Rigid-body transform: a rotation matrix plus a translation vector. More...

#include <lib/numeric/include/ufo/numeric/transform.hpp>

Public Types
using	size_type = std::size_t

using	value_type = T

Public Member Functions
constexpr	Transform () noexcept=default
	Default constructor; initializes to the identity transform (zero translation and identity rotation).

template<std::floating_point U>
constexpr	Transform (Mat< Dim+1, Dim+1, U > const &m)
	Constructs from a `(Dim+1) × (Dim+1)` homogeneous matrix.

constexpr	Transform (Mat< Dim, Dim, T > const &rotation)
	Constructs a pure-rotation transform (zero translation).

constexpr	Transform (Mat< Dim, Dim, T > const &rotation, Vec< Dim, T > const &translation)
	Constructs from a rotation matrix and a translation vector (same scalar type).

template<std::floating_point T1, std::floating_point T2>
constexpr	Transform (Mat< Dim, Dim, T1 > const &rotation, Vec< Dim, T2 > const &translation)
	Constructs from rotation and translation with potentially different scalar types.

template<std::floating_point U>
constexpr	Transform (Mat< Dim, Dim, U > const &rotation)
	Constructs a pure-rotation transform from a rotation matrix of a different type.

template<std::floating_point T1, std::floating_point T2> requires (Dim == 3)
constexpr	Transform (Quat< T1 > const &rotation, Vec< 3, T2 > const &translation)
	(3D only) Constructs from a quaternion and a translation vector.

template<std::floating_point U> requires (Dim == 3)
constexpr	Transform (Quat< U > const &rotation)
	(3D only) Constructs a pure-rotation transform from a quaternion.

template<std::floating_point T1, std::floating_point T2> requires (Dim == 2)
constexpr	Transform (T1 const &angle, Vec< 2, T2 > const &translation)
	(2D only) Constructs from a rotation angle and a translation vector.

constexpr	Transform (Transform const &) noexcept=default
	Copy constructor.

template<std::floating_point U>
constexpr	Transform (Transform< Dim, U > const &other) noexcept
	Converting constructor from a `Transform<Dim, U>` with a different scalar type.

template<std::floating_point U> requires (Dim == 2)
constexpr	Transform (U const &angle)
	(2D only) Constructs a pure-rotation transform from an angle.

template<std::floating_point U>
constexpr	operator Mat< Dim+1, Dim+1, U > () const
	Converts to a `(Dim+1) × (Dim+1)` row-major homogeneous matrix.

template<std::floating_point U>
constexpr	operator Mat< Dim, Dim, U > () const
	Extracts the rotation component as a `Dim × Dim` matrix.

template<std::floating_point U> requires (Dim == 3)
constexpr	operator Quat< U > () const
	(3D only) Converts the rotation component to a quaternion.

template<std::floating_point U> requires (Dim == 3)
constexpr Quat< U >	operator() (Quat< U > const &q) const
	(3D only) Applies the rotation component to a quaternion.

template<std::floating_point U>
constexpr Vec< Dim, U >	operator() (Vec< Dim, U > const &v) const
	Applies the transform to a vector: `result = R * v + t`.

constexpr Transform &	operator*= (Transform const &t)
	Composes this transform with `t` in place: `this = this * t`.

constexpr Transform &	operator= (Transform const &) noexcept=default
	Default copy assignment operator.

template<std::floating_point U>
constexpr Transform &	operator= (Transform< Dim, U > const &rhs) noexcept
	Converting assignment from a `Transform<Dim, U>` with a different scalar type.

constexpr bool	operator== (Transform const &other) const noexcept=default
	Equality comparison; two transforms are equal if their rotation and translation components are equal.

constexpr T	theta () const
	(2D only) Returns the rotation angle θ in `[-π, π]`.

Public Attributes
Mat< Dim, Dim, T >	rotation = Mat<Dim, Dim, T>::identity()
	Rotation component of the transform, represented as a `Dim × Dim` matrix.

Vec< Dim, T >	translation {}
	Translation component of the transform.

Detailed Description

template<std::size_t Dim, std::floating_point T = float>
requires (Dim == 2 || Dim == 3)
struct ufo::Transform< Dim, T >

Rigid-body transform: a rotation matrix plus a translation vector.

Template Parameters

Dim	Spatial dimension; must be `2` or `3`.
T	Floating-point scalar type (default: `float`).

Applying the transform to a vector v computes R * v + t where R is the rotation matrix and t is the translation. Composition (*) follows the convention (t1 * t2)(v) = t1(t2(v)).

Definition at line 81 of file transform.hpp.

Member Typedef Documentation

◆ size_type

template<std::size_t Dim, std::floating_point T = float>

using ufo::Transform< Dim, T >::size_type = std::size_t

Definition at line 83 of file transform.hpp.

◆ value_type

template<std::size_t Dim, std::floating_point T = float>

using ufo::Transform< Dim, T >::value_type = T

Definition at line 82 of file transform.hpp.

