Struct Quaternion

Represents a Quaternion.

Implements

IEquatable<Quaternion>

Inherited Members

Object.Equals(Object, Object)

Object.ReferenceEquals(Object, Object)

Object.GetType()

Namespace: OpenTK

Assembly: OpenTK.dll

Syntax

[Serializable]
public struct Quaternion : IEquatable<Quaternion>

Constructors

Quaternion(Vector3)

Construct a new Quaternion from given Euler angles. 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, Single)

Construct a new Quaternion from vector and w components

Declaration

public Quaternion(Vector3 v, float w)

Parameters

Type	Name	Description
Vector3	v	The vector part
Single	w	The w part

Quaternion(Single, Single, Single)

Construct a new Quaternion 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
Single	rotationX	Counterclockwise rotation around X axis in radian
Single	rotationY	Counterclockwise rotation around Y axis in radian
Single	rotationZ	Counterclockwise rotation around Z axis in radian

Quaternion(Single, Single, Single, Single)

Construct a new Quaternion

Declaration

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

Parameters

Type	Name	Description
Single	x	The x component
Single	y	The y component
Single	z	The z component
Single	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
Single

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
Single

See Also

LengthSquared

LengthSquared

Gets the square of the quaternion length (magnitude).

Declaration

public readonly float LengthSquared { get; }

Property Value

Type	Description
Single

X

Gets or sets the X component of this instance.

Declaration

public float X { get; set; }

Property Value

Type	Description
Single

Y

Gets or sets the Y component of this instance.

Declaration

public float Y { get; set; }

Property Value

Type	Description
Single

Z

Gets or sets the Z component of this instance.

Declaration

public float Z { get; set; }

Property Value

Type	Description
Single

Methods

Add(Quaternion, Quaternion)

Add two quaternions

Declaration

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(ref Quaternion, ref Quaternion, out Quaternion)

Add two quaternions

Declaration

public static void Add(ref Quaternion left, ref 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

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(ref Quaternion, out Quaternion)

Get the conjugate of the given quaternion

Declaration

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

Parameters

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

Equals(Quaternion)

Compares this Quaternion instance to another Quaternion for equality.

Declaration

public bool Equals(Quaternion other)

Parameters

Type	Name	Description
Quaternion	other	The other Quaternion to be used in the comparison.

Returns

Type	Description
Boolean	True if both instances are equal; false otherwise.

Equals(Object)

Compares this object instance to another object for equality.

Declaration

public override bool Equals(object other)

Parameters

Type	Name	Description
Object	other	The other object to be used in the comparison.

Returns

Type	Description
Boolean	True if both objects are Quaternions of equal value. Otherwise it returns false.

Overrides

ValueType.Equals(Object)

FromAxisAngle(Vector3, Single)

Build a quaternion from the given axis and angle in radians

Declaration

public static Quaternion FromAxisAngle(Vector3 axis, float angle)

Parameters

Type	Name	Description
Vector3	axis	The axis to rotate about
Single	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

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(ref 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(ref Vector3 eulerAngles, out Quaternion result)

Parameters

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

FromEulerAngles(Single, Single, Single)

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

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

Parameters

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

Returns

Type	Description
Quaternion

FromMatrix(Matrix3)

Builds a quaternion from the given rotation matrix

Declaration

public static Quaternion FromMatrix(Matrix3 matrix)

Parameters

Type	Name	Description
Matrix3	matrix	A rotation matrix

Returns

Type	Description
Quaternion	The equivalent quaternion

FromMatrix(ref Matrix3, out Quaternion)

Builds a quaternion from the given rotation matrix

Declaration

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

Parameters

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

GetHashCode()

Provides the hash code for this object.

Declaration

public override int GetHashCode()

Returns

Type	Description
Int32	A hash code formed from the bitwise XOR of this objects members.

Overrides

ValueType.GetHashCode()

Invert()

Inverts this Quaternion.

Declaration

public void Invert()

Invert(Quaternion)

Get the inverse of the given quaternion

Declaration

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(ref Quaternion, out Quaternion)

Get the inverse of the given quaternion

Declaration

public static void Invert(ref 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 Quaternion Inverted()

Returns

Type	Description
Quaternion

Multiply(Quaternion, Quaternion)

Multiplies two instances.

Declaration

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, Single)

Multiplies an instance by a scalar.

Declaration

public static Quaternion Multiply(Quaternion quaternion, float scale)

Parameters

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

Returns

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

Multiply(ref Quaternion, ref Quaternion, out Quaternion)

Multiplies two instances.

Declaration

public static void Multiply(ref Quaternion left, ref 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(ref Quaternion, Single, out Quaternion)

Multiplies an instance by a scalar.

Declaration

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

Parameters

Type	Name	Description
Quaternion	quaternion	The instance.
Single	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

public static Quaternion Normalize(Quaternion q)

Parameters

Type	Name	Description
Quaternion	q	The quaternion to normalize

Returns

Type	Description
Quaternion	The normalized quaternion

Normalize(ref Quaternion, out Quaternion)

Scale the given quaternion to unit length

Declaration

public static void Normalize(ref 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 Quaternion Normalized()

Returns

Type	Description
Quaternion

Slerp(Quaternion, Quaternion, Single)

Do Spherical linear interpolation between two quaternions

Declaration

public static Quaternion Slerp(Quaternion q1, Quaternion q2, float blend)

Parameters

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

Returns

Type	Description
Quaternion	A smooth blend between the given quaternions

Sub(Quaternion, Quaternion)

Subtracts two instances.

Declaration

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(ref Quaternion, ref Quaternion, out Quaternion)

Subtracts two instances.

Declaration

public static void Sub(ref Quaternion left, ref 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 Single)

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
Single	angle	The resultant angle

ToString()

Returns a System.String that represents the current Quaternion.

Declaration

public override string ToString()

Returns

Type	Description
String

Overrides

ValueType.ToString()

Operators

Addition(Quaternion, Quaternion)

Adds two instances.

Declaration

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.

Equality(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
Boolean	True, if left equals right; false otherwise.

Inequality(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
Boolean	True, if left does not equal right; false otherwise.

Multiply(Quaternion, Quaternion)

Multiplies two instances.

Declaration

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.

Multiply(Quaternion, Single)

Multiplies an instance by a scalar.

Declaration

public static Quaternion operator *(Quaternion quaternion, float scale)

Parameters

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

Returns

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

Multiply(Single, Quaternion)

Multiplies an instance by a scalar.

Declaration

public static Quaternion operator *(float scale, Quaternion quaternion)

Parameters

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

Returns

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

Subtraction(Quaternion, Quaternion)

Subtracts two instances.

Declaration

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

System.IEquatable<T>