#include <iostream>
#include <CGAL/Cartesian.h>
#include <CGAL/Gmpq.h>
#include <CGAL/Lazy_exact_nt.h>
#include <CGAL/Linear_algebraCd.h>
#include <CGAL/double.h>
#include <CGAL/Arr_segment_traits_2.h>
#include <CGAL/Arr_default_dcel.h>
#include <CGAL/Arrangement_2.h>
#include <CGAL/IO/Arr_iostream.h>
#include <CGAL/Arr_walk_along_line_point_location.h>
#include <CGAL/Arr_naive_point_location.h>
#include <CGAL/Polygon_2.h>
#include <CGAL/Polygon_2_algorithms.h>
#include <CGAL/intersections.h>
#include <CGAL/Bbox_2.h>
#include <CGAL/Random.h>
#include <CGAL/Extended_cartesian.h>
#include <CGAL/Nef_polyhedron_2.h>

Classes
class	Polygons

class	LineTes
	Polygonal tessellation of a bounded rectangular domain. More...

class	LineTes::Seg
	Segment in a line tessellation. More...

class	LineTes::Seg_list
	List of Seg objects. More...

class	LineTes::Seg_sublist
	Sublist of Seg objects. More...

class	LineTes_halfedge
	Halfedge class used by the LineTes class. More...

struct	IVertex
	Data about removal of an I-vertex. More...

struct	ModList
	Representation of a modification to be applied to a line tessellation. More...

class	TTessel
	Dynamic T-tessellation. More...

class	TTessel::Modification
	Abstract class representing a modification of a T-tessellation. More...

class	TTessel::Split
	A split that can be applied to a T-tessellation. More...

class	TTessel::Merge
	A merge that can be applied to a T-tessellation. More...

class	TTessel::Flip
	A flip that can be applied to a T-tessellation. More...

struct	CatItems< T >
	Storage structure for categorized items. More...

struct	Features
	Set of vertex, edge, face and segment features. More...

class	Energy
	Energy of a Gibbsian random T-tessellation. More...

struct	ModifCounts
	Data summarizing changes occuring through SMF iterations. More...

class	SMFChain
	Markovian T-tessellation. More...

class	PseudoLikDiscrete
	Discrete approximation of the log-pseudolikelihood of a Gibbsian T-tessellation. More...

class	PLInferenceNOIS
	Pseudo-likelihood inference of a Gibsian T-tessellation with alternate updates. More...

Typedefs
typedef CGAL::Lazy_exact_nt < CGAL::Gmpq >	NT
	The CGAL numeric type used for exact computations in LiTe.

typedef CGAL::Cartesian< NT >	Kernel
	The CGAL type of coordinates used in LiTe.

typedef CGAL::Arr_segment_traits_2 < Kernel >	Traits
	The CGAL arrangement traits class used for representing tessellations.

typedef CGAL::Vector_2< Kernel >	Vector
	The CGAL class used for representing vectors.

typedef Traits::Point_2	Point2
	CGAL class representing a point from a tessellation.

typedef Traits::Segment_2	Segment
	CGAL class representing a line segment from a tessellation.

typedef Traits::X_monotone_curve_2	Curve
	CGAL class representing a curve (line segment) from a tessellation.

typedef CGAL::Iso_rectangle_2 < Kernel >	Rectangle
	CGAL class representing a rectangle with horizontal and vertical sides. More...

typedef CGAL::Line_2< Kernel >	Line
	CGAL class representing an infinite line.

typedef CGAL::Ray_2< Kernel >	Rayon
	CGAL class representing a half-line.

typedef CGAL::Direction_2< Kernel >	Direction
	CGAL class representing a direction in the plane.

typedef CGAL::Aff_transformation_2 < Kernel >	Transformation
	CGAL class representing an affine transformation.

typedef CGAL::Polygon_2< Kernel >	Polygon
	CGAL class representing a polygon.

typedef std::vector< Point2 >	Points
	Class representing a series of points.

typedef CGAL::Linear_algebraCd < double >	LA
	Class used for basic linear algebra. More...

typedef LA::Vector	FVector
	Class used for representing a vector (in the linear algebra sense)

typedef LA::Matrix	FMatrix
	Class used for representing a matrix.

typedef CGAL::Arr_dcel_base < CGAL::Arr_vertex_base < Point2 >, LineTes_halfedge, CGAL::Arr_face_base >	Dcel
	Class used as a template parameter for the Arrangement class. More...

typedef CGAL::Arrangement_2 < Traits, Dcel >	Arrangement
	Class representing a tessellation.

typedef Dcel::Size	Size
	Number type used for indexing tessellation features.

typedef CatItems< double >	CatVector
	Storage structure for vector of doubles associated with categories vertices, edges, faces or segs.

typedef CatItems< CatVector >	CatMatrix
	Storage structure for matrices (vector of vectors) of doubles associated with categories vertices, edges, faces or segs.

