Quaternion Class Reference

Quaternion represents a rotation in 3D space using four components (x, y, z, w). It supports construction from axis-angle, Euler angles, or component values, and provides utility functions for normalization, interpolation, and conversion to matrices. More...

#include <Quaternion.h>

Public Member Functions
	Quaternion ()
	Default constructor initializes the quaternion to the identity quaternion. The identity quaternion represents no rotation and is defined as (0, 0, 0, 1).
	Quaternion (float inX, float inY, float inZ, float inW)
	Constructs a quaternion using four float values representing the components (x, y, z, w).
	Quaternion (const Vector3 &axis, float angle)
	Constructs a quaternion from an axis of rotation and an angle in radians. The axis is assumed to be normalized.
	Quaternion (float pitch, float yaw, float roll)
	Constructs a quaternion from pitch, yaw, and roll (Euler angles). The pitch is rotation about the X-axis, yaw about the Y-axis, and roll about the Z-axis.
void	Set (float inX, float inY, float inZ, float inW)
	Sets the quaternion components explicitly. This method is intended for direct initialization, not for converting axis/angle or Euler angles.
void	Conjugate ()
	Conjugates the quaternion, flipping the sign of the vector part (x, y, z).
void	Normalize ()
	Normalizes the quaternion, ensuring it has a unit length (i.e., it represents a valid rotation). This method alters the current quaternion.
float	LengthSqr () const
	Computes and returns the squared length of the quaternion. The squared length is the sum of the squares of the quaternion components.
float	Length () const
	Computes and returns the length (magnitude) of the quaternion. This is the square root of the squared length.
float	GetPitch () const
	Computes the pitch (rotation around the X-axis) of the quaternion.
float	GetYaw () const
	Computes the yaw (rotation around the Y-axis) of the quaternion.
float	GetRoll () const
	Computes the roll (rotation around the Z-axis) of the quaternion.
Quaternion	operator+ (const Quaternion &p)
class Matrix4	AsMatrix () const
	Converts the quaternion to a 4x4 matrix representation. The resulting matrix can be used for transforming 3D vectors by the quaternion's rotation.

Static Public Member Functions
static float	Dot (const Quaternion &a, const Quaternion &b)
	Computes the dot product between two quaternions.
static Quaternion	Normalize (const Quaternion &q)
	Returns a normalized version of the given quaternion. Normalization scales the quaternion so that its length is 1.
static Quaternion	Lerp (const Quaternion &a, const Quaternion &b, float f)
	Performs linear interpolation (Lerp) between two quaternions.
static Quaternion	Slerp (const Quaternion &a, const Quaternion &b, float f)
	Performs spherical linear interpolation (Slerp) between two quaternions.
static Quaternion	Concatenate (const Quaternion &q, const Quaternion &p)
	Concatenates two quaternions (i.e., applies one rotation after the other). This is equivalent to multiplying the two quaternions.
static Quaternion	LookAt (const Vector3 &forward, const Vector3 &up)
	Creates a quaternion representing the rotation to "look at" a target point. The resulting quaternion aligns the forward vector with the target direction, with the given up vector providing the direction of the "up" axis.
static Quaternion	LookAt (const Vector3 &origin, const Vector3 &target, const Vector3 &up)
	Creates a quaternion representing the rotation to "look at" a target point from an origin. This is equivalent to creating a "look at" rotation from the origin to the target, with the up vector.

Public Attributes
float	x
float	y
float	z
float	w

Static Public Attributes
static const Quaternion	Identity
	Identity quaternion: represents no rotation (used as a reference for default state).

Detailed Description

Quaternion represents a rotation in 3D space using four components (x, y, z, w). It supports construction from axis-angle, Euler angles, or component values, and provides utility functions for normalization, interpolation, and conversion to matrices.

Constructor & Destructor Documentation

Quaternion() [1/4]

Quaternion::Quaternion ( )

inline

Default constructor initializes the quaternion to the identity quaternion. The identity quaternion represents no rotation and is defined as (0, 0, 0, 1).

Quaternion() [2/4]

Quaternion::Quaternion ( float inX, float inY, float inZ, float inW )

explicit

Constructs a quaternion using four float values representing the components (x, y, z, w).

Parameters

inX	The x component of the quaternion's vector part.
inY	The y component of the quaternion's vector part.
inZ	The z component of the quaternion's vector part.
inW	The scalar component of the quaternion.

Quaternion() [3/4]

Quaternion::Quaternion ( const Vector3 & axis, float angle )

explicit

Constructs a quaternion from an axis of rotation and an angle in radians. The axis is assumed to be normalized.

Parameters

axis	The normalized axis of rotation.
angle	The rotation angle in radians.

Quaternion() [4/4]

Quaternion::Quaternion ( float pitch, float yaw, float roll )

explicit

Constructs a quaternion from pitch, yaw, and roll (Euler angles). The pitch is rotation about the X-axis, yaw about the Y-axis, and roll about the Z-axis.

