Struct Quaternion

Represents a four dimensional mathematical quaternion. Euler angles are stored in: pitch, yaw, roll order (x, y, z).

Assembly: FlaxEngine.dll

File: Engine/Core/Math/Quaternion.h

Syntax

public struct Quaternion

Constructors

Quaternion()

Empty constructor.

Declaration

public Quaternion() = default

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

Init

Declaration

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

Parameters

float x X component value.

float y Y component value.

float z Z component value.

float w W component value.

Quaternion(const Float4& value)

Init

Declaration

public Quaternion(const Float4& value)

Parameters

Float4 value Vector to set value.

Fields

Identity

Identity quaternion (represents no rotation).

Declaration

public static Quaternion Identity

Field Value

Quaternion

One

Quaternion with all components equal 1.

Declaration

public static Quaternion One

Field Value

Quaternion

Raw

The raw value.

Declaration

public float Raw[4]

Field Value

float

Tolerance

Equality tolerance factor used when comparing quaternions via dot operation.

Declaration

public static constexpr Real Tolerance = 0.999999f

Field Value

constexpr Real

W

The W component of the quaternion.

Declaration

public float W

Field Value

float

X

The X component of the quaternion.

Declaration

public float X

Field Value

float

Y

The Y component of the quaternion.

Declaration

public float Y

Field Value

float

Z

The Z component of the quaternion.

Declaration

public float Z

Field Value

float

Zero

Quaternion with all components equal 0.

Declaration

public static Quaternion Zero

Field Value

Quaternion

Methods

Add(const Quaternion& left, const Quaternion& right, Quaternion& result)

Declaration

public static void Add(const Quaternion& left, const Quaternion& right, Quaternion& result)

Parameters

Quaternion left

Quaternion right

Quaternion result

AngleBetween(const Quaternion& a, const Quaternion& b)

Calculates the angle between two quaternions.

Declaration

public static float AngleBetween(const Quaternion& a, const Quaternion& b)

Parameters

Quaternion a First source quaternion.

Quaternion b Second source quaternion.

Returns

float Returns the angle in degrees between two rotations a and b.

Billboard(const Float3& objectPosition, const Float3& cameraPosition, const Float3& cameraUpFloat, const Float3& cameraForwardFloat, Quaternion& result)

Declaration

public static void Billboard(const Float3& objectPosition, const Float3& cameraPosition, const Float3& cameraUpFloat, const Float3& cameraForwardFloat, Quaternion& result)

Parameters

Float3 objectPosition

Float3 cameraPosition

Float3 cameraUpFloat

Float3 cameraForwardFloat

Quaternion result

Conjugate()

Conjugates the quaternion

Declaration

public void Conjugate()

Conjugated()

Gets the conjugated quaternion.

Declaration

public Quaternion Conjugated() const

Returns

Quaternion

Dot(const Quaternion& left, const Quaternion& right)

Calculates the dot product of two quaternions.

Declaration

public static float Dot(const Quaternion& left, const Quaternion& right)

Parameters

Quaternion left The first source quaternion.

Quaternion right The second source quaternion.

Returns

float The dot product of the two quaternions.

Euler(const Float3& euler)

Declaration

public static Quaternion Euler(const Float3& euler)

Parameters

Float3 euler

Returns

Quaternion

Euler(float x, float y, float z)

Declaration

public static Quaternion Euler(float x, float y, float z)

Parameters

float x

float y

float z

Returns

Quaternion

FindBetween(const Float3& from, const Float3& to)

Gets the quaternion that will rotate vector from into vector to, around their plan perpendicular axis.The input vectors don't need to be normalized.

Declaration

public static Quaternion FindBetween(const Float3& from, const Float3& to)

Parameters

Float3 from The source vector.

Float3 to The destination vector.

Returns

Quaternion The rotation.

FindBetween(const Float3& from, const Float3& to, Quaternion& result)

Gets the quaternion that will rotate vector from into vector to, around their plan perpendicular axis.The input vectors don't need to be normalized.

Declaration

public static void FindBetween(const Float3& from, const Float3& to, Quaternion& result)

Parameters

Float3 from The source vector.

Float3 to The destination vector.

