Quaternion with Quantity components. More...

#include <Quaternion.hpp>

Public Member Functions
constexpr	Quaternion ()
	Default constructor - identity quaternion (1 + 0i + 0j + 0k)

constexpr	Quaternion (T w_, T x_, T y_, T z_)
	Construct from scalar and vector components.

constexpr	Quaternion (T w_, const Vector3< T > &v_)
	Construct from scalar and vector parts.

constexpr	Quaternion (const Vector3< T > &v_)
	Construct from vector part only (scalar part = 0)

constexpr Vector3< T >	ToVector () const
	Extract the vector part as a Vector3.

constexpr T	ToQuantity () const
	Extract the scalar part.

auto	LengthSquared () const
	Squared magnitude.

auto	Length () const
	Magnitude (sqrt of LengthSquared)

constexpr Quaternion	Conjugated () const
	Conjugate: (w + xi + yj + zk) -> (w - xi - yj - zk)

auto	Inversed () const
	Inverse: q^(-1) = conjugate / \|q\|^2.

auto	Normalized () const
	Normalized quaternion (unit quaternion)

bool	IsUnit () const
	Check if the quaternion is a unit quaternion.

auto	Rotated (const Vector3< T > &v) const
	Rotate a vector by this quaternion.

template<typename U >
constexpr auto	operator* (const Quaternion< U > &other) const
	Quaternion multiplication.

template<typename U >
constexpr auto	operator+ (const Quaternion< U > &other) const
	Quaternion addition.

template<typename U >
constexpr auto	operator- (const Quaternion< U > &other) const
	Quaternion subtraction.

constexpr auto	operator- () const
	Unary negation.

template<typename U >
constexpr auto	operator* (Quantity< U > scalar) const
	Scalar multiplication.

template<typename U >
constexpr auto	operator/ (U scalar) const
	Scalar division.

template<typename U >
constexpr Quaternion &	operator+= (const Quaternion< U > &other)
	Addition assignment.

template<typename U >
constexpr Quaternion &	operator-= (const Quaternion< U > &other)
	Subtraction assignment.

template<typename U >
constexpr Quaternion &	operator*= (U scalar)
	Scalar multiplication assignment.

template<typename U >
constexpr Quaternion &	operator/= (U scalar)
	Scalar division assignment.

template<typename U >
constexpr bool	operator== (const Quaternion< U > &other) const
	Equality comparison.

template<typename U >
constexpr bool	operator!= (const Quaternion< U > &other) const
	Inequality comparison.

template<typename UnitT >
Quaternion< Quantity< UnitT > >	as () const
	Convert all components to a different unit of the same dimension.

template<typename U >
constexpr auto	Dot (const Quaternion< U > &other) const
	Dot product of two quaternions.

constexpr T &	operator[] (int i)
	Index-based access (non-const)

constexpr const T &	operator[] (int i) const
	Index-based access (const)

Static Public Member Functions
static Quaternion	FromAxisAngle (const Vector3< T > &axis, const Scalar theta)
	Create a unit quaternion from axis and angle.

static Quaternion	FromEuler (const Scalar yaw, const Scalar pitch, const Scalar roll)
	Create a unit quaternion from Euler angles (ZYX convention)

template<typename U >
static auto	Slerp (const Quaternion &q1, const Quaternion< U > &q2, const Scalar t)
	Spherical linear interpolation between two quaternions.

Public Attributes
T	w

T	x

T	y

T	z

Friends
std::ostream &	operator<< (std::ostream &os, const Quaternion &q)
	Stream insertion operator for Quaternion.

Detailed Description

template<typename T>
struct Phyth::Quaternion< T >

Quaternion with Quantity components.

A quaternion represents rotations in 3D space. It consists of a scalar part (w) and a vector part (x, y, z).

This implementation uses Quantity types for all components, ensuring that quaternion operations are dimensionally consistent. For rotation quaternions, all components should be dimensionless (Scalar type).

Template Parameters

T	Component type (must be a Quantity instantiation, typically Scalar)

Example: using Rotation = Quaternion<Scalar>;

// Rotate a vector by 90 degrees around Z axis auto q = Rotation::FromAxisAngle(Vector3<Scalar>(0, 0, 1), 90.0_deg); auto v = Vector3<Quantity<Meter>>(1.0_m, 0_m, 0_m); auto rotated = q.Rotated(v); // (0_m, 1_m, 0_m)

Definition at line 33 of file Quaternion.hpp.

