affine::AffineMap< Mat > Class Template Reference

AffineMap class definition. More...

#include <affine_map.hpp>

Public Types
using	T = linalg::matrix_scalar_t< Mat >
	alias to extract underlying type of affine set
using	DomVec = linalg::Vector< T, N >
	alias for underlying vector spanning R^n (domain)
using	AmbientVec = linalg::Vector< T, M >
	alias for underlying vector spanning R^m (codomain)

Public Member Functions
constexpr	AffineMap ()
	CTOR.
constexpr	AffineMap (const Mat &U_in)
	CTOR.
constexpr	AffineMap (const Mat &U_in, const AmbientVec &c_in)
	CTOR.
constexpr	AffineMap (const linalg::Matrix< T, M+1, N+1 > &H)
	CTOR.
template<linalg::MatrixContainer OtherMat> requires (std::same_as<T, linalg::matrix_scalar_t<OtherMat>> && linalg::mat_rows_v<OtherMat> == N)
constexpr auto	compose (const AffineMap< OtherMat > &other) const
	compose function
constexpr auto	inverse () const
	inverse mapping
constexpr auto	linear_part () const
	linear part
constexpr auto	translation () const
	translation
constexpr bool	operator== (const AffineMap< Mat > &other) const
	equality comparison overload
constexpr bool	operator!= (const AffineMap< Mat > &other) const
	inequality comparison overload
constexpr auto	operator() (const DomVec &x) const
	transform point to coords

Static Public Attributes
static constexpr std::size_t	M = linalg::mat_rows_v<Mat>
	helpers to extracting M x N matrix
static constexpr std::size_t	N = linalg::mat_cols_v<Mat>

Detailed Description

template<linalg::MatrixContainer Mat>
class affine::AffineMap< Mat >

AffineMap class definition.

forward declaration of affine map

Valid mapping which transforms one affine set to another.

f(x) = U x + c

Applies linear transform via U and then translation by vector c

Definition at line 63 of file affine_map.hpp.

Member Typedef Documentation

AmbientVec

template<linalg::MatrixContainer Mat>

using affine::AffineMap< Mat >::AmbientVec = linalg::Vector<T, M>

alias for underlying vector spanning R^m (codomain)

Definition at line 76 of file affine_map.hpp.

DomVec

template<linalg::MatrixContainer Mat>

using affine::AffineMap< Mat >::DomVec = linalg::Vector<T, N>

alias for underlying vector spanning R^n (domain)

Definition at line 73 of file affine_map.hpp.

T

template<linalg::MatrixContainer Mat>

using affine::AffineMap< Mat >::T = linalg::matrix_scalar_t<Mat>

alias to extract underlying type of affine set

Definition at line 66 of file affine_map.hpp.

Constructor & Destructor Documentation

AffineMap() [1/4]

template<linalg::MatrixContainer Mat>

constexpr affine::AffineMap< Mat >::AffineMap ( )

inlineexplicitconstexpr

CTOR.

empty map

Definition at line 83 of file affine_map.hpp.

Referenced by affine::AffineMap< Mat >::inverse().

AffineMap() [2/4]

template<linalg::MatrixContainer Mat>

constexpr affine::AffineMap< Mat >::AffineMap ( const Mat &  U_in )

inlineexplicitconstexpr

CTOR.

Parameters

matrix

M x N

Definition at line 90 of file affine_map.hpp.

AffineMap() [3/4]

template<linalg::MatrixContainer Mat>

constexpr affine::AffineMap< Mat >::AffineMap ( const Mat &  U_in, const AmbientVec &  c_in  )

inlineexplicitconstexpr

CTOR.

Parameters

matrix	of type T M x N elements
vector	of type T M elements

Definition at line 98 of file affine_map.hpp.

AffineMap() [4/4]

template<linalg::MatrixContainer Mat>

constexpr affine::AffineMap< Mat >::AffineMap ( const linalg::Matrix< T, M+1, N+1 > &  H )

inlineexplicitconstexpr

CTOR.

