

public readonly Vector3 ToEulerAngles()

Returns

Type	Description
Vector3	The Euler angles in radians.

ToEulerAngles(in Quaternion, out Vector3)

Converts a quaternion to it's euler angle representation.

Declaration

public static void ToEulerAngles(in Quaternion q, out Vector3 result)

Parameters

Type	Name	Description
Quaternion	q	The Quaternion.
Vector3	result	The resulting euler angles in radians.

ToEulerAngles(out Vector3)

Convert the current quaternion to Euler angle representation.

Declaration

public readonly void ToEulerAngles(out Vector3 angles)

Parameters

Type	Name	Description
Vector3	angles	The Euler angles in radians.

ToString()

Returns a System.String that represents the current Quaternion.

Declaration

public override readonly string ToString()

Returns

Type	Description
string	A human-readable representation of the quaternion.

Overrides

ValueType.ToString()

ToString(IFormatProvider)

Declaration

public readonly string ToString(IFormatProvider formatProvider)

Parameters

Type	Name	Description
IFormatProvider	formatProvider

Returns

Type	Description
string

ToString(string, IFormatProvider)

Declaration

public readonly string ToString(string format, IFormatProvider formatProvider)

Parameters

Type	Name	Description
string	format
IFormatProvider	formatProvider

Returns

Type	Description
string

ToString(string)

Declaration

public readonly string ToString(string format)

Parameters

Type	Name	Description
string	format

Returns

Type	Description
string

Operators

operator +(Quaternion, Quaternion)

Adds two instances.

Declaration

[Pure]
public static Quaternion operator +(Quaternion left, Quaternion right)

Parameters

Type	Name	Description
Quaternion	left	The first instance.
Quaternion	right	The second instance.

Returns

Type	Description
Quaternion	The result of the calculation.

operator ==(Quaternion, Quaternion)

Compares two instances for equality.

Declaration

public static bool operator ==(Quaternion left, Quaternion right)

Parameters

Type	Name	Description
Quaternion	left	The first instance.
Quaternion	right	The second instance.

Returns

Type	Description
bool	True, if left equals right; false otherwise.

explicit operator Quaternion(Quaternion)

Converts Quaternion to Quaternion.

Declaration

[Pure]
public static explicit operator Quaternion(Quaternion quat)

Parameters

Type	Name	Description
Quaternion	quat	The Quaternion to cast.

Returns

Type	Description
Quaternion

explicit operator Quaternion(Quaternion)

Converts Quaternion to Quaternion.

Declaration

[Pure]
public static explicit operator Quaternion(Quaternion quat)

Parameters

Type	Name	Description
Quaternion	quat	The Quaternion to cast.

Returns

Type	Description
Quaternion

operator !=(Quaternion, Quaternion)

Compares two instances for inequality.

Declaration

public static bool operator !=(Quaternion left, Quaternion right)

Parameters

Type	Name	Description
Quaternion	left	The first instance.
Quaternion	right	The second instance.

Returns

Type	Description
bool	True, if left does not equal right; false otherwise.

operator *(Quaternion, Quaternion)

Multiplies two instances.

Declaration

[Pure]
public static Quaternion operator *(Quaternion left, Quaternion right)

Parameters

Type	Name	Description
Quaternion	left	The first instance.
Quaternion	right	The second instance.

Returns

Type	Description
Quaternion	The result of the calculation.

operator *(Quaternion, float)

Multiplies an instance by a scalar.

Declaration

[Pure]
public static Quaternion operator *(Quaternion quaternion, float scale)

Parameters

Type	Name	Description
Quaternion	quaternion	The instance.
float	scale	The scalar.

Returns

Type	Description
Quaternion	A new instance containing the result of the calculation.

operator *(float, Quaternion)

Multiplies an instance by a scalar.

Declaration

[Pure]
public static Quaternion operator *(float scale, Quaternion quaternion)

Parameters

Type	Name	Description
float	scale	The scalar.
Quaternion	quaternion	The instance.

Returns

Type	Description
Quaternion	A new instance containing the result of the calculation.

operator -(Quaternion, Quaternion)

Subtracts two instances.

Declaration

[Pure]
public static Quaternion operator -(Quaternion left, Quaternion right)

Parameters

Type	Name	Description
Quaternion	left	The first instance.
Quaternion	right	The second instance.

Returns

Type	Description
Quaternion	The result of the calculation.

Implements

IEquatable<T>

IFormattable