Constructor & Destructor Documentation

◆ Quaternion() [1/4]

template<typename T >

constexpr Phyth::Quaternion< T >::Quaternion ( )

inlineconstexpr

Default constructor - identity quaternion (1 + 0i + 0j + 0k)

Definition at line 49 of file Quaternion.hpp.

◆ Quaternion() [2/4]

template<typename T >

constexpr Phyth::Quaternion< T >::Quaternion	(	T	w_,
		T	x_,
		T	y_,
		T	z_
	)

inlineconstexpr

Construct from scalar and vector components.

Parameters

w_	Scalar part
x_	X component of vector part
y_	Y component of vector part
z_	Z component of vector part

Definition at line 60 of file Quaternion.hpp.

◆ Quaternion() [3/4]

template<typename T >

constexpr Phyth::Quaternion< T >::Quaternion	(	T	w_,
		const Vector3< T > &	v_
	)

inlineconstexpr

Construct from scalar and vector parts.

Parameters

w_	Scalar part
v_	Vector part (x, y, z)

Definition at line 69 of file Quaternion.hpp.

◆ Quaternion() [4/4]

template<typename T >

constexpr Phyth::Quaternion< T >::Quaternion ( const Vector3< T > & v_ )

inlineexplicitconstexpr

Construct from vector part only (scalar part = 0)

This creates a pure quaternion (0 + v), useful for representing vectors in quaternion form.

Parameters

v_	Vector part

Definition at line 80 of file Quaternion.hpp.

Member Function Documentation

◆ as()

template<typename T >

template<typename UnitT >

Quaternion< Quantity< UnitT > > Phyth::Quaternion< T >::as ( ) const

inline

Convert all components to a different unit of the same dimension.

Template Parameters

UnitT The target unit type

Returns: Quaternion with each component converted to UnitT

Definition at line 351 of file Quaternion.hpp.

◆ Conjugated()

template<typename T >

constexpr Quaternion Phyth::Quaternion< T >::Conjugated ( ) const

inlineconstexpr

Conjugate: (w + xi + yj + zk) -> (w - xi - yj - zk)

For unit quaternions, the conjugate is also the inverse.

Definition at line 157 of file Quaternion.hpp.

◆ Dot()

template<typename T >

template<typename U >

constexpr auto Phyth::Quaternion< T >::Dot ( const Quaternion & other ) const

inlineconstexpr

Dot product of two quaternions.

Template Parameters

U	Component type of the other quaternion

Parameters

other The other quaternion

Returns: The dot product as a Quantity

Definition at line 408 of file Quaternion.hpp.

◆ FromAxisAngle()

template<typename T >

static Quaternion Phyth::Quaternion< T >::FromAxisAngle	(	const Vector3< T > &	axis,
		const Scalar	theta
	)

inlinestatic

Create a unit quaternion from axis and angle.

Parameters

axis	Unit vector axis of rotation (must be normalized)
theta	Rotation angle in radians (dimensionless)

Returns: Unit quaternion representing the rotation

Example: auto axis = Vector3<Scalar>(0, 0, 1); auto q = Quaternion<Scalar>::FromAxisAngle(axis, 90.0_deg);

Definition at line 94 of file Quaternion.hpp.

◆ FromEuler()

template<typename T >

static Quaternion Phyth::Quaternion< T >::FromEuler	(	const Scalar	yaw,
		const Scalar	pitch,
		const Scalar	roll
	)

inlinestatic

Create a unit quaternion from Euler angles (ZYX convention)

Converts yaw-pitch-roll Euler angles to a quaternion. The rotation order is: first roll (X), then pitch (Y), then yaw (Z).

Parameters

yaw	Rotation around Z axis (radians, dimensionless)
pitch	Rotation around Y axis (radians, dimensionless)
roll	Rotation around X axis (radians, dimensionless)

Returns: Unit quaternion representing the combined rotation

Definition at line 112 of file Quaternion.hpp.

◆ Inversed()

template<typename T >

auto Phyth::Quaternion< T >::Inversed ( ) const

inline

Inverse: q^(-1) = conjugate / |q|^2.

For unit quaternions, inverse equals conjugate.

Definition at line 166 of file Quaternion.hpp.

◆ IsUnit()

template<typename T >

bool Phyth::Quaternion< T >::IsUnit ( ) const

inline

Check if the quaternion is a unit quaternion.

Returns true if |w^2 + x^2 + y^2 + z^2 - 1| < Config::tolerance

Definition at line 193 of file Quaternion.hpp.

