mln::topo Namespace Reference

Namespace of "point-wise" expression tools. More...

Classes
class	adj_higher_dim_connected_n_face_bkd_iter
	Backward iterator on all the n-faces sharing an adjacent (n+1)-face with a (reference) n-face of an mln::complex<D>. More...
class	adj_higher_dim_connected_n_face_fwd_iter
	Forward iterator on all the n-faces sharing an adjacent (n+1)-face with a (reference) n-face of an mln::complex<D>. More...
class	adj_higher_face_bkd_iter
	Backward iterator on all the adjacent (n+1)-faces of the n-face of an mln::complex<D>. More...
class	adj_higher_face_fwd_iter
	Forward iterator on all the adjacent (n+1)-faces of the n-face of an mln::complex<D>. More...
class	adj_lower_dim_connected_n_face_bkd_iter
	Backward iterator on all the n-faces sharing an adjacent (n-1)-face with a (reference) n-face of an mln::complex<D>. More...
class	adj_lower_dim_connected_n_face_fwd_iter
	Forward iterator on all the n-faces sharing an adjacent (n-1)-face with a (reference) n-face of an mln::complex<D>. More...
class	adj_lower_face_bkd_iter
	Backward iterator on all the adjacent (n-1)-faces of the n-face of an mln::complex<D>. More...
class	adj_lower_face_fwd_iter
	Forward iterator on all the adjacent (n-1)-faces of the n-face of an mln::complex<D>. More...
class	adj_lower_higher_face_bkd_iter
	Forward iterator on all the adjacent (n-1)-faces and (n+1)-faces of the n-face of an mln::complex<D>. More...
class	adj_lower_higher_face_fwd_iter
	Forward iterator on all the adjacent (n-1)-faces and (n+1)-faces of the n-face of an mln::complex<D>. More...
class	adj_m_face_bkd_iter
	Backward iterator on all the m-faces transitively adjacent to a (reference) n-face in a complex. More...
class	adj_m_face_fwd_iter
	Forward iterator on all the m-faces transitively adjacent to a (reference) n-face in a complex. More...
struct	algebraic_face
	Algebraic face handle in a complex; the face dimension is dynamic. More...
class	algebraic_n_face
	Algebraic N-face handle in a complex. More...
class	center_only_iter
	Iterator on all the adjacent (n-1)-faces of the n-face of an mln::complex<D>. More...
class	centered_bkd_iter_adapter
	Forward complex relative iterator adapters adding the central (reference) point to the set of iterated faces. More...
class	centered_fwd_iter_adapter
	Backward complex relative iterator adapters adding the central (reference) point to the set of iterated faces. More...
class	complex
	General complex of dimension D. More...
struct	face
	Face handle in a complex; the face dimension is dynamic. More...
class	face_bkd_iter
	Backward iterator on all the faces of an mln::complex<D>. More...
class	face_fwd_iter
	Forward iterator on all the faces of an mln::complex<D>. More...
struct	is_n_face
	A functor testing wheter a mln::complex_psite is an N -face. More...
class	is_simple_cell
	A predicate for the simplicity of a point based on the collapse property of the attachment. More...
class	n_face
	N-face handle in a complex. More...
class	n_face_bkd_iter
	Backward iterator on all the faces of an mln::complex<D>. More...
class	n_face_fwd_iter
	Forward iterator on all the faces of an mln::complex<D>. More...
class	n_faces_set
	Set of face handles of dimension N. More...
class	static_n_face_bkd_iter
	Backward iterator on all the N-faces of a mln::complex<D>. More...
class	static_n_face_fwd_iter
	Forward iterator on all the N-faces of a mln::complex<D>. More...
Functions
template<unsigned D, typename G>
void	detach (const complex_psite< D, G > &f, complex_image< D, G, bool > &ima)
	Detach the cell corresponding to f from ima.
