Struct quaternion

Namespace: Unity.Mathematics

Syntax

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

Constructors

quaternion(Single, Single, Single, Single)

Constructs a quaternion from four float values.

Declaration

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

Parameters

Type	Name	Description
System.Single	x
System.Single	y
System.Single	z
System.Single	w

quaternion(float3x3)

Constructs a unit quaternion from a float3x3 rotation matrix. The matrix must be orthonormal.

Declaration

public quaternion(float3x3 m)

Parameters

Type	Name	Description
float3x3	m

quaternion(float4)

Constructs a quaternion from float4 vector.

Declaration

public quaternion(float4 value)

Parameters

Type	Name	Description
float4	value

quaternion(float4x4)

Constructs a unit quaternion from an orthonormal float4x4 matrix.

Declaration

public quaternion(float4x4 m)

Parameters

Type	Name	Description
float4x4	m

Fields

identity

A quaternion representing the identity transform.

Declaration

public static readonly quaternion identity

Field Value

Type	Description
quaternion

value

Declaration

public float4 value

Field Value

Type	Description
float4

Methods

AxisAngle(float3, Single)

Returns a quaternion representing a rotation around a unit axis by an angle in radians. The rotation direction is clockwise when looking along the rotation axis towards the origin.

Declaration

public static quaternion AxisAngle(float3 axis, float angle)

Parameters

Type	Name	Description
float3	axis
System.Single	angle

Returns

Type	Description
quaternion

Equals(Object)

Returns whether true if the quaternion is equal to a given quaternion, false otherwise.

Declaration

public override bool Equals(object x)

Parameters

Type	Name	Description
System.Object	x

Returns

Type	Description
System.Boolean

Overrides

System.ValueType.Equals(System.Object)

Equals(quaternion)

Returns true if the quaternion is equal to a given quaternion, false otherwise.

Declaration

public bool Equals(quaternion x)

Parameters

Type	Name	Description
quaternion	x

Returns

Type	Description
System.Boolean

Euler(Single, Single, Single, math.RotationOrder)

Returns a quaternion constructed by first performing 3 rotations around the principal axes in a given order. All rotation angles are in radians and clockwise when looking along the rotation axis towards the origin. When the rotation order is known at compile time, it is recommended for performance reasons to use specific Euler rotation constructors such as EulerZXY(...).

Declaration

public static quaternion Euler(float x, float y, float z, math.RotationOrder order = math.RotationOrder.ZXY)

Parameters

Type	Name	Description
System.Single	x	The rotation angle around the x-axis in radians.
System.Single	y	The rotation angle around the y-axis in radians.
System.Single	z	The rotation angle around the z-axis in radians.
math.RotationOrder	order	The order in which the rotations are applied.

Returns

Type	Description
quaternion

Euler(float3, math.RotationOrder)

Returns a quaternion constructed by first performing 3 rotations around the principal axes in a given order. All rotation angles are in radians and clockwise when looking along the rotation axis towards the origin. When the rotation order is known at compile time, it is recommended for performance reasons to use specific Euler rotation constructors such as EulerZXY(...).

Declaration

public static quaternion Euler(float3 xyz, math.RotationOrder order = math.RotationOrder.ZXY)

Parameters

Type	Name	Description
float3	xyz	A float3 vector containing the rotation angles around the x-, y- and z-axis measures in radians.
math.RotationOrder	order	The order in which the rotations are applied.

Returns

Type	Description
quaternion

EulerXYZ(Single, Single, Single)

Returns a quaternion constructed by first performing a rotation around the x-axis, then the y-axis and finally the z-axis. All rotation angles are in radians and clockwise when looking along the rotation axis towards the origin.

Declaration

public static quaternion EulerXYZ(float x, float y, float z)

Parameters

Type	Name	Description
System.Single	x	The rotation angle around the x-axis in radians.
System.Single	y	The rotation angle around the y-axis in radians.
System.Single	z	The rotation angle around the z-axis in radians.

Returns

Type	Description
quaternion

EulerXYZ(float3)

Returns a quaternion constructed by first performing a rotation around the x-axis, then the y-axis and finally the z-axis. All rotation angles are in radians and clockwise when looking along the rotation axis towards the origin.