◆ Length()

template<typename T >

auto Phyth::Quaternion< T >::Length ( ) const

inline

Magnitude (sqrt of LengthSquared)

Definition at line 148 of file Quaternion.hpp.

◆ LengthSquared()

template<typename T >

auto Phyth::Quaternion< T >::LengthSquared ( ) const

inline

Squared magnitude.

Returns w^2 + x^2 + y^2 + z^2

Definition at line 143 of file Quaternion.hpp.

◆ Normalized()

template<typename T >

auto Phyth::Quaternion< T >::Normalized ( ) const

inline

Normalized quaternion (unit quaternion)

Definition at line 178 of file Quaternion.hpp.

◆ operator!=()

template<typename T >

template<typename U >

constexpr bool Phyth::Quaternion< T >::operator!= ( const Quaternion & other ) const

inlineconstexpr

Inequality comparison.

Definition at line 340 of file Quaternion.hpp.

◆ operator*() [1/2]

template<typename T >

template<typename U >

constexpr auto Phyth::Quaternion< T >::operator* ( const Quaternion & other ) const

inlineconstexpr

Quaternion multiplication.

The product of two quaternions represents the composition of their rotations.

Definition at line 223 of file Quaternion.hpp.

◆ operator*() [2/2]

template<typename T >

template<typename U >

constexpr auto Phyth::Quaternion< T >::operator* ( Quantity scalar ) const

inlineconstexpr

Scalar multiplication.

Parameters

scalar The scalar multiplier (must be a Quantity, typically Scalar)

Returns: Quaternion with all components multiplied by scalar

Definition at line 267 of file Quaternion.hpp.

◆ operator*=()

template<typename T >

template<typename U >

constexpr Quaternion & Phyth::Quaternion< T >::operator*= ( U scalar )

inlineconstexpr

Scalar multiplication assignment.

Definition at line 314 of file Quaternion.hpp.

◆ operator+()

template<typename T >

template<typename U >

constexpr auto Phyth::Quaternion< T >::operator+ ( const Quaternion & other ) const

inlineconstexpr

Quaternion addition.

Definition at line 235 of file Quaternion.hpp.

◆ operator+=()

template<typename T >

template<typename U >

constexpr Quaternion & Phyth::Quaternion< T >::operator+= ( const Quaternion & other )

inlineconstexpr

Addition assignment.

Definition at line 294 of file Quaternion.hpp.

◆ operator-() [1/2]

template<typename T >

constexpr auto Phyth::Quaternion< T >::operator- ( ) const

inlineconstexpr

Unary negation.

Definition at line 256 of file Quaternion.hpp.

◆ operator-() [2/2]

template<typename T >

template<typename U >

constexpr auto Phyth::Quaternion< T >::operator- ( const Quaternion & other ) const

inlineconstexpr

Quaternion subtraction.

Definition at line 246 of file Quaternion.hpp.

◆ operator-=()

template<typename T >

template<typename U >

constexpr Quaternion & Phyth::Quaternion< T >::operator-= ( const Quaternion & other )

inlineconstexpr

Subtraction assignment.

Definition at line 304 of file Quaternion.hpp.

◆ operator/()

template<typename T >

template<typename U >

constexpr auto Phyth::Quaternion< T >::operator/ ( U scalar ) const

inlineconstexpr

Scalar division.

Parameters

scalar The scalar divisor (must be a Quantity, typically Scalar)

Returns: Quaternion with all components divided by scalar

Definition at line 283 of file Quaternion.hpp.

◆ operator/=()

template<typename T >

template<typename U >

constexpr Quaternion & Phyth::Quaternion< T >::operator/= ( U scalar )

inlineconstexpr

Scalar division assignment.

Definition at line 324 of file Quaternion.hpp.

◆ operator==()

template<typename T >

template<typename U >

constexpr bool Phyth::Quaternion< T >::operator== ( const Quaternion & other ) const

inlineconstexpr

Equality comparison.

Definition at line 334 of file Quaternion.hpp.

◆ operator[]() [1/2]

template<typename T >

constexpr T & Phyth::Quaternion< T >::operator[] ( int i )

inlineconstexpr

Index-based access (non-const)

Parameters

i	Index: 0 = w, 1 = x, 2 = y, 3 = z

Returns: Reference to the component

Definition at line 418 of file Quaternion.hpp.