Functions
bool	compare_ivertices (IVertex v1, IVertex v2)
	Comparison of I-vertices based on length variation. More...

template<typename T >
const CatItems< T >	operator+ (const CatItems< T > &x1, const CatItems< T > &x2)
	Addition operator for CatItems objects.

template<typename T >
const CatItems< T >	operator* (const double &scalar, const CatItems< T > &x)
	Product of a CatItems object with a scalar.

template<typename T >
const CatItems< T >	operator- (const CatItems< T > &x1, const CatItems< T > &x2)
	Subtraction of two CatItems objects.

template<typename T >
const CatItems< T >	operator* (const CatItems< T > &x1, const CatItems< T > &x2)
	Term by term product of CatItems objects.

void	fill (CatVector &, FVector &)
	Fill a CatVector object with the elements of a FVector object. More...

std::vector< double >	asVectorOfDoubles (const CatVector &)
	Generate a vector of doubles from a CatVector object.

FVector	asFVector (const CatVector &)
	Generate a FVector object from CatVector object.

std::ostream &	operator<< (std::ostream &, const CatVector &)
	Print a CatVector to an output stream.

double	sum (const CatVector &)
	Compute the sum of components of a CatVector object.

FMatrix	asFMatrix (const CatMatrix &)
	Generate a FMatrix object from a CatMatrix object.

CatMatrix	outer (const CatVector &, const CatVector &)
	Outer product of two CatVector objects.

bool	are_aligned (Point2 p, Point2 q, Point2 r, bool verbose=false)
	Test whether three points are aligned. More...

Segment	clip_segment_by_convex_polygon (Segment, Polygon)
	Clip a segment by a convex polygon. More...

double	precompute_lengthening (Arrangement::Halfedge_handle, Arrangement::Halfedge_handle , Point2 )
	Predict added length when lengthening an edge in an arrangement. More...

bool	exist_halfedge (LineTes &, LineTes::Halfedge_handle)
	Test whether a halfedge handle is valid. More...

LineTes::Halfedge_handle	compute_prev_hf (LineTes::Halfedge_handle)
	Compute the previous halfedge along a segment. More...

LineTes::Halfedge_handle	compute_next_hf (LineTes::Halfedge_handle)
	Compute the next halfedge along a segment. More...

void	set_junction (LineTes::Halfedge_handle, LineTes::Halfedge_handle)
	Set neighbour relationships between two halfedges. More...

LineTes::Halfedge_handle	find_halfedge (LineTes &, Point2, Point2)
	Find a tessellation halfedge ending at two given points. More...

bool	is_a_T_vertex (LineTes::Vertex_handle, bool verbose=false)
	Test whether a vertex of a line tessellation is a T-vertex. More...

unsigned long int	number_of_internal_vertices (TTessel &)
	Return the total number of internal vertices. More...

Polygon	face2poly (TTessel::Face_handle)
	Returns a Polygon object representing a face of the tessellation. More...

double	face_number (Polygon, TTessel *)
	Return 1. More...

double	face_area_2 (Polygon, TTessel *)
	Return the squared face area of a tessellation face. More...

double	face_sum_of_angles (Polygon, TTessel *)
	Measure the deviation of a T-tessellation face from a rectangle. More...

double	face_shape (Polygon, TTessel *)

double	angle_between_vectors (Vector v1, Vector v2)
	Return the angle between two planar vectors. More...

double	edge_length (Segment, TTessel *)
	Return the length of an internal T-tessellation segment. More...

double	is_point_inside_window (Point2, LineTes *)
	Test whether a point is in the interior of the tessellated domain. More...

double	is_point_inside_window (Point2, TTessel *)
	Test whether a point is in the interior of the tessellated domain. More...

