Namespace of all things related to geometry. More...

Namespaces
namespace	impl
	Implementation namespace of geom namespace.
namespace	internal
Classes
class	complex_geometry
	A functor returning the sites of the faces of a complex where the locations of each 0-face is stored. More...
Functions
template<typename S >
box< typename S::site >	bbox (const Site_Set< S > &pset)
	Compute the precise bounding box of a point set `pset`.
template<typename I >
box< typename I::site >	bbox (const Image< I > &ima)
	Compute the precise bounding box of a point set `pset`.
template<typename W >
box< typename W::psite >	bbox (const Window< W > &win)
	Compute the precise bounding box of a window `win`.
template<typename W >
box< typename W::psite >	bbox (const Weighted_Window< W > &win)
	Compute the precise bounding box of a weighted window `win`.
template<typename I , typename W >
mln::trait::ch_value< I, unsigned >::ret	chamfer (const Image< I > &input_, const W &w_win_, unsigned max=mln_max(unsigned))
	Apply chamfer algorithm to a binary image.
template<typename W >
unsigned	delta (const Window< W > &win)
	Compute the delta of a window `win`.
template<typename W >
unsigned	delta (const Weighted_Window< W > &wwin)
	Compute the delta of a weighted window `wwin`.
template<typename N >
unsigned	delta (const Neighborhood< N > &nbh)
	Compute the delta of a neighborhood `nbh`.
template<typename I >
I::site::coord	max_col (const Image< I > &ima)
	Give the maximum column of an image.
template<typename B >
B::point::coord	max_col (const Box< B > &b)
	Give the maximum col of an box 2d or 3d.
template<typename I >
I::site::coord	max_ind (const Image< I > &ima)
	Give the maximum ind of an image.
template<typename B >
B::point::coord	max_row (const Box< B > &b)
	Give the maximum row of an box 2d or 3d.
template<typename I >
I::site::coord	max_row (const Image< I > &ima)
	Give the maximum row of an image.
template<typename I >
I::site::coord	max_sli (const Image< I > &ima)
	Give the maximum sli of an image.
std::pair< complex_image < 2, mln::space_2complex_geometry, algebra::vec< 3, float > >, complex_image < 2, mln::space_2complex_geometry, float > >	mesh_corner_point_area (const p_complex< 2, space_2complex_geometry > &mesh)
	Compute the area ``belonging'' to normals at vertices.
std::pair< complex_image < 2, mln::space_2complex_geometry, float >, complex_image < 2, mln::space_2complex_geometry, float > >	mesh_curvature (const p_complex< 2, space_2complex_geometry > &mesh)
	Compute the principal curvatures of a surface at vertices.
complex_image < 2, mln::space_2complex_geometry, algebra::vec< 3, float > >	mesh_normal (const p_complex< 2, space_2complex_geometry > &mesh)
	Compute normals at vertices.
template<typename I >
I::site::coord	min_col (const Image< I > &ima)
	Give the minimum column of an image.
template<typename B >
B::point::coord	min_col (const Box< B > &b)
	Give the minimum column of an box 2d or 3d.
template<typename I >
I::site::coord	min_ind (const Image< I > &ima)
	Give the minimum ind of an image.
template<typename I >
I::site::coord	min_row (const Image< I > &ima)
	Give the minimum row of an image.
template<typename B >
B::point::coord	min_row (const Box< B > &b)
	Give the minimum row of an box 2d or 3d.
template<typename I >
I::site::coord	min_sli (const Image< I > &ima)
	Give the minimum sli of an image.
template<typename I >
unsigned	ncols (const Image< I > &ima)
	Give the number of columns of an image.
template<typename B >
unsigned	ncols (const Box< B > &b)
	Give the number of cols of a box 2d or 3d.
template<typename I >
unsigned	ninds (const Image< I > &ima)
	Give the number of inds of an image.
template<typename I >
unsigned	nrows (const Image< I > &ima)
	Give the number of rows of an image.
template<typename B >
unsigned	nrows (const Box< B > &b)
	Give the number of rows of a box 2d or 3d.
template<typename I >
unsigned	nsites (const Image< I > &input)
	Compute the number of sites of the image `input`.
template<typename I >
unsigned	nslis (const Image< I > &ima)
	Give the number of slices of an image.
template<typename I >
void	pmin_pmax (const Site_Iterator< I > &p, typename I::site &pmin, typename I::site &pmax)
	Compute the minimum and maximum points, `pmin` and `max`, when browsing with iterator `p`.
template<typename S >
void	pmin_pmax (const Site_Set< S > &s, typename S::site &pmin, typename S::site &pmax)
	Compute the minimum and maximum points, `pmin` and `max`, of point set `s`.
template<typename I >
std::pair< typename I::site, typename I::site >	pmin_pmax (const Site_Iterator< I > &p)
	Compute the minimum and maximum points when browsing with iterator `p`.
template<typename S >
std::pair< typename S::site, typename S::site >	pmin_pmax (const Site_Set< S > &s)
	Compute the minimum and maximum points of point set `s`.
template<typename I >
mln::trait::concrete< I >::ret	rotate (const Image< I > &input, double angle)
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts. Use literal::zero as default value for the extension.
template<typename I , typename Ext >
mln::trait::concrete< I >::ret	rotate (const Image< I > &input, double angle, const Ext &extension)
template<typename I , typename Ext , typename S >
mln::trait::concrete< I >::ret	rotate (const Image< I > &input, double angle, const Ext &extension, const Site_Set< S > &output_domain)
	Perform a rotation from the center of an image.
template<typename I , typename N >
mln::trait::concrete< I >::ret	seeds2tiling (const Image< I > &ima_, const Neighborhood< N > &nbh)
	Take a labeled image `ima_` with seeds and extend them until creating tiles.


