mln::geom Namespace Reference

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

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...
Namespaces
namespace	impl
	Implementation namespace of geom namespace.
Functions
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 W>
box< typename W::psite >	bbox (const Window< W > &win)
	Compute the precise bounding box of a window win.
template<typename I>
box< typename I::site >	bbox (const Image< I > &ima)
	Compute the precise bounding box of a point set pset.
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, 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 N>
unsigned	delta (const Neighborhood< N > &nbh)
	Compute the delta of a neighborhood nbh.
template<typename W>
unsigned	delta (const Weighted_Window< W > &wwin)
	Compute the delta of a weighted window wwin.
template<typename W>
unsigned	delta (const Window< W > &win)
	Compute the delta of a window win.
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_col (const Image< I > &ima)
	Give the maximum column of an image.
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 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_col (const Image< I > &ima)
	Give the minimum column of an image.
template<typename I>
I::site::coord	min_ind (const Image< I > &ima)
	Give the minimum ind 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_row (const Image< I > &ima)
	Give the minimum row of an image.
template<typename I>
I::site::coord	min_sli (const Image< I > &ima)
	Give the minimum sli 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	ncols (const Image< I > &ima)
	Give the number of columns of an image.
template<typename I>
unsigned	ninds (const Image< I > &ima)
	Give the number of inds 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	nrows (const Image< I > &ima)
	Give the number of rows of an image.
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 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>
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 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, 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 V>
mln::trait::concrete< I >::ret	translate (const Image< I > &input, const algebra::vec< I::site::dim, V > &ref)
	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 V, typename Ext, typename S>
mln::trait::concrete< I >::ret	translate (const Image< I > &input, const algebra::vec< I::site::dim, V > &ref, const Ext &extension, const Site_Set< S > &output_domain)
	Perform a translation from the center of an image.
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 W>

box< typename W::psite > mln::geom::bbox

(

const Weighted_Window< W > &

win

)

[inline]

Compute the precise bounding box of a weighted window win.

References bbox().

template<typename W>

box< typename W::psite > mln::geom::bbox

(

const Window< W > &

win

)

[inline]

Compute the precise bounding box of a window win.

References mln::literal::origin, and mln::accu::shape::bbox< P >::take().

template<typename I>

box< typename I::site > mln::geom::bbox

(

const Image< I > &

ima

)

[inline]

Compute the precise bounding box of a point set pset.

References bbox().

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.

Referenced by bbox(), mln::transform::distance_and_closest_point_geodesic(), mln::registration::icp(), max_col(), max_row(), max_sli(), min_col(), min_row(), min_sli(), mln::debug::println(), mln::debug::println_with_border(), and rotate().

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)
	)			[inline]

Apply chamfer algorithm to a binary image.

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

template<typename N>

unsigned mln::geom::delta

(

const Neighborhood< N > &

nbh

)

[inline]

Compute the delta of a neighborhood nbh.

References delta().

template<typename W>

unsigned mln::geom::delta

(

const Weighted_Window< W > &

wwin

)

[inline]

Compute the delta of a weighted window wwin.

References delta().

template<typename W>

unsigned mln::geom::delta

(

const Window< W > &

win

)

[inline]

Compute the delta of a window win.

Referenced by mln::extension::adjust(), delta(), and mln::morpho::impl::generic::rank_filter().

template<typename B>

B::point::coord mln::geom::max_col

(

const Box< B > &

b

)

[inline]

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

template<typename I>

I::site::coord mln::geom::max_col

(

const Image< I > &

ima

)

[inline]

Give the maximum column of an image.

References bbox().

Referenced by ncols().

template<typename I>

I::site::coord mln::geom::max_ind

(

const Image< I > &

ima

)

[inline]

Give the maximum ind of an image.

Referenced by ninds().

template<typename B>

B::point::coord mln::geom::max_row

(

const Box< B > &

b

)

[inline]

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

template<typename I>

I::site::coord mln::geom::max_row

(

const Image< I > &

ima

)

[inline]

Give the maximum row of an image.

References bbox().

Referenced by nrows().

template<typename I>

I::site::coord mln::geom::max_sli

(

const Image< I > &

ima

)

[inline]

Give the maximum sli of an image.

References bbox().

Referenced by nslis().

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).''

References mln::data::fill(), 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.

References mln::c2(), mln::algebra::ldlt_decomp(), mln::algebra::ldlt_solve(), mesh_corner_point_area(), mesh_normal(), 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.