template<unsigned D, typename G>
bool	is_facet (const complex_psite< D, G > &f)
	Is f a facet, i.e., a face not ``included in'' (adjacent to) a face of higher dimension?
template<unsigned D>
algebraic_face< D >	make_algebraic_face (const face< D > &f, bool sign)
	Create an algebraic face handle of a D-complex.
template<unsigned N, unsigned D>
algebraic_n_face< N, D >	make_algebraic_n_face (const n_face< N, D > &f, bool sign)
	Create an algebraic N-face handle of a D-complex.
template<unsigned N, unsigned D>
std::ostream &	operator<< (std::ostream &ostr, const n_face< N, D > &f)
	Print an mln::topo::n_face.
template<unsigned D>
std::ostream &	operator<< (std::ostream &ostr, const face< D > &f)
	Print an mln::topo::face.
template<unsigned D>
std::ostream &	operator<< (std::ostream &ostr, const complex< D > &c)
	Pretty print a complex.
template<unsigned N, unsigned D>
std::ostream &	operator<< (std::ostream &ostr, const algebraic_n_face< N, D > &f)
	Print an mln::topo::algebraic_n_face.
template<unsigned D>
std::ostream &	operator<< (std::ostream &ostr, const algebraic_face< D > &f)
	Print an mln::topo::algebraic_face.
template<unsigned D>
bool	operator== (const complex< D > &lhs, const complex< D > &rhs)
	Compare two complexes for equality.
template<unsigned D>
algebraic_n_face< 1, D >	edge (const n_face< 0, D > &f1, const n_face< 0, D > &f2)
	Helpers.
template<unsigned N, unsigned D>
bool	operator!= (const n_face< N, D > &lhs, const n_face< N, D > &rhs)
	Is lhs different from rhs?
template<unsigned N, unsigned D>
bool	operator< (const n_face< N, D > &lhs, const n_face< N, D > &rhs)
	Is lhs ``less'' than rhs?
template<unsigned N, unsigned D>
bool	operator== (const n_face< N, D > &lhs, const n_face< N, D > &rhs)
	Comparison of two instances of mln::topo::n_face.
template<unsigned D>
bool	operator!= (const face< D > &lhs, const face< D > &rhs)
	Is lhs different from rhs?
template<unsigned D>
bool	operator< (const face< D > &lhs, const face< D > &rhs)
	Is lhs ``less'' than rhs?
template<unsigned D>
bool	operator== (const face< D > &lhs, const face< D > &rhs)
	Comparison of two instances of mln::topo::face.
template<unsigned N, unsigned D>
bool	operator!= (const algebraic_n_face< N, D > &lhs, const algebraic_n_face< N, D > &rhs)
	Is lhs different from rhs?
template<unsigned N, unsigned D>
bool	operator< (const algebraic_n_face< N, D > &lhs, const algebraic_n_face< N, D > &rhs)
	Is lhs ``less'' than rhs?
template<unsigned N, unsigned D>
bool	operator== (const algebraic_n_face< N, D > &lhs, const algebraic_n_face< N, D > &rhs)
	Comparison of two instances of mln::topo::algebraic_n_face.
template<unsigned D>
bool	operator!= (const algebraic_face< D > &lhs, const algebraic_face< D > &rhs)
	Is lhs different from rhs?
template<unsigned D>
bool	operator< (const algebraic_face< D > &lhs, const algebraic_face< D > &rhs)
	Is lhs ``less'' than rhs?
template<unsigned D>
bool	operator== (const algebraic_face< D > &lhs, const algebraic_face< D > &rhs)
	Comparison of two instances of mln::topo::algebraic_face.
template<unsigned N, unsigned D>
n_faces_set< N, D >	operator+ (const algebraic_n_face< N, D > &f1, const algebraic_n_face< N, D > &f2)
	Addition.
template<unsigned N, unsigned D>
n_faces_set< N, D >	operator- (const algebraic_n_face< N, D > &f1, const algebraic_n_face< N, D > &f2)
	Subtraction.
template<unsigned N, unsigned D>
algebraic_n_face< N, D >	operator- (const n_face< N, D > &f)
	Inversion operators.
template<unsigned D>
algebraic_face< D >	operator- (const face< D > &f)
	Inversion operators.