Declaration

public static quaternion EulerXYZ(float3 xyz)

Parameters

Type	Name	Description
float3	xyz	A float3 vector containing the rotation angles around the x-, y- and z-axis measures in radians.

Returns

Type	Description
quaternion

EulerXZY(Single, Single, Single)

Returns a quaternion constructed by first performing a rotation around the x-axis, then the z-axis and finally the y-axis. All rotation angles are in radians and clockwise when looking along the rotation axis towards the origin.

Declaration

public static quaternion EulerXZY(float x, float y, float z)

Parameters

Type	Name	Description
System.Single	x	The rotation angle around the x-axis in radians.
System.Single	y	The rotation angle around the y-axis in radians.
System.Single	z	The rotation angle around the z-axis in radians.

Returns

Type	Description
quaternion

EulerXZY(float3)

Returns a quaternion constructed by first performing a rotation around the x-axis, then the z-axis and finally the y-axis. All rotation angles are in radians and clockwise when looking along the rotation axis towards the origin.

Declaration

public static quaternion EulerXZY(float3 xyz)

Parameters

Type	Name	Description
float3	xyz	A float3 vector containing the rotation angles around the x-, y- and z-axis measures in radians.

Returns

Type	Description
quaternion

EulerYXZ(Single, Single, Single)

Returns a quaternion constructed by first performing a rotation around the y-axis, then the x-axis and finally the z-axis. All rotation angles are in radians and clockwise when looking along the rotation axis towards the origin.

Declaration

public static quaternion EulerYXZ(float x, float y, float z)

Parameters

Type	Name	Description
System.Single	x	The rotation angle around the x-axis in radians.
System.Single	y	The rotation angle around the y-axis in radians.
System.Single	z	The rotation angle around the z-axis in radians.

Returns

Type	Description
quaternion

EulerYXZ(float3)

Returns a quaternion constructed by first performing a rotation around the y-axis, then the x-axis and finally the z-axis. All rotation angles are in radians and clockwise when looking along the rotation axis towards the origin.

Declaration

public static quaternion EulerYXZ(float3 xyz)

Parameters

Type	Name	Description
float3	xyz	A float3 vector containing the rotation angles around the x-, y- and z-axis measures in radians.

Returns

Type	Description
quaternion

EulerYZX(Single, Single, Single)

Returns a quaternion constructed by first performing a rotation around the y-axis, then the z-axis and finally the x-axis. All rotation angles are in radians and clockwise when looking along the rotation axis towards the origin.

Declaration

public static quaternion EulerYZX(float x, float y, float z)

Parameters

Type	Name	Description
System.Single	x	The rotation angle around the x-axis in radians.
System.Single	y	The rotation angle around the y-axis in radians.
System.Single	z	The rotation angle around the z-axis in radians.

Returns

Type	Description
quaternion

EulerYZX(float3)

Returns a quaternion constructed by first performing a rotation around the y-axis, then the z-axis and finally the x-axis. All rotation angles are in radians and clockwise when looking along the rotation axis towards the origin.

Declaration

public static quaternion EulerYZX(float3 xyz)

Parameters

Type	Name	Description
float3	xyz	A float3 vector containing the rotation angles around the x-, y- and z-axis measures in radians.

Returns

Type	Description
quaternion

EulerZXY(Single, Single, Single)

Returns a quaternion constructed by first performing a rotation around the z-axis, then the x-axis and finally the y-axis. All rotation angles are in radians and clockwise when looking along the rotation axis towards the origin. This is the default order rotation order in Unity.

Declaration

public static quaternion EulerZXY(float x, float y, float z)

Parameters

Type	Name	Description
System.Single	x	The rotation angle around the x-axis in radians.
System.Single	y	The rotation angle around the y-axis in radians.
System.Single	z	The rotation angle around the z-axis in radians.

Returns

Type	Description
quaternion

EulerZXY(float3)

Returns a quaternion constructed by first performing a rotation around the z-axis, then the x-axis and finally the y-axis. All rotation angles are in radians and clockwise when looking along the rotation axis towards the origin. This is the default order rotation order in Unity.

Declaration

public static quaternion EulerZXY(float3 xyz)

Parameters

Type	Name	Description
float3	xyz	A float3 vector containing the rotation angles around the x-, y- and z-axis measures in radians.