Constructor & Destructor Documentation

◆ Transform() [1/10]

template<std::size_t Dim, std::floating_point T = float>

constexpr ufo::Transform< Dim, T >::Transform	(	Mat< Dim, Dim, T > const &	rotation,
		Vec< Dim, T > const &	translation
	)

inlineconstexpr

Constructs from a rotation matrix and a translation vector (same scalar type).

Parameters

[in]	rotation	Rotation component.
[in]	translation	Translation component.

Definition at line 116 of file transform.hpp.

◆ Transform() [2/10]

template<std::size_t Dim, std::floating_point T = float>

constexpr ufo::Transform< Dim, T >::Transform ( Mat< Dim, Dim, T > const & rotation )

inlineexplicitconstexpr

Constructs a pure-rotation transform (zero translation).

Parameters

[in] rotation Rotation matrix.

Definition at line 125 of file transform.hpp.

◆ Transform() [3/10]

template<std::size_t Dim, std::floating_point T = float>

template<std::floating_point T1, std::floating_point T2>

constexpr ufo::Transform< Dim, T >::Transform	(	Mat< Dim, Dim, T1 > const &	rotation,
		Vec< Dim, T2 > const &	translation
	)

inlineconstexpr

Constructs from rotation and translation with potentially different scalar types.

Template Parameters

T1	Scalar type of the rotation matrix.
T2	Scalar type of the translation vector.

Parameters

[in]	rotation	Rotation component (converted to `T`).
[in]	translation	Translation component (converted to `T`).

Definition at line 136 of file transform.hpp.

◆ Transform() [4/10]

template<std::size_t Dim, std::floating_point T = float>

template<std::floating_point U>

constexpr ufo::Transform< Dim, T >::Transform ( Mat< Dim, Dim, U > const & rotation )

inlineexplicitconstexpr

Constructs a pure-rotation transform from a rotation matrix of a different type.

Template Parameters

U	Source scalar type.

Parameters

[in] rotation Rotation matrix (converted to T).

Definition at line 148 of file transform.hpp.

◆ Transform() [5/10]

template<std::size_t Dim, std::floating_point T = float>

template<std::floating_point T1, std::floating_point T2>
requires (Dim == 2)

constexpr ufo::Transform< Dim, T >::Transform	(	T1 const &	angle,
		Vec< 2, T2 > const &	translation
	)

inlineconstexpr

(2D only) Constructs from a rotation angle and a translation vector.

Template Parameters

T1	Scalar type of the angle.
T2	Scalar type of the translation vector.

Parameters

[in]	angle	Rotation angle in radians.
[in]	translation	Translation vector.

Definition at line 161 of file transform.hpp.

◆ Transform() [6/10]

template<std::size_t Dim, std::floating_point T = float>

template<std::floating_point U>
requires (Dim == 2)

constexpr ufo::Transform< Dim, T >::Transform ( U const & angle )

inlineexplicitconstexpr

(2D only) Constructs a pure-rotation transform from an angle.

Template Parameters

U	Scalar type of the angle.

Parameters

[in] angle Rotation angle in radians.

Definition at line 176 of file transform.hpp.

◆ Transform() [7/10]

template<std::size_t Dim, std::floating_point T = float>

template<std::floating_point T1, std::floating_point T2>
requires (Dim == 3)

constexpr ufo::Transform< Dim, T >::Transform	(	Quat< T1 > const &	rotation,
		Vec< 3, T2 > const &	translation
	)

inlineconstexpr

(3D only) Constructs from a quaternion and a translation vector.

Template Parameters

T1	Scalar type of the quaternion.
T2	Scalar type of the translation vector.

Parameters

[in]	rotation	Unit quaternion specifying the rotation.
[in]	translation	Translation vector.

Definition at line 192 of file transform.hpp.

◆ Transform() [8/10]

template<std::size_t Dim, std::floating_point T = float>

template<std::floating_point U>
requires (Dim == 3)

constexpr ufo::Transform< Dim, T >::Transform ( Quat const & rotation )

inlineexplicitconstexpr

(3D only) Constructs a pure-rotation transform from a quaternion.

Template Parameters

U	Scalar type of the quaternion.

Parameters

[in] rotation Unit quaternion specifying the rotation.

Definition at line 204 of file transform.hpp.

◆ Transform() [9/10]

template<std::size_t Dim, std::floating_point T = float>

template<std::floating_point U>

constexpr ufo::Transform< Dim, T >::Transform ( Mat< Dim+1, Dim+1, U > const & m )

inlineexplicitconstexpr

Constructs from a (Dim+1) × (Dim+1) homogeneous matrix.

Extracts the upper-left Dim × Dim block as the rotation and column Dim rows 0..Dim-1 as the translation.

Template Parameters

U	Scalar type of the source matrix.

Parameters

[in] m Row-major homogeneous transformation matrix.

Definition at line 217 of file transform.hpp.

