#include <AH/Math/Quaternion.hpp>

Detailed Description

Type for quaternions of floating point numbers.

Quaternions can be multiplied (Hamiltonian product), normalized and can perform rotations of vectors. Quaternion also has an implementation of the following operators:

- (conjugate)
+, +=, -, -= (Hamiltonian product of quaternions, adds and subtracts angles)
*, *=, /, /= (multiplication and division by scalars)
==, != (equality)
<< (printing)

Examples: Quaternion.ino.

Definition at line 57 of file Quaternion.hpp.

Collaboration diagram for Quaternion:

Public Member Functions
	Quaternion ()=default
	Create a quaternion that is initialized to the identity quaternion. More...

	Quaternion (float w, float x, float y, float z)
	Create a quaterion with the given values for w, x, y and z. More...

Quaternion &	operator+= (Quaternion rhs)
	Sum of two quaterions uses quaternion multiplication. More...

Quaternion	operator+ (Quaternion rhs) const
	Sum of two quaternions uses quaternion multiplication. More...

Quaternion	conjugated () const
	Complex conjugate (doesn't change the original quaternion). More...

Quaternion	operator- () const
	Negated quaternion is its conjugate. More...

Quaternion &	operator-= (Quaternion rhs)
	Difference of two quaternions `a` and `b` is the quaternion multiplication of `a` and the conjugate of `b`. More...

Quaternion	operator- (Quaternion rhs) const
	Difference of two quaternions `a` and `b` is the quaternion multiplication of `a` and the conjugate of `b`. More...

Quaternion &	operator*= (float rhs)
	Scalar multiplication. More...

Quaternion	operator* (float rhs) const
	Scalar multiplication. More...

Quaternion &	operator/= (float rhs)
	Scalar division. More...

Quaternion	operator/ (float rhs) const
	Scalar division. More...

float	normSquared () const
	Norm squared. More...

float	norm () const
	Norm. More...

Quaternion &	normalize ()
	Normalize this quaternion. More...

Quaternion	normalized () const
	Normalize a copy of this quaternion (doesn't change the original quaternion). More...

Vec3f	rotate (Vec3f v) const
	Rotate vector by this quaternion. More...

bool	operator== (Quaternion rhs) const
	Equality check. More...

bool	operator!= (Quaternion rhs) const
	Inequality check. More...

Static Public Member Functions
static Quaternion	identity ()
	Identity quaternion (1,0,0,0). More...

static Quaternion	fromDirection (Vec3f v)
	Calculate the quaternion that satisfies the following: `result.rotate(Vec3f{0, 0, 1}) == v.normalized()`. More...

static Quaternion	fromXYAngle (float xAngle, float yAngle)
	Calculate the quaternion from a vector that makes a given angle with the XZ plane and a given angle with the YZ plane. More...

static Quaternion	hamiltonianProduct (Quaternion q, Quaternion r)
	Quaternion multiplication. More...

Public Attributes
float	w = 1.0
	Scalar (real) component. More...

float	x = 0.0
	First vector (imaginary) component \( \mathbf{i} \). More...

float	y = 0.0
	Second vector (imaginary) component \( \mathbf{j} \). More...

float	z = 0.0
	Third vector (imaginary) component \( \mathbf{k} \). More...

Related Functions
(Note that these are not member functions.)
Quaternion	operator* (float lhs, Quaternion rhs)
	Scalar multiplication. More...

Print &	operator<< (Print &os, Quaternion e)
	Printing. More...

Constructor & Destructor Documentation

◆ Quaternion() [1/2]

Quaternion ( )

default

Create a quaternion that is initialized to the identity quaternion.

◆ Quaternion() [2/2]

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

inline

Create a quaterion with the given values for w, x, y and z.

Definition at line 66 of file Quaternion.hpp.

Member Function Documentation

◆ operator+=()

Quaternion & operator+= ( Quaternion rhs )

inline

Sum of two quaterions uses quaternion multiplication.

(Composition of the two rotations.)

Definition at line 70 of file Quaternion.hpp.

◆ operator+()

Quaternion operator+ ( Quaternion rhs ) const

inline

Sum of two quaternions uses quaternion multiplication.

(Composition of the two rotations.)

Definition at line 75 of file Quaternion.hpp.

◆ conjugated()

Quaternion conjugated ( ) const

inline

Complex conjugate (doesn't change the original quaternion).

Definition at line 80 of file Quaternion.hpp.

◆ operator-() [1/2]

Quaternion operator- ( ) const

inline

Negated quaternion is its conjugate.

Definition at line 82 of file Quaternion.hpp.

◆ operator-=()

Quaternion & operator-= ( Quaternion rhs )

inline

Difference of two quaternions a and b is the quaternion multiplication of a and the conjugate of b.

(Composition of the rotation of a and the inverse rotation of b.)

Definition at line 87 of file Quaternion.hpp.