Quaternion result The result.

FromDirection(const Float3& direction)

Calculates the orientation from the direction vector.

Declaration

public static Quaternion FromDirection(const Float3& direction)

Parameters

Float3 direction The direction vector (normalized).

Returns

Quaternion The orientation.

GetAngle()

Gets the angle of the quaternion.

Declaration

public float GetAngle() const

Returns

float

GetAxis()

Gets the axis components of the quaternion.

Declaration

public Float3 GetAxis() const

Returns

Float3

GetEuler()

Gets the euler angle (pitch, yaw, roll) in degrees.

Declaration

public Float3 GetEuler() const

Returns

Float3

GetRotationFromNormal(const Vector3& normal, const Transform& reference)

Gets rotation from a normal in relation to a transform. This function is especially useful for axis aligned faces, and with

Physics::RayCast

.

Declaration

public static Quaternion GetRotationFromNormal(const Vector3& normal, const Transform& reference)

Parameters

Vector3 normal The normal vector.

Transform reference The reference transform.

Returns

Quaternion The rotation from the normal vector.

GetRotationFromTo(const Float3& from, const Float3& to, const Float3& fallbackAxis)

Gets the shortest arc quaternion to rotate this vector to the destination vector.

Declaration

public static Quaternion GetRotationFromTo(const Float3& from, const Float3& to, const Float3& fallbackAxis)

Parameters

Float3 from The source vector.

Float3 to The destination vector.

Float3 fallbackAxis The fallback axis.

Returns

Quaternion The rotation.

GetRotationFromTo(const Float3& from, const Float3& to, Quaternion& result, const Float3& fallbackAxis)

Gets the shortest arc quaternion to rotate this vector to the destination vector.

Declaration

public static void GetRotationFromTo(const Float3& from, const Float3& to, Quaternion& result, const Float3& fallbackAxis)

Parameters

Float3 from The source vector.

Float3 to The destination vector.

Quaternion result The result.

Float3 fallbackAxis The fallback axis.

Invert()

Conjugates and renormalizes the quaternion.

Declaration

public void Invert()

Invert(const Quaternion& value)

Calculates the inverse of the specified quaternion.

Declaration

public static Quaternion Invert(const Quaternion& value)

Parameters

Quaternion value The quaternion whose inverse is to be calculated.

Returns

Quaternion The inverse of the specified quaternion.

Invert(const Quaternion& value, Quaternion& result)

Calculates the inverse of the specified quaternion.

Declaration

public static void Invert(const Quaternion& value, Quaternion& result)

Parameters

Quaternion value The quaternion whose inverse is to be calculated.

Quaternion result When the method completes, contains the inverse of the specified quaternion.

IsIdentity()

Gets a value indicating whether this instance is equivalent to the identity quaternion.

Declaration

public bool IsIdentity() const

Returns

bool

IsInfinity()

Returns true if quaternion has one or more components equal to +/- infinity.

Declaration

public bool IsInfinity() const

Returns

bool

IsNaN()

Returns true if quaternion has one or more components is not a number (NaN).

Declaration

public bool IsNaN() const

Returns

bool

IsNanOrInfinity()

Returns true if quaternion has one or more components equal to +/- infinity or NaN.

Declaration

public bool IsNanOrInfinity() const

Returns

bool

IsNormalized()

Gets a value indicting whether this instance is normalized.

Declaration

public bool IsNormalized() const

Returns

bool

Length()

Calculates the length of the quaternion.

Declaration

public float Length() const

Returns

float

LengthSquared()

Calculates the squared length of the quaternion.

Declaration

public float LengthSquared() const

Returns

float

Lerp(const Quaternion& start, const Quaternion& end, float amount)

Declaration

public static Quaternion Lerp(const Quaternion& start, const Quaternion& end, float amount)

Parameters

Quaternion start

Quaternion end

float amount

Returns

Quaternion

Lerp(const Quaternion& start, const Quaternion& end, float amount, Quaternion& result)

Declaration

public static void Lerp(const Quaternion& start, const Quaternion& end, float amount, Quaternion& result)

Parameters

Quaternion start

Quaternion end

float amount

Quaternion result

LookAt(const Float3& eye, const Float3& target, const Float3& up, Quaternion& result)

Declaration

public static void LookAt(const Float3& eye, const Float3& target, const Float3& up, Quaternion& result)

Parameters

Float3 eye

Float3 target

Float3 up

Quaternion result

LookRotation(const Float3& forward, const Float3& up)

Creates a rotation with the specified forward and upwards directions.