template<typename I , typename N >
I	seeds2tiling_roundness (Image< I > &ima_, const w_window2d_int &w_win, unsigned max, const Neighborhood< N > &nbh_)
	Take a labeled image `ima_` with seeds and extend them until creating tiles rounder than the primary version.

Detailed Description

Namespace of all things related to geometry.

Namespace of essential things related to geometry.

Function Documentation

template<typename S >

box< typename S::site > mln::geom::bbox ( const Site_Set< S > & pset ) [inline]

Compute the precise bounding box of a point set pset.

References mln::geom::impl::bbox_(), mln::trace::entering(), mln::exact(), and mln::trace::exiting().

Referenced by bbox(), mln::registration::closest_point_with_map::closest_point_with_map(), mln::transform::distance_and_closest_point_geodesic(), mln::convert::impl::from_site_set_to_image(), mln::convert::over_load::from_to_(), mln::registration::icp(), mln::init_(), max_col(), max_row(), min_col(), min_row(), mln::debug::println(), mln::debug::println_with_border(), mln::world::binary_2d::projected_histo(), and rotate().

template<typename I >

box< typename I::site > mln::geom::bbox ( const Image & ima )

Compute the precise bounding box of a point set pset.

References bbox(), mln::trace::entering(), mln::exact(), and mln::trace::exiting().

template<typename W >

box< typename W::psite > mln::geom::bbox ( const Window< W > & win )

Compute the precise bounding box of a window win.

References mln::trace::entering(), mln::exact(), mln::trace::exiting(), mln::literal::origin, and mln::accu::shape::bbox::take().

template<typename W >

box< typename W::psite > mln::geom::bbox ( const Weighted_Window< W > & win )

Compute the precise bounding box of a weighted window win.

References bbox(), mln::trace::entering(), mln::exact(), and mln::trace::exiting().

template<typename I , typename W >

mln::trait::ch_value< I, unsigned >::ret mln::geom::chamfer	(	const Image< I > &	input_,
		const W &	w_win_,
		unsigned	max = `mln_max(unsigned)`
	)

Apply chamfer algorithm to a binary image.

References mln::trace::entering(), mln::exact(), and mln::trace::exiting().

Referenced by mln::geom::impl::seeds2tiling_roundness().

template<typename W >

unsigned mln::geom::delta ( const Window< W > & win )

Compute the delta of a window win.

References mln::geom::internal::delta_dispatch(), and mln::exact().

Referenced by mln::extension::adjust(), delta(), mln::morpho::impl::generic::rank_filter(), mln::morpho::impl::rank_filter_directional(), mln::morpho::impl::rank_filter_line(), mln::accu::transform_diagonal(), mln::accu::transform_directional(), and mln::accu::transform_snake().

template<typename W >

unsigned mln::geom::delta ( const Weighted_Window< W > & wwin )

Compute the delta of a weighted window wwin.

