#include <math/DualQuaternion.hpp>

Public Types
Types
using	value_type = T
	The underlying implementation type.

Public Member Functions
constexpr BasicDualQuaternion< T >	conjugate () const

constexpr BasicDual< T >	normsquared () const

constexpr BasicDual< T >	norm () const

constexpr BasicDual< T >	magnitude () const

const BasicQuaternion< T > &	rotation () const

BasicVector3D< T >	translation () const

constexpr BasicDualQuaternion< T >	normalized () const

constexpr bool	rotation_magnitude_is_one () const

constexpr bool	rotation_and_translation_are_orthogonal () const

constexpr bool	is_unit () const

Constructors
	BasicDualQuaternion ()=default

constexpr	BasicDualQuaternion (const BasicQuaternion< T > &rotation, const BasicQuaternion< T > &translation)

constexpr	BasicDualQuaternion (const BasicQuaternion< T > &rotation, T translation_x, T translation_y, T translation_z)

constexpr	BasicDualQuaternion (const BasicQuaternion< T > &rotation, const BasicVector3D< T > &translation)

constexpr	BasicDualQuaternion (const BasicDual< BasicQuaternion< T > > &underlying_representation)

Element Access
const BasicQuaternion< T > &	real () const

const BasicQuaternion< T > &	dual () const

Invalid Value Check
bool	isNaN () const

bool	isInf () const

Static Public Member Functions
static constexpr BasicVector3D< T >	decode_point (const BasicDualQuaternion< T > &encoded_point)

Constants
static constexpr BasicDualQuaternion< T >	identity ()

static constexpr BasicDualQuaternion< T >	zero ()

Convenience Creation Functions
static constexpr BasicDualQuaternion< T >	make_rotation (const BasicQuaternion< T > &rotation)

static constexpr BasicDualQuaternion< T >	make_translation (T translation_x, T translation_y, T translation_z)

static constexpr BasicDualQuaternion< T >	make_translation (const BasicVector3D< T > &translation)

static constexpr BasicDualQuaternion< T >	make_coordinate_system (const BasicQuaternion< T > &rotation, T translation_x, T translation_y, T translation_z)

static constexpr BasicDualQuaternion< T >	encode_point (const BasicVector3D< T > &point)

Friends
Equality
constexpr bool	operator== (const BasicDualQuaternion< T > &left, const BasicDualQuaternion< T > &right)

constexpr bool	approximately_equal_to (const BasicDualQuaternion< T > &value_to_test, const BasicDualQuaternion< T > &value_it_should_be, T tolerance=T{0.0002})

Operators
constexpr BasicDualQuaternion< T >	operator+ (const BasicDualQuaternion< T > &left_side, const BasicDualQuaternion< T > &right_side)

constexpr BasicDualQuaternion< T >	operator* (T scalar, const BasicDualQuaternion< T > &dual_quaternion)

constexpr BasicDualQuaternion< T >	operator* (const BasicDualQuaternion< T > &dual_quaternion, T scalar)

constexpr BasicDualQuaternion< T >	operator* (const BasicDualQuaternion< T > &dual_quaternion, const BasicDual< T > &dual_scalar)

constexpr BasicDualQuaternion< T >	operator* (const BasicDualQuaternion< T > &left_side, const BasicDualQuaternion< T > &right_side)

constexpr BasicDualQuaternion< T >	operator/ (const BasicDualQuaternion< T > &dual_quaternion, const BasicDual< T > &dual_scalar)

Check
template<std::floating_point OT = float>
bool	check_if_equal (const BasicDualQuaternion< T > &input, const BasicDualQuaternion< T > &near_to, OT tolerance=OT{0.0002})

template<std::floating_point OT = float>
bool	check_if_not_equal (const BasicDualQuaternion< T > &input, const BasicDualQuaternion< T > &near_to, OT tolerance=OT{0.0002})

Assert
template<std::floating_point OT = float>
void	CHECK_IF_EQUAL (const BasicDualQuaternion< T > &input, const BasicDualQuaternion< T > &near_to, OT tolerance=OT{0.0002})

template<std::floating_point OT = float>
void	CHECK_IF_NOT_EQUAL (const BasicDualQuaternion< T > &input, const BasicDualQuaternion< T > &near_to, OT tolerance=OT{0.0002})

template<std::floating_point OT = float>
void	CHECK_IF_ZERO (const BasicDualQuaternion< T > &input, OT tolerance=OT{0.0002})