double	seg_number (std::vector< Point2 >, TTessel *)
	Return 1. More...

double	is_segment_internal (std::vector< Point2 >, TTessel *)
	Test whether a segment of a T-tessellation is internal. More...

double	minus_is_segment_internal (std::vector< Point2 > s, TTessel *t)
	Return -1. More...

double	min_angle (Polygon, TTessel *)
	Return the smallest angle in a tessellation face. More...

double	sum_of_faces_squared_areas (TTessel *)
	Return the sum of squared areas of all faces of a T-tessellation. More...

double	sum_of_min_angles (TTessel *)
	Return the sum of smallest angles on all faces of a T-tessellation. More...

double	sum_of_angles_obt (TTessel *)
	Return the sum of obtuse angles on all faces of a T-tessellation. More...

double	segment_size_2 (std::vector< Point2 >, TTessel *)
	Return the squared number of edges on a segment of a T-tessellation. More...

double	sum_of_segment_squared_sizes (TTessel *t)
	Return the sum of squared numbers of edges on all segments of a T-tessellation. More...

Variables
CGAL::Random *	rnd
	LiTe random generator. More...

LineTes::Halfedge_handle	NULL_HALFEDGE_HANDLE
	Null value for a LineTes halfedge handle.

LineTes::Face_handle	NULL_FACE_HANDLE
	Null value for a LineTes face handle.

LineTes::Seg_handle	NULL_SEG_HANDLE
	Null value for a LineTes segment handle.

Typedef Documentation

Dcel

Class used as a template parameter for the Arrangement class.

Use of non-standard halfedges (class LineTes_halfedge)

LA

Class used for basic linear algebra.

This class is used in particular for some computations on matrices.

typedef CGAL::Iso_rectangle_2<Kernel> Rectangle

CGAL class representing a rectangle with horizontal and vertical sides.

typedef

Function Documentation

double angle_between_vectors	(	Vector	v1,
		Vector	v2
	)

Return the angle between two planar vectors.

Parameters

v1	: first vector.
v2	: second vector.

bool are_aligned	(	Point2	p,
		Point2	q,
		Point2	r,
		bool	verbose
	)

Test whether three points are aligned.

Parameters

p	: first point.
q	: intermediate point.
r	: last point.
verbose	: if true, when points are found not aligned, a message explaining whny is printed to the standard output for logging. Default to false.

Returns: true if the points are aligned, false otherwise. If q is not strictly between p and r, the points are considered as not aligned.

Segment clip_segment_by_convex_polygon	(	Segment	S,
		Polygon	P
	)

Clip a segment by a convex polygon.

Parameters

S	: segment to be clipped.
P	: clipping polygon.

Returns: clipped segment, that is the intersection between the segment and the polygon.

Precondition: The clipping polygon must be convex.

bool compare_ivertices	(	IVertex	v1,
		IVertex	v2
	)

inline

Comparison of I-vertices based on length variation.

Parameters

v1	: data related to the first I-vertex.
v2	: data related to the second I-vertex.

Returns: true if first I-vertex removal induces a length change smaller than the second I-vertex removal.

LineTes::Halfedge_handle compute_next_hf ( LineTes::Halfedge_handle e )

Compute the next halfedge along a segment.

Parameters

e	halfedge whose neighbour is to be computed

Returns: next neighbour, NULL_HALFEDGE_HANDLE if e is the last halfedge on its segment.

LineTes::Halfedge_handle compute_prev_hf ( LineTes::Halfedge_handle e )

Compute the previous halfedge along a segment.

Parameters

e	halfedge whose neighbour is to be computed

Returns: previous neighbour, NULL_HALFEDGE_HANDLE if e is the first halfedge on its segment.

double edge_length	(	Segment	seg,
		TTessel *	t
	)

Return the length of an internal T-tessellation segment.

If the segment is not internal, zero is returned.

bool exist_halfedge	(	LineTes &	tesl,
		LineTes::Halfedge_handle	e
	)

Test whether a halfedge handle is valid.

Just check whether the halfedge handle can be found within the halfedge iterators.

Parameters

tesl	: the line tessellation to be searched.
e	: halfedge to be checked.

Polygon face2poly ( TTessel::Face_handle f )

Returns a Polygon object representing a face of the tessellation.