Declaration

public static Quaternion LookRotation(const Float3& forward, const Float3& up)

Parameters

Float3 forward The forward direction. Direction to orient towards.

Float3 up Up direction. Constrains y axis orientation to a plane this vector lies on. This rule might be broken if forward and up direction are nearly parallel.

Returns

Quaternion The calculated quaternion.

LookRotation(const Float3& forward, const Float3& up, Quaternion& result)

Creates a rotation with the specified forward and upwards directions.

Declaration

public static void LookRotation(const Float3& forward, const Float3& up, Quaternion& result)

Parameters

Float3 forward The forward direction. Direction to orient towards.

Float3 up The up direction. Constrains y axis orientation to a plane this vector lies on. This rule might be broken if forward and up direction are nearly parallel.

Quaternion result The calculated quaternion.

Multiply(const Quaternion& left, const Quaternion& right, Quaternion& result)

Declaration

public static void Multiply(const Quaternion& left, const Quaternion& right, Quaternion& result)

Parameters

Quaternion left

Quaternion right

Quaternion result

Multiply(const Quaternion& other)

Multiplies a quaternion by another.

Declaration

public void Multiply(const Quaternion& other)

Parameters

Quaternion other The other quaternion to multiply by.

Multiply(const Quaternion& value, float scale, Quaternion& result)

Declaration

public static void Multiply(const Quaternion& value, float scale, Quaternion& result)

Parameters

Quaternion value

float scale

Quaternion result

Multiply(float scale)

Scales a quaternion by the given value.

Declaration

public void Multiply(float scale)

Parameters

float scale The amount by which to scale the quaternion.

NearEqual(const Quaternion& a, const Quaternion& b)

Determines whether the specified Quaternion structures are equal.

Declaration

public static bool NearEqual(const Quaternion& a, const Quaternion& b)

Parameters

Quaternion a The first Quaternion to compare.

Quaternion b The second Quaternion to compare.

Returns

bool true if the specified Quaternion structures are equal; otherwise, false.

NearEqual(const Quaternion& a, const Quaternion& b, float epsilon)

Determines whether the specified Quaternion structures are equal.

Declaration

public static bool NearEqual(const Quaternion& a, const Quaternion& b, float epsilon)

Parameters

Quaternion a The first Quaternion to compare.

Quaternion b The second Quaternion to compare.

float epsilon The comparision threshold value.

Returns

bool true if the specified Quaternion structures are equal within the specified epsilon range; otherwise, false.

Negate(const Quaternion& value, Quaternion& result)

Declaration

public static void Negate(const Quaternion& value, Quaternion& result)

Parameters

Quaternion value

Quaternion result

Normalize()

Converts the quaternion into a unit quaternion.

Declaration

public void Normalize()

operator!=(const Quaternion& other)

Determines whether the specified Quaternion is equal to this instance.

Declaration

public bool operator!=(const Quaternion& other) const

Parameters

Quaternion other The Quaternion to compare with this instance.

Returns

bool true if the specified Quaternion isn't equal to this instance; otherwise, false.

operator-(const Quaternion& b)

Subtracts two quaternions.

Declaration

public Quaternion operator-(const Quaternion& b) const

Parameters

Quaternion b The quaternion to subtract.

Returns

Quaternion The difference of the two quaternions.

operator*(const Float3& vector)

Transforms a vector by the given rotation.

Declaration

public Float3 operator*(const Float3& vector) const

Parameters

Float3 vector The vector to transform.

Returns

Float3 The scaled vector.

operator*(const Quaternion& b)

Multiplies two quaternions.

Declaration

public Quaternion operator*(const Quaternion& b) const

Parameters

Quaternion b The quaternion to multiply.

Returns

Quaternion The multiplied quaternion.

operator*(float scale)

Scales a quaternion by the given value.

