Constrained Delaunay Triangulation with vertices that are exact points. Can be used to implement 2D CSG. More...

#include <geogram/delaunay/CDT_2d.h>

Inheritance diagram for GEO::ExactCDT2d:

Public Types
typedef exact::vec2h	ExactPoint

Public Member Functions
	ExactCDT2d ()
	ExactCDT2d constructor.

	~ExactCDT2d () override
	ExactCDT2d destructor.

void	clear () override
	Removes everything from this triangulation. More...

index_t	insert (const ExactPoint &p, index_t id=0, index_t hint=index_t(-1))
	Inserts a point. More...

void	insert_constraint (index_t v1, index_t v2, index_t operand_bits=0)
	Inserts a constraint. More...

void	create_enclosing_quad (const ExactPoint &p1, const ExactPoint &p2, const ExactPoint &p3, const ExactPoint &p4)
	Creates a first large enclosing quad. More...

void	create_enclosing_rectangle (double x1, double y1, double x2, double y2)
	Creates a first large enclosing rectangle. More...

const ExactPoint &	point (index_t v) const
	Gets a point by vertex index. More...

index_t	vertex_id (index_t v) const
	Gets a vertex id by vertex index. More...

void	set_vertex_id (index_t v, index_t id)
	Sets a vertex id by vertex index. More...

void	classify_triangles (const std::string &boolean_expression, bool mark_only=false)
	Used by 2D CSG operations, discards triangles according to a boolean operation. More...

void	save (const std::string &filename) const override

Public Member Functions inherited from GEO::CDTBase2d
	CDTBase2d ()
	CDTBase2d constructor.

virtual	~CDTBase2d ()
	CDTBase2d destructor.

void	insert_constraint (index_t i, index_t j)
	Inserts a constraint. More...

void	remove_external_triangles (bool remove_internal_holes=false)
	Recursively removes all the triangles adjacent to the border, and keeps what's surrounded by constraints. More...

void	set_delaunay (bool delaunay)
	Specifies whether a constrained Delaunay triangulation should be constructed, or just a plain constrained triangulation. More...

index_t	nT () const
	Gets the number of triangles.

index_t	nv () const
	Gets the number of vertices.

index_t	ncnstr () const
	Gets the number of constraints.

index_t	Tv (index_t t, index_t lv) const
	Gets a vertex of a triangle. More...

index_t	Tv_find (index_t t, index_t v) const
	Finds the local index of a vertex in a triangle. More...

index_t	Tadj (index_t t, index_t le) const
	Gets a triangle adjacent to a triangle. More...

index_t	Tadj_find (index_t t1, index_t t2) const
	Finds the edge accross which a triangle is adjacent to another one. More...

index_t	vT (index_t v) const
	Gets a triangle incident to a given vertex. More...

index_t	Tedge_cnstr_first (index_t t, index_t le) const
	Gets the constraint associated with an edge. More...

index_t	edge_cnstr_next (index_t ecit) const
	Gets the successor of an edge constraint iterator. More...

index_t	edge_cnstr (index_t ecit) const
	Gets an edge constraint from an edge constraint iterator. More...

index_t	Tedge_cnstr_nb (index_t t, index_t le) const
	Gets the number of constraints associated with a triange edge. More...

bool	Tedge_is_Delaunay (index_t t, index_t le) const
	Tests whether a triangle edge is Delaunay. More...

void	check_consistency () const
	Checks both combinatorics and geometry, aborts on unconsistency.

Protected Member Functions
void	add_point (const ExactPoint &p, index_t id=index_t(-1))

void	begin_insert_transaction () override

void	commit_insert_transaction () override

void	rollback_insert_transaction () override

Sign	orient2d (index_t i, index_t j, index_t k) const override
	Computes the orientation predicate in 2d. More...

Sign	incircle (index_t i, index_t j, index_t k, index_t l) const override
	Incircle predicate. More...

index_t	create_intersection (index_t E1, index_t i, index_t j, index_t E2, index_t k, index_t l) override
	Given two segments that have an intersection, create the intersection. More...