Only vertices joining non-aligned edges are specified during the Polygon construction.

double face_shape	(	Polygon	,
		TTessel *
	)

(4*sqrt(CGAL::to_double(f.area())));

void fill	(	CatVector &	v,
		FVector &	x
	)

Fill a CatVector object with the elements of a FVector object.

Parameters

v	: the CatVector to be filled
x	: the input object

The lengths of arguments must fit.

LineTes::Halfedge_handle find_halfedge	(	LineTes &	tesl,
		Point2	p1,
		Point2	p2
	)

Find a tessellation halfedge ending at two given points.

Parameters

tesl	: a tessellation.
p1	: a point.
p2	: another point.

bool is_a_T_vertex	(	LineTes::Vertex_handle	v,
		bool	verbose
	)

Test whether a vertex of a line tessellation is a T-vertex.

Parameters

v	: vertex to be tested.
verbose	: if true, information about I-vertex processing is sent to the standard output. Default to false.

double is_point_inside_window	(	Point2	pt,
		LineTes *	t
	)

Test whether a point is in the interior of the tessellated domain.

Returns: a double resulting from conversion from a Boolean.

double is_point_inside_window	(	Point2	pt,
		TTessel *	t
	)

Test whether a point is in the interior of the tessellated domain.

Returns: a double resulting from conversion from a Boolean.

double is_segment_internal	(	std::vector< Point2 >	s,
		TTessel *	t
	)

Test whether a segment of a T-tessellation is internal.

Parameters

s	: a vector containing the two ends of the segment to be tested. The ends must be Point2 objects.
t	: a pointer to the T-tessellation.

Returns: 0 if the segment is internal, 1 otherwise.

Precondition: the segment must be included in the domain of the T-tessellation.

A segment is considered as internal if it is not fully contained in the domain boundary.

double minus_is_segment_internal	(	std::vector< Point2 >	s,
		TTessel *	t
	)

inline

Return -1.

Parameters

s	: a tessellation segment as a vector of its 2 ends.
t	: the tessellation to be considered.

Silly function that can be used by an Energy object for specifying minus the number of segment as a tessellation feature.

unsigned long int number_of_internal_vertices ( TTessel & t )

Return the total number of internal vertices.

Parameters

t	: the T-tessellation.

Returns: the number of internal vertices.

A vertex is internal if it does not lie on the boundary of the tessellated domain.

double precompute_lengthening	(	Arrangement::Halfedge_handle	e,
		Arrangement::Halfedge_handle *	ehit,
		Point2 *	p
	)

Predict added length when lengthening an edge in an arrangement.

Parameters

[in]	e	: halfedge that would be lengthened.
[out]	ehit	: halfedge where lengthening would end.
[out]	p	: location of the end of lengthening.

Returns: added length.

Predict what would happen if an edge in an arrangement is extended to the next existing edge.

double seg_number	(	std::vector< Point2 >	s,
		TTessel *	t
	)

Return 1.

Parameters

s	: a tessellation segment as a vector of its 2 ends.
t	: the tessellation to be considered.

Silly function that can be used by an Energy object for specifying the number of tessellation segments as a feature.

void set_junction	(	LineTes::Halfedge_handle	e1,
		LineTes::Halfedge_handle	e2
	)

Set neighbour relationships between two halfedges.

Parameters

e1	: halfedge.
e2	: other halfedge supposed to follow e1 on the same segment.

Note: {Either e1 or e2 can be null.}

double sum_of_angles_obt ( TTessel * t )

Return the sum of obtuse angles on all faces of a T-tessellation.

Parameters

t	: the tessellation to be considered.

double sum_of_faces_squared_areas ( TTessel * t )

Return the sum of squared areas of all faces of a T-tessellation.

Parameters

t	: the tessellation to be considered.

double sum_of_min_angles ( TTessel * t )

Return the sum of smallest angles on all faces of a T-tessellation.

Parameters

t	: the tessellation to be considered.

double sum_of_segment_squared_sizes ( TTessel * t )

Return the sum of squared numbers of edges on all segments of a T-tessellation.

Parameters

t	: the tessellation to be considered.

Variable Documentation

CGAL::Random* rnd

LiTe random generator.

LiTe implements several stochastic algorihtms where this generator is used.

Classes

Typedefs

Functions

Variables

Typedef Documentation

Function Documentation

Variable Documentation