dz::quat< T > Struct Template Reference

A quaternion class for representing rotations in 3D space. More...

#include <math.hpp>

Inheritance diagram for dz::quat< T >:

Public Types
using	Base = vec<T, 4>

Public Member Functions
	quat ()=default
	Default constructor. Components are uninitialized.
	quat (const quat &)=default
	Copy constructor.
quat &	operator= (const quat &)=default
	Copy assignment operator.
	quat (quat &&) noexcept=default
	Move constructor.
quat &	operator= (quat &&) noexcept=default
	Move assignment operator.
template<typename... Args>
	quat (Args &&... args)
	Variadic constructor forwarding to vec<T, 4>.
	quat (T w, T x, T y, T z)
	Construct quaternion from explicit components.
quat< T >	conjugate () const
	Returns the conjugate of the quaternion.
quat< T >	inverse () const
	Returns the inverse of the quaternion.
vec< T, 3 >	rotate (const vec< T, 3 > &v) const
	Rotates a 3D vector using this quaternion.
quat< T >	operator* (const quat< T > &rhs) const
	Quaternion multiplication.
void	to_axis_angle (vec< T, 3 > &out_axis, T &out_angle) const
	Converts the quaternion to axis-angle representation.
mat< T, 4, 4 >	to_mat4 () const
	Converts the quaternion to a 4x4 rotation matrix.
vec &	operator= (const vec &other)
	Assignment operator for component-wise copy.
vec &	operator+= (const O &other)
	Compound addition-assignment operator.
vec &	operator-= (const O &other)
	Compound subtraction-assignment operator.
vec &	operator*= (const O &other)
	Compound multiplication-assignment operator.
vec &	operator/= (const O &other)
	Compound division-assignment operator.
vec	operator+ (const O &other) const
	Addition operator returning a new vector.
vec	operator- (const O &other) const
	Subtraction operator returning a new vector.
vec	operator- () const
	Unary negation operator.
vec	operator* (const O &other) const
	Multiplication operator returning a new vector.
vec	operator/ (const O &other) const
	Division operator returning a new vector.
T &	operator[] (size_t i)
	Index operator for non-const access to vector components.
const T &	operator[] (size_t i) const
	Index operator for const access to vector components.
T	length () const
	Computes the Euclidean length (magnitude) of the vector.
vec	normalize () const
	Returns a normalized (unit length) copy of the vector.
Public Member Functions inherited from dz::vec< T, 4 >
	vec (Args... args)
	Variadic constructor to initialize vector components.
	vec (const vec< OT, ON > &other)
	Copy constructor to convert from vectors of different types and/or sizes.
vec &	operator= (const vec &other)
	Assignment operator for component-wise copy.
T &	operator[] (size_t i)
	Index operator for non-const access to vector components.
const T &	operator[] (size_t i) const
	Index operator for const access to vector components.
vec &	operator*= (const O &other)
	Compound multiplication-assignment operator.
vec &	operator/= (const O &other)
	Compound division-assignment operator.
vec &	operator+= (const O &other)
	Compound addition-assignment operator.
vec &	operator-= (const O &other)
	Compound subtraction-assignment operator.
vec	operator* (const O &other) const
	Multiplication operator returning a new vector.
vec	operator/ (const O &other) const
	Division operator returning a new vector.
vec	operator+ (const O &other) const
	Addition operator returning a new vector.
vec	operator- (const O &other) const
	Subtraction operator returning a new vector.
vec	operator- () const
	Unary negation operator.
T	length () const
	Computes the Euclidean length (magnitude) of the vector.
vec	normalize () const
	Returns a normalized (unit length) copy of the vector.

Static Public Member Functions
static quat< T >	from_axis_angle (const vec< T, 3 > &axis, T angle)
	Constructs a quaternion from an axis-angle representation.

Public Attributes
T	data [N]
	Underlying array storing vector components.
Public Attributes inherited from dz::vec< T, 4 >
T	data [N]
	Underlying array storing vector components.

Detailed Description

template<typename T>
struct dz::quat< T >

A quaternion class for representing rotations in 3D space.

This struct inherits from vec<T, 4> and represents a quaternion with four components: w, x, y, z. It provides operations including construction, conjugation, inversion, quaternion multiplication, and rotation of a 3D vector.