References delta(), and mln::exact().

template<typename N >

unsigned mln::geom::delta ( const Neighborhood< N > & nbh )

Compute the delta of a neighborhood nbh.

References delta(), and mln::exact().

template<typename I >

I::site::coord mln::geom::max_col ( const Image & ima ) [inline]

Give the maximum column of an image.

References bbox(), mln::trace::entering(), mln::exact(), mln::trace::exiting(), and mln::box::pmax().

Referenced by mln::data::impl::fast_median(), mln::data::impl::hmedian(), mln::io::pbm::internal::load_raw_2d(), mln::io::pnm::load_raw_2d_uncontiguous(), mln::data::impl::median_as_procedure(), ncols(), mln::canvas::browsing::snake_vert_t::operator()(), mln::canvas::browsing::snake_fwd_t::operator()(), mln::io::pnm::impl::save_data_uncontiguous(), mln::fwd_pixter3d::start_(), and mln::fwd_pixter2d::start_().

template<typename B >

B::point::coord mln::geom::max_col ( const Box & b ) [inline]

Give the maximum col of an box 2d or 3d.

References mln::trace::entering(), mln::exact(), and mln::trace::exiting().

template<typename I >

I::site::coord mln::geom::max_ind ( const Image & ima ) [inline]

Give the maximum ind of an image.

References mln::trace::entering(), mln::exact(), and mln::trace::exiting().

Referenced by ninds().

template<typename B >

B::point::coord mln::geom::max_row ( const Box & b ) [inline]

Give the maximum row of an box 2d or 3d.

References mln::trace::entering(), mln::exact(), and mln::trace::exiting().

template<typename I >

I::site::coord mln::geom::max_row ( const Image & ima ) [inline]

template<typename I >

I::site::coord mln::geom::max_sli ( const Image & ima ) [inline]

Give the maximum sli of an image.

References mln::trace::entering(), mln::exact(), and mln::trace::exiting().

Referenced by nslis(), and mln::bkd_pixter3d::start_().

std::pair< complex_image< 2, mln::space_2complex_geometry, algebra::vec<3, float> >, complex_image< 2, mln::space_2complex_geometry, float > > mln::geom::mesh_corner_point_area ( const p_complex< 2, space_2complex_geometry > & mesh ) [inline]

Compute the area ``belonging'' to normals at vertices.

Inspired from the method Trimesh::need_pointareas of the Trimesh library.

See also:: http://www.cs.princeton.edu/gfx/proj/trimesh2/

From the documentation of Trimesh:

``Compute the area "belonging" to each vertex or each corner of a triangle (defined as Voronoi area restricted to the 1-ring of a vertex, or to the triangle).''

Psites of 0-faces transitively adjacent to F.

The should be exactly three vertices adjacent to F.

References mln::data::fill(), mln::norm::l2(), mln::norm::sqr_l2(), mln::algebra::vprod(), and mln::literal::zero.

Referenced by mesh_curvature().

std::pair< complex_image< 2, mln::space_2complex_geometry, float >, complex_image< 2, mln::space_2complex_geometry, float > > mln::geom::mesh_curvature ( const p_complex< 2, space_2complex_geometry > & mesh ) [inline]

Compute the principal curvatures of a surface at vertices.

These princpal curvatures are names kappa_1 and kappa_2 in

Sylvie Philipp-Foliguet, Michel Jordan Laurent Najman and Jean Cousty. Artwork 3D Model Database Indexing and Classification.

Parameters:

[in] mesh The surface (triangle mesh) on which the curvature is to be computed.

Psites of 0-faces transitively adjacent to F.

The should be exactly three vertices adjacent to F.

References mln::geom::internal::diagonalize_curv(), mln::algebra::ldlt_decomp(), mln::algebra::ldlt_solve(), mesh_corner_point_area(), mesh_normal(), mln::geom::internal::next(), mln::geom::internal::prev(), mln::geom::internal::proj_curv(), mln::algebra::vprod(), and mln::literal::zero.

complex_image< 2, mln::space_2complex_geometry, algebra::vec<3, float> > mln::geom::mesh_normal ( const p_complex< 2, space_2complex_geometry > & mesh ) [inline]

Compute normals at vertices.

Inspired from the method Trimesh::need_normals of the Trimesh library.

See also:: http://www.cs.princeton.edu/gfx/proj/trimesh2/

For simplicity purpose, and contrary to Trimesh, this routine only compute normals from a mesh, not from a cloud of points.