◆ operator[]() [2/2]

template<typename T >

constexpr const T & Phyth::Quaternion< T >::operator[] ( int i ) const

inlineconstexpr

Index-based access (const)

Parameters

i	Index: 0 = w, 1 = x, 2 = y, 3 = z

Returns: Const reference to the component

Definition at line 428 of file Quaternion.hpp.

◆ Rotated()

template<typename T >

auto Phyth::Quaternion< T >::Rotated ( const Vector3< T > & v ) const

inline

Rotate a vector by this quaternion.

The rotation is performed as: q * (0 + v) * q^(-1)

Parameters

v	The vector to rotate

Returns: The rotated vector

Example: auto q = Quaternion<Scalar>::FromAxisAngle(axis, 90.0_deg); auto v = Vector3<Quantity<Meter>>(1.0_m, 0_m, 0_m); auto rotated = q.Rotated(v);

Definition at line 210 of file Quaternion.hpp.

◆ Slerp()

template<typename T >

template<typename U >

static auto Phyth::Quaternion< T >::Slerp	(	const Quaternion< T > &	q1,
		const Quaternion< U > &	q2,
		const Scalar	t
	)

inlinestatic

Spherical linear interpolation between two quaternions.

Interpolates along the shortest path on the unit sphere. Handles negative dot products to maintain the shortest path.

Template Parameters

U	Component type of the second quaternion

Parameters

q1	Start quaternion
q2	End quaternion
t	Interpolation parameter [0, 1] (dimensionless scalar)

Returns: Interpolated quaternion (unit quaternion)

Example: auto q1 = Quaternion<Scalar>(); // identity auto q2 = Quaternion<Scalar>::FromAxisAngle(axis, 90.0_deg); auto q_mid = Quaternion<Scalar>::Slerp(q1, q2, 0.5); // 45-degree rotation

Definition at line 378 of file Quaternion.hpp.

◆ ToQuantity()

template<typename T >

constexpr T Phyth::Quaternion< T >::ToQuantity ( ) const

inlineconstexpr

Extract the scalar part.

Definition at line 134 of file Quaternion.hpp.

◆ ToVector()

template<typename T >

constexpr Vector3< T > Phyth::Quaternion< T >::ToVector ( ) const

inlineconstexpr

Extract the vector part as a Vector3.

Definition at line 129 of file Quaternion.hpp.

Friends And Related Symbol Documentation

◆ operator<<

template<typename T >

std::ostream & operator<<	(	std::ostream &	os,
		const Quaternion< T > &	q
	)

friend

Stream insertion operator for Quaternion.

Output format: "(w + xi + yj + zk)" where each component uses Quantity's stream formatting.

Definition at line 438 of file Quaternion.hpp.

Member Data Documentation

◆ w

template<typename T >

T Phyth::Quaternion< T >::w

Scalar (real) part

Definition at line 38 of file Quaternion.hpp.

◆ x

template<typename T >

T Phyth::Quaternion< T >::x

X component of the vector (imaginary) part

Definition at line 40 of file Quaternion.hpp.

◆ y

template<typename T >

T Phyth::Quaternion< T >::y

Y component of the vector (imaginary) part

Definition at line 42 of file Quaternion.hpp.

◆ z

template<typename T >

T Phyth::Quaternion< T >::z

Z component of the vector (imaginary) part

Definition at line 44 of file Quaternion.hpp.

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

include/Phyth/Tools/Quaternion.hpp

Public Member Functions

Static Public Member Functions

Public Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

◆ Quaternion() [1/4]

◆ Quaternion() [2/4]

◆ Quaternion() [3/4]

◆ Quaternion() [4/4]

Member Function Documentation

◆ as()

◆ Conjugated()

◆ Dot()

◆ FromAxisAngle()

◆ FromEuler()

◆ Inversed()

◆ IsUnit()

◆ Length()

◆ LengthSquared()

◆ Normalized()

◆ operator!=()

◆ operator*() [1/2]

◆ operator*() [2/2]

◆ operator*=()

◆ operator+()

◆ operator+=()

◆ operator-() [1/2]

◆ operator-() [2/2]

◆ operator-=()

◆ operator/()

◆ operator/=()

◆ operator==()

◆ operator[]() [1/2]

◆ operator[]() [2/2]

◆ Rotated()

◆ Slerp()

◆ ToQuantity()

◆ ToVector()

Friends And Related Symbol Documentation

◆ operator<<

Member Data Documentation

◆ w

◆ x

◆ y

◆ z