Template Parameters

T	Underlying scalar type (e.g., float, double).

Member Typedef Documentation

Base

template<typename T>

using dz::quat< T >::Base = vec<T, 4>

Constructor & Destructor Documentation

quat() [1/5]

template<typename T>

dz::quat< T >::quat ( )

default

Default constructor. Components are uninitialized.

quat() [2/5]

template<typename T>

dz::quat< T >::quat ( const quat< T > & )

default

Copy constructor.

Parameters

other

The quaternion to copy.

quat() [3/5]

template<typename T>

dz::quat< T >::quat ( quat< T > && )

defaultnoexcept

Move constructor.

Parameters

other

The quaternion to move.

quat() [4/5]

template<typename T>

template<typename... Args>

dz::quat< T >::quat ( Args &&... args )

inline

Variadic constructor forwarding to vec<T, 4>.

Template Parameters

Args	Variadic template arguments.

Parameters

args	Values forwarded to base class constructor.

quat() [5/5]

template<typename T>

dz::quat< T >::quat ( T w, T x, T y, T z )

inline

Construct quaternion from explicit components.

Parameters

w	Scalar component.
x	X vector component.
y	Y vector component.
z	Z vector component.

Member Function Documentation

conjugate()

template<typename T>

quat< T > dz::quat< T >::conjugate ( ) const

inline

Returns the conjugate of the quaternion.

The conjugate of (w, x, y, z) is (w, -x, -y, -z).

Returns

Conjugated quaternion.

from_axis_angle()

template<typename T>

quat< T > dz::quat< T >::from_axis_angle ( const vec< T, 3 > & axis, T angle )

inlinestatic

Constructs a quaternion from an axis-angle representation.

Parameters

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

Returns

Quaternion representing the rotation.

inverse()

template<typename T>

quat< T > dz::quat< T >::inverse ( ) const

inline

Returns the inverse of the quaternion.

The inverse is the conjugate divided by the squared norm.

Returns

Inverse quaternion.

length()

template<typename T>

T dz::vec< T, N >::length ( ) const

inline

Computes the Euclidean length (magnitude) of the vector.

Calculates the square root of the sum of squares of all components.

Returns

The length of the vector as type T.

normalize()

template<typename T>

vec dz::vec< T, N >::normalize ( ) const

inline

Returns a normalized (unit length) copy of the vector.

Divides all components by the vector length.

Returns

A new vector normalized to length 1.

operator*() [1/2]

template<typename T>

vec dz::vec< T, N >::operator* ( const O & other ) const

inline

Multiplication operator returning a new vector.

Supports multiplication by a scalar or component-wise multiplication by another vector.

Template Parameters

O	Operand type (scalar T or vec<T, N>).

Parameters

other

The scalar or vector to multiply by.

Returns

A new vector resulting from the multiplication.

operator*() [2/2]

template<typename T>

quat< T > dz::quat< T >::operator* ( const quat< T > & rhs ) const

inline

Quaternion multiplication.

Multiplies this quaternion by another.

Parameters

rhs	The right-hand side quaternion.

Returns

Result of multiplication.

operator*=()

template<typename T>

vec & dz::vec< T, N >::operator*= ( const O & other )

inline

Compound multiplication-assignment operator.

Supports multiplication by a scalar or component-wise multiplication by another vector. Throws std::runtime_error if the operand type is unsupported.

Template Parameters

O	Operand type (scalar T or vec<T, N>).

Parameters

other

The scalar or vector to multiply by.

Returns

Reference to this vector after multiplication.

Exceptions

std::runtime_error

if unsupported operand type is used.

operator+()

template<typename T>

vec dz::vec< T, N >::operator+ ( const O & other ) const

inline

Addition operator returning a new vector.

Supports addition by a scalar or component-wise addition by another vector.

Template Parameters

O	Operand type (scalar T or vec<T, N>).

Parameters

other

The scalar or vector to add.

Returns

A new vector resulting from the addition.

operator+=()

template<typename T>

vec & dz::vec< T, N >::operator+= ( const O & other )

inline

Compound addition-assignment operator.

Supports addition by a scalar or component-wise addition by another vector. Throws std::runtime_error if the operand type is unsupported.

Template Parameters

O	Operand type (scalar T or vec<T, N>).