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

Referenced by mesh_curvature().

template<typename B>

B::point::coord mln::geom::min_col

(

const Box< B > &

b

)

[inline]

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

template<typename I>

I::site::coord mln::geom::min_col

(

const Image< I > &

ima

)

[inline]

Give the minimum column of an image.

References bbox().

Referenced by mln::transform::hough(), and ncols().

template<typename I>

I::site::coord mln::geom::min_ind

(

const Image< I > &

ima

)

[inline]

Give the minimum ind of an image.

Referenced by ninds().

template<typename B>

B::point::coord mln::geom::min_row

(

const Box< B > &

b

)

[inline]

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

template<typename I>

I::site::coord mln::geom::min_row

(

const Image< I > &

ima

)

[inline]

Give the minimum row of an image.

References bbox().

Referenced by mln::transform::hough(), and nrows().

template<typename I>

I::site::coord mln::geom::min_sli

(

const Image< I > &

ima

)

[inline]

Give the minimum sli of an image.

References bbox().

Referenced by nslis().

template<typename B>

unsigned mln::geom::ncols

(

const Box< B > &

b

)

[inline]

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

References max_col(), min_col(), and ncols().

template<typename I>

unsigned mln::geom::ncols

(

const Image< I > &

ima

)

[inline]

Give the number of columns of an image.

References max_col(), and min_col().

Referenced by mln::subsampling::gaussian_subsampling(), mln::transform::hough(), ncols(), and mln::subsampling::subsampling().

template<typename I>

unsigned mln::geom::ninds

(

const Image< I > &

ima

)

[inline]

Give the number of inds of an image.

References max_ind(), and min_ind().

template<typename B>

unsigned mln::geom::nrows

(

const Box< B > &

b

)

[inline]

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

References max_row(), min_row(), and nrows().

template<typename I>

unsigned mln::geom::nrows

(

const Image< I > &

ima

)

[inline]

Give the number of rows of an image.

References max_row(), and min_row().

Referenced by mln::subsampling::gaussian_subsampling(), mln::transform::hough(), nrows(), and mln::subsampling::subsampling().

template<typename I>

unsigned mln::geom::nsites

(

const Image< I > &

input

)

[inline]

Compute the number of sites of the image input.

Referenced by pmin_pmax().

template<typename I>

unsigned mln::geom::nslis

(

const Image< I > &

ima

)

[inline]

Give the number of slices of an image.

References max_sli(), and min_sli().

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.

template<typename I>

std::pair< typename I::site, typename I::site > mln::geom::pmin_pmax

(

const Site_Iterator< I > &

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 nsites().

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 nsites().

Referenced by pmin_pmax().

template<typename I>

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

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 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
	)			[inline]

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::compose(), mln::extend(), mln::initialize(), mln::mln_exact(), mln::literal::origin, mln::data::paste(), mln::accu::shape::bbox< P >::take(), and mln::accu::shape::bbox< P >::to_result().

Referenced by rotate().

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.

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.

References mln::duplicate(), mln::p_queue< P >::front(), mln::p_queue< P >::pop(), mln::p_queue< P >::push(), and mln::geom::impl::seeds2tiling().

Referenced by 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 chamfer(), mln::duplicate(), mln::p_priority< P, Q >::pop_front(), mln::p_priority< P, Q >::push(), mln::geom::impl::seeds2tiling_roundness(), and mln::literal::zero.

Referenced by seeds2tiling_roundness().

template<typename I, typename V>

mln::trait::concrete< I >::ret mln::geom::translate	(	const Image< I > &	input,
		const algebra::vec< I::site::dim, V > &	ref
	)			[inline]

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 translate(), and mln::literal::zero.

template<typename I, typename V, typename Ext, typename S>

mln::trait::concrete< I >::ret mln::geom::translate	(	const Image< I > &	input,
		const algebra::vec< I::site::dim, V > &	ref,
		const Ext &	extension,
		const Site_Set< S > &	output_domain
	)			[inline]

Perform a translation from the center of an image.

Parameters:

[in]	input	An image.
[in]	ref	The translation vector.
[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 translation.
[in]	output_domain	The domain of the output image. An invalid domain, causes the routine to use the translated input_ domain.

Returns:

An image with the same domain as input.

References mln::extend(), mln::data::fill(), and mln::mln_exact().

Referenced by translate().