◆ operator-() [2/2]

Quaternion operator- ( Quaternion rhs ) const

inline

Difference of two quaternions a and b is the quaternion multiplication of a and the conjugate of b.

(Composition of the rotation of a and the inverse rotation of b.)

Definition at line 91 of file Quaternion.hpp.

◆ operator*=()

Quaternion & operator*= ( float rhs )

inline

Scalar multiplication.

Definition at line 98 of file Quaternion.hpp.

◆ operator*()

Quaternion operator* ( float rhs ) const

inline

Scalar multiplication.

Definition at line 106 of file Quaternion.hpp.

◆ operator/=()

Quaternion & operator/= ( float rhs )

inline

Scalar division.

Definition at line 113 of file Quaternion.hpp.

◆ operator/()

Quaternion operator/ ( float rhs ) const

inline

Scalar division.

Definition at line 121 of file Quaternion.hpp.

◆ normSquared()

float normSquared ( ) const

inline

Norm squared.

Definition at line 128 of file Quaternion.hpp.

◆ norm()

float norm ( ) const

inline

Norm.

Definition at line 130 of file Quaternion.hpp.

◆ normalize()

Quaternion & normalize ( )

inline

Normalize this quaternion.

Definition at line 132 of file Quaternion.hpp.

◆ normalized()

Quaternion normalized ( ) const

inline

Normalize a copy of this quaternion (doesn't change the original quaternion).

Definition at line 135 of file Quaternion.hpp.

◆ rotate()

Vec3f rotate ( Vec3f v ) const

inline

Rotate vector by this quaternion.

This function uses the normalized version of this quaternion.

Note: This function is not the same as quatrotate in MATLAB! MATLAB rotates by the conjugate of the quaternion, while this function rotates by the quaternion itself.

Examples: Quaternion.ino.

Definition at line 146 of file Quaternion.hpp.

◆ operator==()

bool operator== ( Quaternion rhs ) const

inline

Equality check.

Definition at line 176 of file Quaternion.hpp.

◆ operator!=()

bool operator!= ( Quaternion rhs ) const

inline

Inequality check.

Definition at line 181 of file Quaternion.hpp.

◆ identity()

static Quaternion identity ( )

inlinestatic

Identity quaternion (1,0,0,0).

Definition at line 184 of file Quaternion.hpp.

◆ fromDirection()

static Quaternion fromDirection ( Vec3f v )

inlinestatic

Calculate the quaternion that satisfies the following: result.rotate(Vec3f{0, 0, 1}) == v.normalized().

Examples: Quaternion.ino.

Definition at line 190 of file Quaternion.hpp.

◆ fromXYAngle()

static Quaternion fromXYAngle	(	float	xAngle,
		float	yAngle
	)

inlinestatic

Calculate the quaternion from a vector that makes a given angle with the XZ plane and a given angle with the YZ plane.

Parameters

xAngle	The angle the vector should make with the XZ plane. A positive value represents a positive rotation about the x-axis.
yAngle	The angle the vector should make with the YZ plane. A positive value represents a positive rotation about the y-axis.

Returns: A quaternion from the vector {tan(yAngle), -tan(xAngle), 1}.

Definition at line 253 of file Quaternion.hpp.

◆ hamiltonianProduct()

static Quaternion hamiltonianProduct	(	Quaternion	q,
		Quaternion	r
	)

inlinestatic

Quaternion multiplication.

Definition at line 263 of file Quaternion.hpp.

Member Data Documentation

◆ w

float w = 1.0

Scalar (real) component.

Examples: Quaternion.ino.

Definition at line 58 of file Quaternion.hpp.

◆ x

float x = 0.0

First vector (imaginary) component \( \mathbf{i} \).

Examples: Quaternion.ino.

Definition at line 59 of file Quaternion.hpp.

◆ y

float y = 0.0

Second vector (imaginary) component \( \mathbf{j} \).

Examples: Quaternion.ino.

Definition at line 60 of file Quaternion.hpp.

◆ z

float z = 0.0

Third vector (imaginary) component \( \mathbf{k} \).

Examples: Quaternion.ino.

Definition at line 61 of file Quaternion.hpp.

The documentation for this struct was generated from the following file:

Quaternion.hpp

Detailed Description

Public Member Functions

Static Public Member Functions

Public Attributes

Related Functions

Constructor & Destructor Documentation

◆ Quaternion() [1/2]

◆ Quaternion() [2/2]

Member Function Documentation

◆ operator+=()

◆ operator+()

◆ conjugated()

◆ operator-() [1/2]

◆ operator-=()

◆ operator-() [2/2]

◆ operator*=()

◆ operator*()

◆ operator/=()

◆ operator/()

◆ normSquared()

◆ norm()

◆ normalize()

◆ normalized()

◆ rotate()

◆ operator==()

◆ operator!=()

◆ identity()

◆ fromDirection()

◆ fromXYAngle()

◆ hamiltonianProduct()

Member Data Documentation

◆ w

◆ x

◆ y

◆ z