Struct Quaternion

Represents a Quaternion.

Implements
Inherited Members
Namespace: OpenTK.Mathematics
Assembly: OpenTK.Mathematics.dll
Syntax
[Serializable]
public struct Quaternion : IEquatable<Quaternion>, IFormattable

Constructors

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(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(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.

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.

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

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)

Indicates whether the current object is equal to another object of the same type.

Declaration
public readonly bool Equals(Quaternion other)
Parameters
Type Name Description
Quaternion other

An object to compare with this object.
Returns
Type Description
bool

true if the current object is equal to the other parameter; otherwise, false.

Equals(object)

Indicates whether this instance and a specified object are equal.

Declaration
public override readonly bool Equals(object obj)
Parameters
Type Name Description
object obj

The object to compare with the current instance.
Returns
Type Description
bool

true if obj and this instance are the same type and represent the same value; otherwise, false.
Overrides

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()

Returns the hash code for this instance.

Declaration
public override readonly int GetHashCode()
Returns
Type Description
int

A 32-bit signed integer that is the hash code for this instance.
Overrides

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

ToString(IFormatProvider)

Formats the value of the current instance using the specified format.

Declaration
public readonly string ToString(IFormatProvider formatProvider)
Parameters
Type Name Description
IFormatProvider formatProvider

The provider to use to format the value.

-or-

A null reference (Nothing in Visual Basic) to obtain the numeric format information from the current locale setting of the operating system.
Returns
Type Description
string

The value of the current instance in the specified format.

ToString(string)

Formats the value of the current instance using the specified format.

Declaration
public readonly string ToString(string format)
Parameters
Type Name Description
string format

The format to use.

-or-

A null reference (Nothing in Visual Basic) to use the default format defined for the type of the IFormattable implementation.
Returns
Type Description
string

The value of the current instance in the specified format.

ToString(string, IFormatProvider)

Formats the value of the current instance using the specified format.

Declaration
public readonly string ToString(string format, IFormatProvider formatProvider)
Parameters
Type Name Description
string format

The format to use.

-or-

A null reference (Nothing in Visual Basic) to use the default format defined for the type of the IFormattable implementation.
IFormatProvider formatProvider

The provider to use to format the value.

-or-

A null reference (Nothing in Visual Basic) to obtain the numeric format information from the current locale setting of the operating system.
Returns
Type Description
string

The value of the current instance in the specified format.

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.

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