---

Detailed Description

Namespace of "point-wise" expression tools.

---

Function Documentation

template<unsigned D, typename G>

void mln::topo::detach	(	const complex_psite< D, G > &	f,
		complex_image< D, G, bool > &	ima
	)			[inline]

Detach the cell corresponding to f from ima.

Precondition:

f is a facet (it does not belong to any face of higher dimension).

ima is an image of Boolean values.

References mln::make::detachment(), mln::data::fill(), and is_facet().

template<unsigned D>

algebraic_n_face< 1, D > mln::topo::edge	(	const n_face< 0, D > &	f1,
		const n_face< 0, D > &	f2
	)			[inline]

Helpers.

Return the algebraic 1-face (edge) linking the 0-faces (vertices) f1 and f2. If there is no 1-face between f1 and f2, return an invalid 1-face.

Precondition:

f1 and f2 must belong to the same complex.

Note: this routine assumes the complex is not degenerated, i.e,

• it does not check that f1 and f2 are the only 0-faces adjacent to an hypothetical 1-face; it just checks that f1 and f2 share a common 1-face;

• if there are several ajacent 1-faces shared by f1 and f2 (if the complex is ill-formed), there is no guarantee on the returned 1-face (the current implementation return the first 1-face found, but client code should not rely on this implementation-defined behavior).

References mln::topo::n_face< N, D >::higher_dim_adj_faces().

template<unsigned D, typename G>

bool mln::topo::is_facet

(

const complex_psite< D, G > &

f

)

[inline]

Is f a facet, i.e., a face not ``included in'' (adjacent to) a face of higher dimension?

Referenced by mln::make::attachment(), mln::make::cell(), detach(), and mln::make::detachment().

template<unsigned D>

algebraic_face< D > mln::topo::make_algebraic_face	(	const face< D > &	f,
		bool	sign
	)			[inline]

Create an algebraic face handle of a D-complex.

template<unsigned N, unsigned D>

algebraic_n_face< N, D > mln::topo::make_algebraic_n_face	(	const n_face< N, D > &	f,
		bool	sign
	)			[inline]

Create an algebraic N-face handle of a D-complex.

template<unsigned N, unsigned D>

bool mln::topo::operator!=	(	const n_face< N, D > &	lhs,
		const n_face< N, D > &	rhs
	)			[inline]

Is lhs different from rhs?

Precondition:

Arguments lhs and rhs must belong to the same mln::topo::complex.

References mln::topo::n_face< N, D >::cplx().

template<unsigned D>

bool mln::topo::operator!=	(	const face< D > &	lhs,
		const face< D > &	rhs
	)			[inline]

Is lhs different from rhs?

Precondition:

Arguments lhs and rhs must belong to the same mln::topo::complex.

References mln::topo::face< D >::cplx().

template<unsigned N, unsigned D>

bool mln::topo::operator!=	(	const algebraic_n_face< N, D > &	lhs,
		const algebraic_n_face< N, D > &	rhs
	)			[inline]

Is lhs different from rhs?

Precondition:

Arguments lhs and rhs must belong to the same mln::topo::complex.

References mln::topo::n_face< N, D >::cplx().

template<unsigned D>

bool mln::topo::operator!=	(	const algebraic_face< D > &	lhs,
		const algebraic_face< D > &	rhs
	)			[inline]

Is lhs different from rhs?

Precondition:

Arguments lhs and rhs must belong to the same mln::topo::complex.

References mln::topo::face< D >::cplx().

template<unsigned N, unsigned D>

n_faces_set< N, D > mln::topo::operator+	(	const algebraic_n_face< N, D > &	f1,
		const algebraic_n_face< N, D > &	f2
	)			[inline]

Addition.

References mln::topo::n_faces_set< N, D >::add().

template<unsigned N, unsigned D>

n_faces_set< N, D > mln::topo::operator-	(	const algebraic_n_face< N, D > &	f1,
		const algebraic_n_face< N, D > &	f2
	)			[inline]

Subtraction.

References mln::topo::n_faces_set< N, D >::add().

template<unsigned N, unsigned D>

algebraic_n_face< N, D > mln::topo::operator-

(

const n_face< N, D > &

f

)

[inline]

Inversion operators.

template<unsigned D>

algebraic_face< D > mln::topo::operator-

(

const face< D > &

f

)

[inline]

Inversion operators.

template<unsigned N, unsigned D>

bool mln::topo::operator<	(	const n_face< N, D > &	lhs,
		const n_face< N, D > &	rhs
	)			[inline]

Is lhs ``less'' than rhs?

This comparison is required by algorithms sorting face handles.