◆ Transform() [10/10]

template<std::size_t Dim, std::floating_point T = float>

template<std::floating_point U>

constexpr ufo::Transform< Dim, T >::Transform ( Transform< Dim, U > const & other )

inlineexplicitconstexprnoexcept

Converting constructor from a Transform<Dim, U> with a different scalar type.

Template Parameters

U	Source scalar type.

Parameters

[in] other Source transform; components are converted to T.

Definition at line 232 of file transform.hpp.

Member Function Documentation

◆ operator Mat< Dim+1, Dim+1, U >()

template<std::size_t Dim, std::floating_point T = float>

template<std::floating_point U>

constexpr ufo::Transform< Dim, T >::operator Mat< Dim+1, Dim+1, U > ( ) const

inlineexplicitconstexpr

Converts to a (Dim+1) × (Dim+1) row-major homogeneous matrix.

The upper-left Dim × Dim block holds the rotation, column Dim rows 0..Dim-1 hold the translation, and m[Dim][Dim] = 1.

Template Parameters

U	Target scalar type.

Returns: Homogeneous transformation matrix.

Definition at line 288 of file transform.hpp.

◆ operator Quat()

template<std::size_t Dim, std::floating_point T = float>

template<std::floating_point U>
requires (Dim == 3)

constexpr ufo::Transform< Dim, T >::operator Quat ( ) const

inlineexplicitconstexpr

(3D only) Converts the rotation component to a quaternion.

Template Parameters

U	Target scalar type.

Returns: Quat representing the rotation matrix.

Definition at line 305 of file transform.hpp.

◆ operator()()

template<std::size_t Dim, std::floating_point T = float>

template<std::floating_point U>
requires (Dim == 3)

constexpr Quat ufo::Transform< Dim, T >::operator() ( Quat const & q ) const

inlineconstexpr

(3D only) Applies the rotation component to a quaternion.

Computes Quat(*this) * q, i.e., pre-multiplies q by the rotation.

Template Parameters

U	Scalar type of the quaternion.

Parameters

[in] q Input quaternion.

Returns: Rotated quaternion.

Definition at line 337 of file transform.hpp.

◆ operator*=()

template<std::size_t Dim, std::floating_point T = float>

constexpr Transform & ufo::Transform< Dim, T >::operator*= ( Transform< Dim, T > const & t )

inlineconstexpr

Composes this transform with t in place: *this = *this * t.

Parameters

[in] t Right-hand transform to append.

Returns: Reference to *this.

Definition at line 357 of file transform.hpp.

◆ operator=()

template<std::size_t Dim, std::floating_point T = float>

template<std::floating_point U>

constexpr Transform & ufo::Transform< Dim, T >::operator= ( Transform< Dim, U > const & rhs )

inlineconstexprnoexcept

Converting assignment from a Transform<Dim, U> with a different scalar type.

Template Parameters

U	Source scalar type.

Parameters

[in] rhs Source transform.

Returns: Reference to *this.

Definition at line 256 of file transform.hpp.

◆ operator==()

template<std::size_t Dim, std::floating_point T = float>

constexpr bool ufo::Transform< Dim, T >::operator== ( Transform< Dim, T > const & other ) const

constexprdefaultnoexcept

Equality comparison; two transforms are equal if their rotation and translation components are equal.

Parameters

[in] other Transform to compare with.

Returns: true if the transforms are equal; false otherwise.

◆ theta()

template<std::size_t Dim, std::floating_point T = float>

constexpr T ufo::Transform< Dim, T >::theta ( ) const

inlineconstexpr

(2D only) Returns the rotation angle θ in [-π, π].

Returns: atan2(rotation[0][1], rotation[0][0]).

Definition at line 346 of file transform.hpp.

Member Data Documentation

◆ rotation

template<std::size_t Dim, std::floating_point T = float>

Mat<Dim, Dim, T> ufo::Transform< Dim, T >::rotation = Mat<Dim, Dim, T>::identity()

Rotation component of the transform, represented as a Dim × Dim matrix.

Definition at line 88 of file transform.hpp.

◆ translation

template<std::size_t Dim, std::floating_point T = float>

Vec<Dim, T> ufo::Transform< Dim, T >::translation {}

Translation component of the transform.

Definition at line 92 of file transform.hpp.

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

lib/numeric/include/ufo/numeric/transform.hpp

Public Types

Public Member Functions

Public Attributes

Detailed Description

Member Typedef Documentation

◆ size_type

◆ value_type

Constructor & Destructor Documentation

◆ Transform() [1/10]

◆ Transform() [2/10]

◆ Transform() [3/10]

◆ Transform() [4/10]

◆ Transform() [5/10]

◆ Transform() [6/10]

◆ Transform() [7/10]

◆ Transform() [8/10]

◆ Transform() [9/10]

◆ Transform() [10/10]

Member Function Documentation

◆ operator Mat< Dim+1, Dim+1, U >()

◆ operator Quat< U >()

◆ operator()()

◆ operator*=()

◆ operator=()

◆ operator==()

◆ theta()

Member Data Documentation

◆ rotation

◆ translation