Global Functions
constexpr BasicDualQuaternion< T >	normalized (const BasicDualQuaternion< T > &input)

template<std::floating_point OT = float>
constexpr BasicDualQuaternion< T >	blend (const BasicDualQuaternion< T > &beginning, const BasicDualQuaternion< T > &end, OT percentage)

constexpr BasicDualQuaternion< T >	conjugate (const BasicDualQuaternion< T > &input)

std::string	format (const BasicDualQuaternion< T > &input)

Related Symbols
(Note that these are not member symbols.)
Type Aliases
using	DualQuaternionf = BasicDualQuaternion< float >

using	DualQuaterniond = BasicDualQuaternion< double >

using	DualQuaternion = BasicDualQuaternion< double >

using	DualQuaternionl = BasicDualQuaternion< long double >

Detailed Description

template<class T>
class Math::BasicDualQuaternion< T >

The definition of a DualQuaternion

Here, we just compose the ideas of the BasicDual and BasicQuaternion classes together to create a DualQuaternion class.

See also: BasicDual; BasicQuaternion

Definition at line 31 of file DualQuaternion.hpp.

Member Typedef Documentation

◆ value_type

template<class T >

using value_type = T

The underlying implementation type.

Definition at line 37 of file DualQuaternion.hpp.

Constructor & Destructor Documentation

◆ BasicDualQuaternion() [1/5]

template<class T >

BasicDualQuaternion ( )

default

◆ BasicDualQuaternion() [2/5]

template<class T >

constexpr BasicDualQuaternion	(	const BasicQuaternion< T > &	rotation,
		const BasicQuaternion< T > &	translation
	)

inlineconstexpr

Constructs a DualQuaternion directly from the two given quaternions

Parameters

rotation	The Quaternion to place into the real() part
translation	The Quaternion to place into the dual() part

Note: The user takes full responsibility for the input. This could possibly be used to construct a non-unit DualQuaternion!

Definition at line 53 of file DualQuaternion.hpp.

◆ BasicDualQuaternion() [3/5]

template<class T >

constexpr BasicDualQuaternion	(	const BasicQuaternion< T > &	rotation,
		T	translation_x,
		T	translation_y,
		T	translation_z
	)

inlineconstexpr

Constructs a DualQuaternion from a unit Quaternion (rotation) and a translation

Note: This is the proper way to construct a unit DualQuaternion.

Definition at line 64 of file DualQuaternion.hpp.

◆ BasicDualQuaternion() [4/5]

template<class T >

constexpr BasicDualQuaternion	(	const BasicQuaternion< T > &	rotation,
		const BasicVector3D< T > &	translation
	)

inlineconstexpr

Definition at line 74 of file DualQuaternion.hpp.

◆ BasicDualQuaternion() [5/5]

template<class T >

constexpr BasicDualQuaternion ( const BasicDual< BasicQuaternion< T > > & underlying_representation )

inlineexplicitconstexpr

Constructs a DualQuaternion directly from a BasicDual<BasicQuaternion>

Parameters

underlying_representation The BasicDual number that will ultimately be used as the internal representation

Definition at line 87 of file DualQuaternion.hpp.

Member Function Documentation

◆ conjugate()

template<class T >

constexpr BasicDualQuaternion< T > conjugate ( ) const

inlineconstexpr

Create the conjugate of a DualQuaternion

Returns: the conjugate of this object

Note: This is a bit different from the definition of a conjugate for a Dual, in that the conjugate of a Dual is just { real, dual.conjugate() }, while for a DualQuaternion the operation needs to be { real.conjugate(), dual.conjugate() }.

Definition at line 216 of file DualQuaternion.hpp.

◆ decode_point()

template<class T >

static constexpr BasicVector3D< T > decode_point ( const BasicDualQuaternion< T > & encoded_point )

inlinestaticconstexpr

Definition at line 202 of file DualQuaternion.hpp.

◆ dual()

template<class T >

const BasicQuaternion< T > & dual ( ) const

inline

Definition at line 269 of file DualQuaternion.hpp.

◆ encode_point()

template<class T >

static constexpr BasicDualQuaternion< T > encode_point ( const BasicVector3D< T > & point )

inlinestaticconstexpr

Definition at line 196 of file DualQuaternion.hpp.

◆ identity()

template<class T >

static constexpr BasicDualQuaternion< T > identity ( )

inlinestaticconstexpr

Create a DualQuaternion representing no rotation and no translation

Returns: A DualQuaternion representing no rotation or translation

Definition at line 102 of file DualQuaternion.hpp.