Protected Member Functions inherited from GEO::CDTBase2d
index_t	insert (index_t v, index_t hint=index_t(-1))
	Inserts a new point. More...

void	create_enclosing_triangle (index_t v1, index_t v2, index_t v3)
	Creates the combinatorics for a first large enclosing triangle. More...

void	create_enclosing_quad (index_t v1, index_t v2, index_t v3, index_t v4)
	Creates the combinatorics for a first large enclosing quad. More...

void	Tset_flag (index_t t, index_t flag)
	Sets a triangle flag. More...

void	Treset_flag (index_t t, index_t flag)
	Resets a triangle flag. More...

bool	Tflag_is_set (index_t t, index_t flag)
	Tests a triangle flag. More...

bool	Tis_in_list (index_t t) const
	Tests whether a triangle is in a DList. More...

void	insert_vertex_in_edge (index_t v, index_t t, index_t le, DList &S)
	Inserts a vertex in an edge. More...

void	insert_vertex_in_edge (index_t v, index_t t, index_t le)
	Inserts a vertex in an edge. More...

void	insert_vertex_in_triangle (index_t v, index_t t, DList &S)
	Inserts a vertex in a triangle. More...

index_t	find_intersected_edges (index_t i, index_t j, DList &Q)
	Finds the edges intersected by a constraint. More...

void	walk_constraint_v (CDT2d_ConstraintWalker &W)
	Used by find_intersected_edges()

void	walk_constraint_t (CDT2d_ConstraintWalker &W, DList &Q)
	Used by find_intersected_edges()

void	constrain_edges (index_t i, index_t j, DList &Q, DList &N)
	Constrains an edge by iteratively flipping the intersected edges. More...

void	Delaunayize_vertex_neighbors (index_t from_v)
	Restores Delaunay condition starting from the triangles incident to a given vertex. More...

void	Delaunayize_vertex_neighbors (index_t v, DList &S)
	Restores Delaunay condition starting from the triangles incident to a given vertex. More...

void	Delaunayize_new_edges (DList &N)
	Restores Delaunay condition for a set of edges after inserting a constrained edge. More...

void	Tset (index_t t, index_t v1, index_t v2, index_t v3, index_t adj1, index_t adj2, index_t adj3, index_t e1cnstr=index_t(-1), index_t e2cnstr=index_t(-1), index_t e3cnstr=index_t(-1))
	Sets all the combinatorial information of a triangle and edge flags. More...

void	Trot (index_t t, index_t lv)
	Rotates indices in triangle t in such a way that a given vertex becomes vertex 0. More...

void	swap_edge (index_t t1, bool swap_t1_t2=false)
	Swaps an edge. More...

void	Tadj_set (index_t t, index_t le, index_t adj)
	Sets a triangle adjacency relation. More...

index_t	Topp (index_t t, index_t e=0) const
	Gets the neighboring triangle vertex opposite to a given vertex.

void	Tadj_back_connect (index_t t1, index_t le1, index_t prev_t2_adj_e2)
	After having changed connections from triangle to a neighbor, creates connections from neighbor to triangle. More...

index_t	Tnew ()
	Creates a new triangle. More...

void	Tset_edge_cnstr_first (index_t t, index_t le, index_t ecit)
	Sets the constraints list associated with an edge. More...

void	Tadd_edge_cnstr (index_t t, index_t le, index_t cnstr_id)
	Adds a constraint to a triangle edge. More...

void	Tadd_edge_cnstr_with_neighbor (index_t t, index_t le, index_t cnstr_id)
	Adds a constraint to a triangle edge and to the neighboring edge if it exists. More...

bool	Tedge_is_constrained (index_t t, index_t le) const
	Tests whether an edge is constrained. More...

void	for_each_T_around_v (index_t v, std::function< bool(index_t t, index_t lv)> doit)
	Calls a user-defined function for each triangle around a vertex. More...

index_t	locate (index_t v, index_t hint=index_t(-1), Sign *orient=nullptr) const
	Locates a vertex. More...

bool	is_convex_quad (index_t t) const
	Tests whether triange t and its neighbor accross edge 0 form a strictly convex quad. More...

void	remove_marked_triangles ()
	Removes all the triangles that have the flag T_MARKED_FLAG set. More...