Returns

Type	Description
quaternion

EulerZYX(Single, Single, Single)

Returns a quaternion constructed by first performing a rotation around the z-axis, then the y-axis and finally the x-axis. All rotation angles are in radians and clockwise when looking along the rotation axis towards the origin.

Declaration

public static quaternion EulerZYX(float x, float y, float z)

Parameters

Type	Name	Description
System.Single	x	The rotation angle around the x-axis in radians.
System.Single	y	The rotation angle around the y-axis in radians.
System.Single	z	The rotation angle around the z-axis in radians.

Returns

Type	Description
quaternion

EulerZYX(float3)

Returns a quaternion constructed by first performing a rotation around the z-axis, then the y-axis and finally the x-axis. All rotation angles are in radians and clockwise when looking along the rotation axis towards the origin.

Declaration

public static quaternion EulerZYX(float3 xyz)

Parameters

Type	Name	Description
float3	xyz	A float3 vector containing the rotation angles around the x-, y- and z-axis measures in radians.

Returns

Type	Description
quaternion

GetHashCode()

Returns a hash code for the quaternion.

Declaration

public override int GetHashCode()

Returns

Type	Description
System.Int32

Overrides

System.ValueType.GetHashCode()

LookRotation(float3, float3)

Returns a quaternion view rotation given a unit length forward vector and a unit length up vector. The two input vectors are assumed to be unit length and not collinear. If these assumptions are not met use float3x3.LookRotationSafe instead.

Declaration

public static quaternion LookRotation(float3 forward, float3 up)

Parameters

Type	Name	Description
float3	forward
float3	up

Returns

Type	Description
quaternion

LookRotationSafe(float3, float3)

Returns a quaternion view rotation given a forward vector and an up vector. The two input vectors are not assumed to be unit length. If the magnitude of either of the vectors is so extreme that the calculation cannot be carried out reliably or the vectors are collinear, the identity will be returned instead.

Declaration

public static quaternion LookRotationSafe(float3 forward, float3 up)

Parameters

Type	Name	Description
float3	forward
float3	up

Returns

Type	Description
quaternion

RotateX(Single)

Returns a float4x4 matrix that rotates around the x-axis by a given number of radians.

Declaration

public static quaternion RotateX(float angle)

Parameters

Type	Name	Description
System.Single	angle	The clockwise rotation angle when looking along the x-axis towards the origin in radians.

Returns

Type	Description
quaternion

RotateY(Single)

Returns a float4x4 matrix that rotates around the y-axis by a given number of radians.

Declaration

public static quaternion RotateY(float angle)

Parameters

Type	Name	Description
System.Single	angle	The clockwise rotation angle when looking along the y-axis towards the origin in radians.

Returns

Type	Description
quaternion

RotateZ(Single)

Returns a float4x4 matrix that rotates around the z-axis by a given number of radians.

Declaration

public static quaternion RotateZ(float angle)

Parameters

Type	Name	Description
System.Single	angle	The clockwise rotation angle when looking along the z-axis towards the origin in radians.

Returns

Type	Description
quaternion

ToString()

Returns a string representation of the quaternion.

Declaration

public override string ToString()

Returns

Type	Description
System.String

Overrides

System.ValueType.ToString()

ToString(String, IFormatProvider)

Returns a string representation of the quaternion using a specified format and culture-specific format information.

Declaration

public string ToString(string format, IFormatProvider formatProvider)

Parameters

Type	Name	Description
System.String	format
System.IFormatProvider	formatProvider

Returns

Type	Description
System.String

Operators

Implicit(Quaternion to quaternion)

Declaration

public static implicit operator quaternion(Quaternion q)

Parameters

Type	Name	Description
Quaternion	q

Returns

Type	Description
quaternion

Implicit(float4 to quaternion)

Implicitly converts a float4 vector to a quaternion.

Declaration

public static implicit operator quaternion(float4 v)

Parameters

Type	Name	Description
float4	v

Returns

Type	Description
quaternion

Implicit(quaternion to Quaternion)

Declaration

public static implicit operator Quaternion(quaternion q)

Parameters

Type	Name	Description
quaternion	q

Returns

Type	Description
Quaternion