◆ is_unit()

template<class T >

constexpr bool is_unit ( ) const

inlineconstexpr

Checks if a DualQuaternion is a "unit" representation

Returns: true if it is in unit form, false otherwise

Definition at line 315 of file DualQuaternion.hpp.

◆ isInf()

template<class T >

bool isInf ( ) const

inline

Definition at line 324 of file DualQuaternion.hpp.

◆ isNaN()

template<class T >

bool isNaN ( ) const

inline

Definition at line 323 of file DualQuaternion.hpp.

◆ magnitude()

template<class T >

constexpr BasicDual< T > magnitude ( ) const

inlineconstexpr

Creates the magnitude of a DualQuaternion

Returns: A Dual that is the magnitude of the object

See also: norm

Definition at line 263 of file DualQuaternion.hpp.

◆ make_coordinate_system()

template<class T >

static constexpr BasicDualQuaternion< T > make_coordinate_system	(	const BasicQuaternion< T > &	rotation,
		T	translation_x,
		T	translation_y,
		T	translation_z
	)

inlinestaticconstexpr

Encode both the rotation and translation together

Parameters

rotation	The rotation to inject
translation_x	The X component of the translation vector
translation_y	The Y component of the translation vector
translation_z	The Z component of the translation vector

Returns: A DualQuaternion containing both the rotation and translation

Precondition: rotation is a unit BasicQuaternion

Postcondition: result.real == rotation. result.dual.isPure()

Definition at line 186 of file DualQuaternion.hpp.

◆ make_rotation()

template<class T >

static constexpr BasicDualQuaternion< T > make_rotation ( const BasicQuaternion< T > & rotation )

inlinestaticconstexpr

Creates a DualQuaternion containing a rotation only

Parameters

rotation The rotation to apply, expressed as a Quaternion

Returns: A DualQuaternion representing a rotation only

Precondition: rotation is a unit Quaternion

Postcondition: result.real == rotation. result.dual == BasicQuaternion::zero()

Definition at line 129 of file DualQuaternion.hpp.

◆ make_translation() [1/2]

template<class T >

static constexpr BasicDualQuaternion< T > make_translation ( const BasicVector3D< T > & translation )

inlinestaticconstexpr

Create a DualQuaternion containing a translation only

Parameters

translation The translation to apply

Returns: A DualQuaternion representing a translation only

Postcondition: result.real == BasicQuaternion::identity() result.dual.isPure()

Definition at line 164 of file DualQuaternion.hpp.

◆ make_translation() [2/2]

template<class T >

static constexpr BasicDualQuaternion< T > make_translation	(	T	translation_x,
		T	translation_y,
		T	translation_z
	)

inlinestaticconstexpr

Create a DualQuaternion containing a translation only

Parameters

translation_x	The X component of the translation vector
translation_y	The Y component of the translation vector
translation_z	The Z component of the translation vector

Returns: A DualQuaternion representing a translation only

Postcondition: result.real == BasicQuaternion::identity() result.dual.isPure()

Definition at line 146 of file DualQuaternion.hpp.

◆ norm()

template<class T >

constexpr BasicDual< T > norm ( ) const

inlineconstexpr

Create the norm of a DualQuaternion

Returns: A Dual that is the norm of the object

Note: The norm is also known as the magnitude

Definition at line 252 of file DualQuaternion.hpp.

◆ normalized()

template<class T >

constexpr BasicDualQuaternion< T > normalized ( ) const

inlineconstexpr

Create the normalized version of a DualQuaternion

Returns: A DualQuaternion that is the normalized version of the object

See also: norm

Definition at line 284 of file DualQuaternion.hpp.

◆ normsquared()

template<class T >

constexpr BasicDual< T > normsquared ( ) const

inlineconstexpr

Create the square of the norm of the input

Returns: A Dual that is the square of the norm of this object

Note: The norm is also known as the magnitude

Definition at line 227 of file DualQuaternion.hpp.

◆ real()

template<class T >

const BasicQuaternion< T > & real ( ) const

inline

Definition at line 268 of file DualQuaternion.hpp.

◆ rotation()

template<class T >

const BasicQuaternion< T > & rotation ( ) const

inline

Definition at line 272 of file DualQuaternion.hpp.