void	Tcheck (index_t t) const
	Consistency check for a triangle. More...

void	debug_Tcheck (index_t t) const
	Consistency check for a triangle in debug mode, ignored in release mode. More...

void	check_combinatorics () const
	Consistency combinatorial check for all the triangles. More...

void	debug_check_combinatorics () const
	Consistency combinatorial check for all the triangles in debug mode, ignored in release mode. More...

virtual void	check_geometry () const
	Consistency geometrical check for all the triangles. More...

void	debug_check_geometry () const
	Consistency geometrical check for all the triangles in debug mode, ignored in release mode. More...

void	debug_check_consistency () const
	Checks both combinatorics and geometry in debug mode, ignored in release mode, aborts on unconsistency.

bool	segment_segment_intersect (index_t u1, index_t u2, index_t v1, index_t v2) const
	Tests whether two segments have a frank intersection. More...

bool	segment_edge_intersect (index_t v1, index_t v2, index_t t, index_t le) const
	Tests whether an edge triangle and a segment have a frank intersection. More...

void	check_edge_intersections (index_t v1, index_t v2, const DList &Q)
	Checks that the edges stored in a DList exactly correspond to all edge intersections between a segment and the triangle edges. More...

index_t	eT (Edge E)
	Gets a triangle incident a a given edge. More...

index_t	locate_naive (index_t v, index_t hint=index_t(-1), Sign *orient=nullptr) const
	Simpler version of locate() kept for reference. More...

void	constrain_edges_naive (index_t i, index_t j, DList &Q, vector< Edge > &N)
	Simpler version of constrain_edges() kept for reference. More...

void	Delaunayize_new_edges_naive (vector< Edge > &N)
	Simpler version of Delaunayize_new_edges() that uses a vector instead of a DList, kept for reference.

Protected Attributes
vector< ExactPoint >	point_

vector< double >	length_

vector< index_t >	id_

vector< index_t >	cnstr_operand_bits_

vector< index_t >	facet_inclusion_bits_

std::map< trindex, Sign >	pred_cache_

bool	use_pred_cache_insert_buffer_

std::vector< std::pair< trindex, Sign > >	pred_cache_insert_buffer_

vector< bindex >	constraints_

Protected Attributes inherited from GEO::CDTBase2d
index_t	nv_

index_t	ncnstr_

vector< index_t >	T_

vector< index_t >	Tadj_

vector< index_t >	v2T_

vector< uint8_t >	Tflags_

vector< index_t >	Tecnstr_first_

vector< index_t >	ecnstr_val_

vector< index_t >	ecnstr_next_

vector< index_t >	Tnext_

vector< index_t >	Tprev_

bool	delaunay_

Sign	orient_012_

bool	exact_incircle_

bool	exact_intersections_

Additional Inherited Members
Protected Types inherited from GEO::CDTBase2d
enum	{ DLIST_S_ID =0 , DLIST_Q_ID =1 , DLIST_N_ID =2 , DLIST_NB =3 }
	Constants for list_id.

enum	{ T_MARKED_FLAG = DLIST_NB , T_VISITED_FLAG = DLIST_NB+1 }
	Constants for triangle flags.

typedef std::pair< index_t, index_t >	Edge

Static Protected Member Functions inherited from GEO::CDTBase2d
static index_t	find_3 (const index_t *T, index_t v)
	Finds the index of an integer in an array of three integers. More...

Detailed Description

Constrained Delaunay Triangulation with vertices that are exact points. Can be used to implement 2D CSG.

Points are represented using exact 2d homogeneous coordinates. Unlike CDT2d, this ensures exact representation of constraints intersections with guaranteed behavior. Under the hood, it inherits CDTBase2d (constrained Delaunay triangulation), and redefines orient2d(), incircle2d() and create_intersection() using vectors with homogeneous coordinates stored as arithmetic expansions (vec2HE) or arbitrary-precision floating point numbers (vec2HEx) if compiled with Tessael's geogramplus extension package.

See also: CDT2d

Definition at line 1537 of file CDT_2d.h.