Psites of 0-faces transitively adjacent to F.

The should be exactly three vertices adjacent to F.

References mln::data::fill(), mln::norm::sqr_l2(), mln::algebra::vprod(), and mln::literal::zero.

Referenced by mesh_curvature().

template<typename I >

I::site::coord mln::geom::min_col ( const Image & ima ) [inline]

Give the minimum column of an image.

References bbox(), mln::trace::entering(), mln::exact(), mln::trace::exiting(), and mln::box::pmin().

Referenced by mln::world::binary_2d::impl::enlargex2(), mln::data::impl::fast_median(), mln::data::impl::hmedian(), mln::transform::hough(), mln::io::pbm::internal::load_raw_2d(), mln::io::pnm::load_raw_2d_uncontiguous(), mln::data::impl::median_as_procedure(), ncols(), mln::canvas::browsing::snake_vert_t::operator()(), mln::canvas::browsing::snake_fwd_t::operator()(), mln::io::pnm::impl::save_data_contiguous(), mln::io::pnm::impl::save_data_uncontiguous(), mln::bkd_pixter3d::start_(), and mln::bkd_pixter2d::start_().

template<typename B >

B::point::coord mln::geom::min_col ( const Box & b ) [inline]

Give the minimum column of an box 2d or 3d.

References mln::trace::entering(), mln::exact(), and mln::trace::exiting().

template<typename I >

I::site::coord mln::geom::min_ind ( const Image & ima ) [inline]

Give the minimum ind of an image.

References mln::trace::entering(), mln::exact(), and mln::trace::exiting().

Referenced by ninds().

template<typename I >

I::site::coord mln::geom::min_row ( const Image & ima ) [inline]

template<typename B >

B::point::coord mln::geom::min_row ( const Box & b ) [inline]

Give the minimum row of an box 2d or 3d.

References mln::trace::entering(), mln::exact(), and mln::trace::exiting().

template<typename I >

I::site::coord mln::geom::min_sli ( const Image & ima ) [inline]

Give the minimum sli of an image.

References mln::trace::entering(), mln::exact(), and mln::trace::exiting().

Referenced by nslis(), and mln::fwd_pixter3d::start_().

template<typename I >

unsigned mln::geom::ncols ( const Image & ima ) [inline]

template<typename B >

unsigned mln::geom::ncols ( const Box & b )

Give the number of cols of a box 2d or 3d.

References mln::trace::entering(), mln::trace::exiting(), max_col(), min_col(), and ncols().

template<typename I >

unsigned mln::geom::ninds ( const Image & ima ) [inline]

Give the number of inds of an image.

References mln::trace::entering(), mln::exact(), mln::trace::exiting(), max_ind(), and min_ind().

Referenced by mln::linear::gaussian_1d(), mln::linear::gaussian::impl::generic_filter_(), and mln::linear::impl::generic_filter_().

template<typename I >

unsigned mln::geom::nrows ( const Image & ima ) [inline]

Give the number of rows of an image.

References mln::trace::entering(), mln::exact(), mln::trace::exiting(), max_row(), and min_row().

Referenced by mln::linear::gaussian_directional_2d(), mln::subsampling::gaussian_subsampling(), mln::linear::gaussian::impl::generic_filter_(), mln::linear::impl::generic_filter_(), mln::transform::hough(), nrows(), mln::world::binary_2d::projected_histo(), mln::io::pnm::save_header(), mln::io::pfm::impl::save_header_(), mln::subsampling::subsampling(), and mln::subsampling::impl::subsampling_().

template<typename B >

unsigned mln::geom::nrows ( const Box & b )

Give the number of rows of a box 2d or 3d.

References mln::trace::entering(), mln::trace::exiting(), max_row(), min_row(), and nrows().

template<typename I >

unsigned mln::geom::nsites ( const Image & input ) [inline]

Compute the number of sites of the image input.

References mln::set::internal::card_dispatch(), mln::trace::entering(), mln::exact(), and mln::trace::exiting().

Referenced by mln::world::inter_pixel::full2image(), mln::world::inter_pixel::immerse(), pmin_pmax(), mln::data::impl::sort_offsets_decreasing_radix(), mln::data::impl::sort_offsets_increasing_radix(), mln::data::impl::sort_psites_decreasing_(), and mln::data::impl::sort_psites_increasing_().

template<typename I >

unsigned mln::geom::nslis ( const Image & ima ) [inline]

Give the number of slices of an image.