Parameters

pitch	The rotation angle around the X-axis in radians.
yaw	The rotation angle around the Y-axis in radians.
roll	The rotation angle around the Z-axis in radians.

Member Function Documentation

AsMatrix()

Matrix4 Quaternion::AsMatrix

(

)

const

Converts the quaternion to a 4x4 matrix representation. The resulting matrix can be used for transforming 3D vectors by the quaternion's rotation.

Returns

A Matrix4 object representing the quaternion as a rotation matrix.

Concatenate()

Quaternion Quaternion::Concatenate ( const Quaternion & q, const Quaternion & p )

static

Concatenates two quaternions (i.e., applies one rotation after the other). This is equivalent to multiplying the two quaternions.

Parameters

q	The first quaternion (rotation to apply first).
p	The second quaternion (rotation to apply after q).

Returns

A new quaternion that represents the combined rotation.

Conjugate()

void Quaternion::Conjugate

(

)

Conjugates the quaternion, flipping the sign of the vector part (x, y, z).

Dot()

float Quaternion::Dot ( const Quaternion & a, const Quaternion & b )

static

Computes the dot product between two quaternions.

Parameters

a	The first quaternion.
b	The second quaternion.

Returns

The dot product between quaternions a and b.

GetPitch()

float Quaternion::GetPitch

(

)

const

Computes the pitch (rotation around the X-axis) of the quaternion.

Returns

The pitch angle in radians.

GetRoll()

float Quaternion::GetRoll

(

)

const

Computes the roll (rotation around the Z-axis) of the quaternion.

Returns

The roll angle in radians.

GetYaw()

float Quaternion::GetYaw

(

)

const

Computes the yaw (rotation around the Y-axis) of the quaternion.

Returns

The yaw angle in radians.

Length()

float Quaternion::Length

(

)

const

Computes and returns the length (magnitude) of the quaternion. This is the square root of the squared length.

Returns

The length of the quaternion.

LengthSqr()

float Quaternion::LengthSqr

(

)

const

Computes and returns the squared length of the quaternion. The squared length is the sum of the squares of the quaternion components.

Returns

The squared length of the quaternion.

Lerp()

Quaternion Quaternion::Lerp ( const Quaternion & a, const Quaternion & b, float f )

static

Performs linear interpolation (Lerp) between two quaternions.

Parameters

a	The starting quaternion.
b	The ending quaternion.
f	The interpolation factor (from 0 to 1).

Returns

The interpolated quaternion.

LookAt() [1/2]

Quaternion Quaternion::LookAt ( const Vector3 & forward, const Vector3 & up )

static

Creates a quaternion representing the rotation to "look at" a target point. The resulting quaternion aligns the forward vector with the target direction, with the given up vector providing the direction of the "up" axis.

Parameters

forward	The forward vector to align the quaternion to.
up	The up vector, typically (0, 1, 0).

Returns

A quaternion that rotates an object to face the target direction.

LookAt() [2/2]

Quaternion Quaternion::LookAt ( const Vector3 & origin, const Vector3 & target, const Vector3 & up )

static

Creates a quaternion representing the rotation to "look at" a target point from an origin. This is equivalent to creating a "look at" rotation from the origin to the target, with the up vector.

Parameters

origin	The starting point (usually the camera or object position).
target	The point to look at (the target position).
up	The up vector (usually (0, 1, 0)).

Returns

A quaternion representing the look-at rotation.

Normalize() [1/2]

void Quaternion::Normalize

(

)

Normalizes the quaternion, ensuring it has a unit length (i.e., it represents a valid rotation). This method alters the current quaternion.

Normalize() [2/2]

Quaternion Quaternion::Normalize ( const Quaternion & q )

static

Returns a normalized version of the given quaternion. Normalization scales the quaternion so that its length is 1.

Parameters

q	The quaternion to normalize.

Returns

A new quaternion that is the normalized version of q.

operator+()

Quaternion Quaternion::operator+ ( const Quaternion & p )

inline

Set()

void Quaternion::Set	(	float	inX,
		float	inY,
		float	inZ,
		float	inW )

Sets the quaternion components explicitly. This method is intended for direct initialization, not for converting axis/angle or Euler angles.

Parameters

inX	The x component of the quaternion.
inY	The y component of the quaternion.
inZ	The z component of the quaternion.
inW	The scalar component of the quaternion.

Slerp()

Quaternion Quaternion::Slerp ( const Quaternion & a, const Quaternion & b, float f )

static

Performs spherical linear interpolation (Slerp) between two quaternions.

Parameters

a	The starting quaternion.
b	The ending quaternion.
f	The interpolation factor (from 0 to 1).

Returns

The interpolated quaternion.

Member Data Documentation

Identity

const Quaternion Quaternion::Identity

static

Identity quaternion: represents no rotation (used as a reference for default state).

w

float Quaternion::w

x

float Quaternion::x

y

float Quaternion::y

z

float Quaternion::z

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The documentation for this class was generated from the following files:

• Engine/GameTool/Utility/Quaternion/Quaternion.h
• Engine/GameTool/Utility/Quaternion/Quaternion.cpp