◆ rotation_and_translation_are_orthogonal()

template<class T >

constexpr bool rotation_and_translation_are_orthogonal ( ) const

inlineconstexpr

Checks if a DualQuaternion has orthogonal rotation and translation axes

Returns: true if they are orthogonal, false otherwise

Note: This is part of the definition of a unit DualQuaternion

Definition at line 306 of file DualQuaternion.hpp.

◆ rotation_magnitude_is_one()

template<class T >

constexpr bool rotation_magnitude_is_one ( ) const

inlineconstexpr

Checks for a DualQuaternion's rotation component has a magnitude of one

Returns: true of the magnitude of the rotation is 1, false otherwise

Note: This is part of the definition of a unit DualQuaternion

Definition at line 295 of file DualQuaternion.hpp.

◆ translation()

template<class T >

BasicVector3D< T > translation ( ) const

inline

Definition at line 273 of file DualQuaternion.hpp.

◆ zero()

template<class T >

static constexpr BasicDualQuaternion< T > zero ( )

inlinestaticconstexpr

Create a DualQuaternion that is all zeros

Definition at line 110 of file DualQuaternion.hpp.

Friends And Related Symbol Documentation

◆ approximately_equal_to

template<class T >

constexpr bool approximately_equal_to	(	const BasicDualQuaternion< T > &	value_to_test,
		const BasicDualQuaternion< T > &	value_it_should_be,
		T	tolerance = `T{0.0002}`
	)

friend

Compares two BasicDualQuaternion inputs equal, component-wise, to within a tolerance

Parameters

value_to_test
value_it_should_be
tolerance	How close they should be to be considered equal

Returns: true if they are equal

See also: Equality

Definition at line 361 of file DualQuaternion.hpp.

◆ blend

template<class T >

template<std::floating_point OT = float>

constexpr BasicDualQuaternion< T > blend	(	const BasicDualQuaternion< T > &	beginning,
		const BasicDualQuaternion< T > &	end,
		OT	percentage
	)

friend

Generates a linear blend between two BasicDualQuaternion objects

Parameters

beginning	The start state
end	The ending state
percentage	The percentage blend between the two (typically [0..1])

Definition at line 598 of file DualQuaternion.hpp.

◆ conjugate

template<class T >

constexpr BasicDualQuaternion< T > conjugate ( const BasicDualQuaternion< T > & input )

friend

Computes the conjugate of the input

Note: This will just call input.conjugate()

Definition at line 611 of file DualQuaternion.hpp.

◆ format

template<class T >

std::string format ( const BasicDualQuaternion< T > & input )

friend

Definition at line 616 of file DualQuaternion.hpp.

◆ normalized

template<class T >

constexpr BasicDualQuaternion< T > normalized ( const BasicDualQuaternion< T > & input )

friend

Creates the normalized form of a BasicDualQuaternion

Parameters

input The BasicDualQuaternion to normalize

Returns: The normalized version of input

Definition at line 586 of file DualQuaternion.hpp.

◆ operator==

template<class T >

constexpr bool operator==	(	const BasicDualQuaternion< T > &	left,
		const BasicDualQuaternion< T > &	right
	)

friend

Defines equality of two DualQuaternions

Note: Uses approximately_equal_to under-the-hood; Use C++20's ability to generate the operator !=() from operator ==()

See also: Equality

Definition at line 344 of file DualQuaternion.hpp.

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

lib/include/Math/math/DualQuaternion.hpp

Public Types

Public Member Functions

Static Public Member Functions

Friends

Related Symbols

Detailed Description

Member Typedef Documentation

◆ value_type

Constructor & Destructor Documentation

◆ BasicDualQuaternion() [1/5]

◆ BasicDualQuaternion() [2/5]

◆ BasicDualQuaternion() [3/5]

◆ BasicDualQuaternion() [4/5]

◆ BasicDualQuaternion() [5/5]

Member Function Documentation

◆ conjugate()

◆ decode_point()

◆ dual()

◆ encode_point()

◆ identity()

◆ is_unit()

◆ isInf()

◆ isNaN()

◆ magnitude()

◆ make_coordinate_system()

◆ make_rotation()

◆ make_translation() [1/2]

◆ make_translation() [2/2]

◆ norm()

◆ normalized()

◆ normsquared()

◆ real()

◆ rotation()

◆ rotation_and_translation_are_orthogonal()

◆ rotation_magnitude_is_one()

◆ translation()

◆ zero()

Friends And Related Symbol Documentation

◆ approximately_equal_to

◆ blend

◆ conjugate

◆ format

◆ normalized

◆ operator==