Parameters

other

The scalar or vector to add.

Returns

Reference to this vector after addition.

Exceptions

std::runtime_error

if unsupported operand type is used.

operator-() [1/2]

template<typename T>

vec dz::vec< T, N >::operator- ( ) const

inline

Unary negation operator.

Returns a new vector with all components negated.

Returns

A new vector with negated components.

operator-() [2/2]

template<typename T>

vec dz::vec< T, N >::operator- ( const O & other ) const

inline

Subtraction operator returning a new vector.

Supports subtraction by a scalar or component-wise subtraction by another vector.

Template Parameters

O	Operand type (scalar T or vec<T, N>).

Parameters

other

The scalar or vector to subtract.

Returns

A new vector resulting from the subtraction.

operator-=()

template<typename T>

vec & dz::vec< T, N >::operator-= ( const O & other )

inline

Compound subtraction-assignment operator.

Supports subtraction by a scalar or component-wise subtraction by another vector. Throws std::runtime_error if the operand type is unsupported.

Template Parameters

O	Operand type (scalar T or vec<T, N>).

Parameters

other

The scalar or vector to subtract.

Returns

Reference to this vector after subtraction.

Exceptions

std::runtime_error

if unsupported operand type is used.

operator/()

template<typename T>

vec dz::vec< T, N >::operator/ ( const O & other ) const

inline

Division operator returning a new vector.

Supports division by a scalar or component-wise division by another vector.

Template Parameters

O	Operand type (scalar T or vec<T, N>).

Parameters

other

The scalar or vector to divide by.

Returns

A new vector resulting from the division.

operator/=()

template<typename T>

vec & dz::vec< T, N >::operator/= ( const O & other )

inline

Compound division-assignment operator.

Supports division by a scalar or component-wise division by another vector. Throws std::runtime_error if the operand type is unsupported.

Template Parameters

O	Operand type (scalar T or vec<T, N>).

Parameters

other

The scalar or vector to divide by.

Returns

Reference to this vector after division.

Exceptions

std::runtime_error

if unsupported operand type is used.

operator=() [1/3]

template<typename T>

quat & dz::quat< T >::operator= ( const quat< T > & )

default

Copy assignment operator.

Parameters

other

The quaternion to assign from.

Returns

Reference to this quaternion.

operator=() [2/3]

template<typename T>

vec & dz::vec< T, N >::operator= ( const vec & other )

inline

Assignment operator for component-wise copy.

Copies all components from the other vector using memcpy for efficiency.

Parameters

other

The vector to copy from.

Returns

Reference to this vector after assignment.

operator=() [3/3]

template<typename T>

quat & dz::quat< T >::operator= ( quat< T > && )

defaultnoexcept

Move assignment operator.

Parameters

other

The quaternion to move from.

Returns

Reference to this quaternion.

operator[]() [1/2]

template<typename T>

T & dz::vec< T, N >::operator[] ( size_t i )

inline

Index operator for non-const access to vector components.

No bounds checking is performed.

Parameters

i	The component index to access.

Returns

Reference to the component at index i.

operator[]() [2/2]

template<typename T>

const T & dz::vec< T, N >::operator[] ( size_t i ) const

inline

Index operator for const access to vector components.

No bounds checking is performed.

Parameters

i	The component index to access.

Returns

Const reference to the component at index i.

rotate()

template<typename T>

vec< T, 3 > dz::quat< T >::rotate ( const vec< T, 3 > & v ) const

inline

Rotates a 3D vector using this quaternion.

Parameters

v	The 3D vector to rotate.

Returns

Rotated vector.

to_axis_angle()

template<typename T>

void dz::quat< T >::to_axis_angle ( vec< T, 3 > & out_axis, T & out_angle ) const

inline

Converts the quaternion to axis-angle representation.

Parameters

out_axis	Normalized axis of rotation (output).
out_angle	Angle in radians (output).

to_mat4()

template<typename T>

mat< T, 4, 4 > dz::quat< T >::to_mat4 ( ) const

inline

Converts the quaternion to a 4x4 rotation matrix.

Returns

4x4 rotation matrix.

Member Data Documentation

data

template<typename T>

T dz::vec< T, N >::data[N]

Underlying array storing vector components.

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

• include/dz/math.hpp