Declaration

public Quaternion operator*(float scale) const

Parameters

float scale The amount by which to scale the quaternion.

Returns

Quaternion The scaled quaternion.

operator*=(const Quaternion& b)

Multiplies two quaternions.

Declaration

public Quaternion operator*=(const Quaternion& b)

Parameters

Quaternion b The quaternion to multiply.

Returns

Quaternion The multiplied quaternion.

operator*=(float scale)

Scales a quaternion by the given value.

Declaration

public Quaternion operator*=(float scale)

Parameters

float scale The amount by which to scale the quaternion.

Returns

Quaternion This instance.

operator+(const Quaternion& b)

Adds two quaternions.

Declaration

public Quaternion operator+(const Quaternion& b) const

Parameters

Quaternion b The quaternion to add.

Returns

Quaternion The sum of the two quaternions.

operator+=(const Quaternion& b)

Adds two quaternions.

Declaration

public Quaternion operator+=(const Quaternion& b)

Parameters

Quaternion b The quaternion to add.

Returns

Quaternion The sum of the two quaternions.

operator-=(const Quaternion& b)

Subtracts two quaternions.

Declaration

public Quaternion operator-=(const Quaternion& b)

Parameters

Quaternion b The quaternion to subtract.

Returns

Quaternion The difference of the two quaternions.

operator==(const Quaternion& other)

Determines whether the specified Quaternion is equal to this instance.

Declaration

public bool operator==(const Quaternion& other) const

Parameters

Quaternion other The Quaternion to compare with this instance.

Returns

bool true if the specified Quaternion is equal to this instance; otherwise, false.

RotationAxis(const Float3& axis, float angle, Quaternion& result)

Declaration

public static void RotationAxis(const Float3& axis, float angle, Quaternion& result)

Parameters

Float3 axis

float angle

Quaternion result

RotationCosAxis(const Float3& axis, float cos, Quaternion& result)

Declaration

public static void RotationCosAxis(const Float3& axis, float cos, Quaternion& result)

Parameters

Float3 axis

float cos

Quaternion result

RotationLookAt(const Float3& forward, const Float3& up, Quaternion& result)

Declaration

public static void RotationLookAt(const Float3& forward, const Float3& up, Quaternion& result)

Parameters

Float3 forward

Float3 up

Quaternion result

RotationMatrix(const Matrix& matrix)

Declaration

public static Quaternion RotationMatrix(const Matrix& matrix)

Parameters

Matrix matrix

Returns

Quaternion

RotationMatrix(const Matrix& matrix, Quaternion& result)

Declaration

public static void RotationMatrix(const Matrix& matrix, Quaternion& result)

Parameters

Matrix matrix

Quaternion result

RotationMatrix(const Matrix3x3& matrix, Quaternion& result)

Declaration

public static void RotationMatrix(const Matrix3x3& matrix, Quaternion& result)

Parameters

Matrix3x3 matrix

Quaternion result

RotationYawPitchRoll(float yaw, float pitch, float roll)

Declaration

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

Parameters

float yaw

float pitch

float roll

Returns

Quaternion

RotationYawPitchRoll(float yaw, float pitch, float roll, Quaternion& result)

Declaration

public static void RotationYawPitchRoll(float yaw, float pitch, float roll, Quaternion& result)

Parameters

float yaw

float pitch

float roll

Quaternion result

Slerp(const Quaternion& start, const Quaternion& end, float amount)

Declaration

public static Quaternion Slerp(const Quaternion& start, const Quaternion& end, float amount)

Parameters

Quaternion start

Quaternion end

float amount

Returns

Quaternion

Slerp(const Quaternion& start, const Quaternion& end, float amount, Quaternion& result)

Declaration

public static void Slerp(const Quaternion& start, const Quaternion& end, float amount, Quaternion& result)

Parameters

Quaternion start

Quaternion end

float amount

Quaternion result

Subtract(const Quaternion& left, const Quaternion& right, Quaternion& result)

Declaration

public static void Subtract(const Quaternion& left, const Quaternion& right, Quaternion& result)

Parameters

Quaternion left

Quaternion right

Quaternion result

ToString()

Declaration

public String ToString() const

Returns

String