Parameters

matrix

of type T (M + 1) x (N + 1) elements

Definition at line 106 of file affine_map.hpp.

Member Function Documentation

compose()

template<linalg::MatrixContainer Mat>

template<linalg::MatrixContainer OtherMat>
requires (std::same_as<T, linalg::matrix_scalar_t<OtherMat>> && linalg::mat_rows_v<OtherMat> == N)

constexpr auto affine::AffineMap< Mat >::compose ( const AffineMap< OtherMat > &  other ) const

inlineconstexpr

compose function

Compose a sequence of affine maps as such: f circ g = f(g(x))

g(x) = A_g x + b_g f(x) = A_f x + b_f f(g(x)) = A_f (A_g x + b_g) + b_f = (A_f A_g) x + (A_f b_g + b_f)

Parameters

valid

reference to an affine map object

Returns

new affine map object with the new applied mapping

Definition at line 127 of file affine_map.hpp.

References affine::AffineMap< Mat >::linear_part(), linalg::mat_rows_v, and affine::AffineMap< Mat >::translation().

inverse()

template<linalg::MatrixContainer Mat>

constexpr auto affine::AffineMap< Mat >::inverse ( ) const

inlineconstexpr

inverse mapping

Apply the inverse of the linear transformation matrix U and back out the translation by the inverse.

f(x) = U x + c f^{-1}(f(x)) = id or x

f^{-1}(x) = U^{-1} x - U^{-1} c f^{-1}(f(x)) = U^{-1}(U x + c) - U^{-1} c == x

Returns

new affine map object that is the inverse of the forward mapping

Definition at line 148 of file affine_map.hpp.

References affine::AffineMap< Mat >::AffineMap(), affine::AffineMap< Mat >::M, linalg::mat_rows_v, and affine::AffineMap< Mat >::N.

linear_part()

template<linalg::MatrixContainer Mat>

constexpr auto affine::AffineMap< Mat >::linear_part ( ) const

inlineconstexpr

linear part

Returns

U

Definition at line 160 of file affine_map.hpp.

Referenced by affine::AffineMap< Mat >::compose().

operator!=()

template<linalg::MatrixContainer Mat>

constexpr bool affine::AffineMap< Mat >::operator!= ( const AffineMap< Mat > &  other ) const

inlineconstexpr

inequality comparison overload

Parameters

affine

set

Returns

T/F

Definition at line 187 of file affine_map.hpp.

operator()()

template<linalg::MatrixContainer Mat>

constexpr auto affine::AffineMap< Mat >::operator() ( const DomVec &  x ) const

inlineconstexpr

transform point to coords

Parameters

point

in R^n

Returns

transformed point

Definition at line 198 of file affine_map.hpp.

operator==()

template<linalg::MatrixContainer Mat>

constexpr bool affine::AffineMap< Mat >::operator== ( const AffineMap< Mat > &  other ) const

inlineconstexpr

equality comparison overload

Parameters

affine

set

Returns

T/F

Definition at line 176 of file affine_map.hpp.

translation()

template<linalg::MatrixContainer Mat>

constexpr auto affine::AffineMap< Mat >::translation ( ) const

inlineconstexpr

translation

Returns

c

Definition at line 167 of file affine_map.hpp.

Referenced by affine::AffineMap< Mat >::compose().

Member Data Documentation

M

template<linalg::MatrixContainer Mat>

constexpr std::size_t affine::AffineMap< Mat >::M = linalg::mat_rows_v<Mat>

staticconstexpr

helpers to extracting M x N matrix

Definition at line 69 of file affine_map.hpp.

Referenced by affine::AffineMap< Mat >::inverse().

N

template<linalg::MatrixContainer Mat>

constexpr std::size_t affine::AffineMap< Mat >::N = linalg::mat_cols_v<Mat>

staticconstexpr

Definition at line 70 of file affine_map.hpp.

Referenced by affine::AffineMap< Mat >::inverse().

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

• include/akreon/linalg/affine/affine_map.hpp