References mln::trace::entering(), mln::exact(), mln::trace::exiting(), max_sli(), and min_sli().

Referenced by mln::linear::gaussian::impl::generic_filter_(), and mln::linear::impl::generic_filter_().

template<typename S >

std::pair< typename S::site, typename S::site > mln::geom::pmin_pmax ( const Site_Set< S > & s ) [inline]

Compute the minimum and maximum points of point set s.

References mln::exact(), and nsites().

Referenced by pmin_pmax(), and mln::geom::impl::pmin_pmax_().

template<typename I >

std::pair< typename I::site, typename I::site > mln::geom::pmin_pmax ( const Site_Iterator & p ) [inline]

Compute the minimum and maximum points when browsing with iterator p.

References pmin_pmax().

template<typename S >

void mln::geom::pmin_pmax	(	const Site_Set< S > &	s,
		typename S::site &	pmin,
		typename S::site &	pmax
	)			`[inline]`

Compute the minimum and maximum points, pmin and max, of point set s.

References mln::exact(), nsites(), and mln::geom::impl::pmin_pmax_().

template<typename I >

void mln::geom::pmin_pmax	(	const Site_Iterator< I > &	p,
		typename I::site &	pmin,
		typename I::site &	pmax
	)			`[inline]`

Compute the minimum and maximum points, pmin and max, when browsing with iterator p.

References mln::exact().

template<typename I , typename Ext >

mln::trait::concrete< I >::ret mln::geom::rotate	(	const Image< I > &	input,
		double	angle,
		const Ext &	extension
	)

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

References rotate().

template<typename I , typename Ext , typename S >

mln::trait::concrete< I >::ret mln::geom::rotate	(	const Image< I > &	input,
		double	angle,
		const Ext &	extension,
		const Site_Set< S > &	output_domain
	)

Perform a rotation from the center of an image.

Parameters:

`[in]`	input	An image.
`[in]`	angle	An angle in degrees.
`[in]`	extension	Function, image or value which will be used as extension. This extension allows to map values to sites which where not part of the domain before the rotation.
`[in]`	output_domain	The domain of the output image. An invalid domain, causes the routine to use the rotated input_ domain.

Returns:: An image with the same domain as input.

References bbox(), mln::box::center(), mln::compose(), mln::trace::entering(), mln::exact(), mln::trace::exiting(), mln::extend(), mln::initialize(), mln::mln_exact(), mln::literal::origin, mln::data::paste(), mln::math::pi, mln::accu::shape::bbox::take(), mln::accu::shape::bbox::to_result(), and mln::transposed_image().

Referenced by rotate().

template<typename I >

mln::trait::concrete< I >::ret mln::geom::rotate	(	const Image< I > &	input,
		double	angle
	)

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts. Use literal::zero as default value for the extension.

References rotate(), and mln::literal::zero.

template<typename I , typename N >

mln::trait::concrete< I >::ret mln::geom::seeds2tiling	(	const Image< I > &	ima_,
		const Neighborhood< N > &	nbh
	)			`[inline]`

Take a labeled image ima_ with seeds and extend them until creating tiles.

Parameters:

`[in,out]`	ima_	The labeled image with seed.
`[in]`	nbh	The neighborhood to use on this algorithm.

Returns:: A tiled image.

Precondition:: ima_ has to be initialized.

References mln::trace::entering(), mln::exact(), mln::trace::exiting(), and mln::geom::impl::seeds2tiling().

template<typename I , typename N >

I mln::geom::seeds2tiling_roundness	(	Image< I > &	ima_,
		const w_window2d_int &	w_win,
		unsigned	max,
		const Neighborhood< N > &	nbh_
	)			`[inline]`

Take a labeled image ima_ with seeds and extend them until creating tiles rounder than the primary version.

Parameters:

`[in,out]`	ima_	The labeled image with seed.
`[in]`	w_win	The weight window using by geom::chamfer to compute distance.
`[in]`	max	Unsigned using by geom::chamfer to compute the distance.
`[in]`	nbh_	The neighborhood to use on this algorithm.

Precondition:: ima_ has to be initialized.

References mln::trace::entering(), mln::exact(), mln::trace::exiting(), and mln::geom::impl::seeds2tiling_roundness().

mln::geom Namespace Reference

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Detailed Description

Function Documentation