Precondition:

Arguments lhs and rhs must belong to the same mln::topo::complex.

template<unsigned D>

bool mln::topo::operator<	(	const face< D > &	lhs,
		const face< D > &	rhs
	)			[inline]

Is lhs ``less'' than rhs?

This comparison is required by algorithms sorting face handles.

Precondition:

Arguments lhs and rhs must belong to the same mln::topo::complex.

Arguments lhs and rhs must have the same dimension.

template<unsigned N, unsigned D>

bool mln::topo::operator<	(	const algebraic_n_face< N, D > &	lhs,
		const algebraic_n_face< N, D > &	rhs
	)			[inline]

Is lhs ``less'' than rhs?

This comparison is required by algorithms sorting algebraic face handles.

Precondition:

Arguments lhs and rhs must belong to the same mln::topo::complex.

template<unsigned D>

bool mln::topo::operator<	(	const algebraic_face< D > &	lhs,
		const algebraic_face< D > &	rhs
	)			[inline]

Is lhs ``less'' than rhs?

This comparison is required by algorithms sorting algebraic face handles.

Precondition:

Arguments lhs and rhs must belong to the same mln::topo::complex.

Arguments lhs and rhs must have the same dimension.

template<unsigned N, unsigned D>

std::ostream & mln::topo::operator<<	(	std::ostream &	ostr,
		const n_face< N, D > &	f
	)			[inline]

Print an mln::topo::n_face.

template<unsigned D>

std::ostream & mln::topo::operator<<	(	std::ostream &	ostr,
		const face< D > &	f
	)			[inline]

Print an mln::topo::face.

template<unsigned D>

std::ostream & mln::topo::operator<<	(	std::ostream &	ostr,
		const complex< D > &	c
	)			[inline]

Pretty print a complex.

References mln::topo::complex< D >::print().

template<unsigned N, unsigned D>

std::ostream & mln::topo::operator<<	(	std::ostream &	ostr,
		const algebraic_n_face< N, D > &	f
	)			[inline]

Print an mln::topo::algebraic_n_face.

template<unsigned D>

std::ostream & mln::topo::operator<<	(	std::ostream &	ostr,
		const algebraic_face< D > &	f
	)			[inline]

Print an mln::topo::algebraic_face.

template<unsigned N, unsigned D>

bool mln::topo::operator==	(	const n_face< N, D > &	lhs,
		const n_face< N, D > &	rhs
	)			[inline]

Comparison of two instances of mln::topo::n_face.

Is lhs equal to rhs?

Precondition:

Arguments lhs and rhs must belong to the same mln::topo::complex.

References mln::topo::n_face< N, D >::cplx(), and mln::topo::n_face< N, D >::face_id().

template<unsigned D>

bool mln::topo::operator==	(	const face< D > &	lhs,
		const face< D > &	rhs
	)			[inline]

Comparison of two instances of mln::topo::face.

Is lhs equal to rhs?

Precondition:

Arguments lhs and rhs must belong to the same mln::topo::complex.

References mln::topo::face< D >::cplx(), mln::topo::face< D >::face_id(), and mln::topo::face< D >::n().

template<unsigned D>

bool mln::topo::operator==	(	const complex< D > &	lhs,
		const complex< D > &	rhs
	)			[inline]

Compare two complexes for equality.

template<unsigned N, unsigned D>

bool mln::topo::operator==	(	const algebraic_n_face< N, D > &	lhs,
		const algebraic_n_face< N, D > &	rhs
	)			[inline]

Comparison of two instances of mln::topo::algebraic_n_face.

Is lhs equal to rhs?

Precondition:

Arguments lhs and rhs must belong to the same mln::topo::complex.

References mln::topo::n_face< N, D >::cplx(), mln::topo::n_face< N, D >::face_id(), and mln::topo::algebraic_n_face< N, D >::sign().

template<unsigned D>

bool mln::topo::operator==	(	const algebraic_face< D > &	lhs,
		const algebraic_face< D > &	rhs
	)			[inline]

Comparison of two instances of mln::topo::algebraic_face.

Is lhs equal to rhs?

Precondition:

Arguments lhs and rhs must belong to the same mln::topo::complex.

References mln::topo::face< D >::cplx(), mln::topo::face< D >::face_id(), mln::topo::face< D >::n(), and mln::topo::algebraic_face< D >::sign().