Member Function Documentation

◆ classify_triangles()

void GEO::ExactCDT2d::classify_triangles	(	const std::string &	boolean_expression,
		bool	mark_only = `false`
	)

Used by 2D CSG operations, discards triangles according to a boolean operation.

Discards all the triangles that are outside the object defined by the boolean expression. It uses the operand bits associated with the constraints.

Parameters

[in]	boolean_expression	a string with the boolean expression, as defined by BooleanExpression constructor. Each variable corresponds to an operand bit associated with the constraints. There can be up to 32 operands.
	mark_only	if set, triangles to be discarded are marked (but not discarded)

See also: BooleanExpression, insert_constraint()

◆ clear()

void GEO::ExactCDT2d::clear ( )

overridevirtual

Removes everything from this triangulation.

Reimplemented from GEO::CDTBase2d.

◆ create_enclosing_quad()

void GEO::ExactCDT2d::create_enclosing_quad	(	const ExactPoint &	p1,
		const ExactPoint &	p2,
		const ExactPoint &	p3,
		const ExactPoint &	p4
	)

Creates a first large enclosing quad.

Parameters

[in] p1,p2,p3,p4 the four vertices of the quad

The quad needs to be convex. create_enclosing_rectangle() or create_enclosing_quad() need to be called before anything else

◆ create_enclosing_rectangle()

void GEO::ExactCDT2d::create_enclosing_rectangle	(	double	x1,
		double	y1,
		double	x2,
		double	y2
	)

inline

Creates a first large enclosing rectangle.

Parameters

[in] x1,y1,x2,y2 rectangle bounds

create_enclosing_triangle(), create_enclosing_rectangle() or create_enclosing_quad() need to be called before anything else

Definition at line 1604 of file CDT_2d.h.

◆ create_intersection()

index_t GEO::ExactCDT2d::create_intersection	(	index_t	E1,
		index_t	i,
		index_t	j,
		index_t	E2,
		index_t	k,
		index_t	l
	)

overrideprotectedvirtual

Given two segments that have an intersection, create the intersection.

The intersection is given both as the indices of segment extremities (i,j) and (k,l), that one can use to retreive the points in derived classes, and constraint indices E1 and E2, that derived classes may use to retreive symbolic information attached to the constraint

Parameters

[in]	E1	the index of the first edge, corresponding to the value of ncnstr() when insert_constraint() was called for that edge
[in]	i,j	the vertices of the first segment
[in]	E2	the index of the second edge, corresponding to the value of ncnstr() when insert_constraint() was called for that edge
[in]	k,l	the vertices of the second segment

Returns: the index of a newly created vertex that corresponds to the intersection between [i , j] and [k , l]

Implements GEO::CDTBase2d.

◆ incircle()

Sign GEO::ExactCDT2d::incircle	(	index_t	i,
		index_t	j,
		index_t	k,
		index_t	l
	)		const

overrideprotectedvirtual

Incircle predicate.

Parameters

[in]	i,j,k	the three vertices of a triangle
[in]	l	another vertex

Return values

POSITIVE	if `l` is inside the circumscribed circle of the triangle
ZERO	if `l` is on the circumscribed circle of the triangle
NEGATIVE	if `l` is outside the circumscribed circle of the triangle

Implements GEO::CDTBase2d.

◆ insert()

index_t GEO::ExactCDT2d::insert	(	const ExactPoint &	p,
		index_t	id = `0`,
		index_t	hint = `index_t(-1)`
	)

Inserts a point.

Parameters

[in]	p	the point to be inserted
[in]	hint	a triangle not too far away from the point to be inserted
[in]	id	an opaque identifier attached to the vertex that can be used by client code for instance to keep relations with a mesh. It can be queried using the vertex_id() function.

Returns: the index of the created point. Duplicated points are detected (and then the index of the existing point is returned)

◆ insert_constraint()

void GEO::ExactCDT2d::insert_constraint	(	index_t	v1,
		index_t	v2,
		index_t	operand_bits = `0`
	)

inline

Inserts a constraint.

Parameters

[in]	v1,v2	the two extremities of the constraint, as returned by insert()
[in]	operand_bits	optional bitfield used by 2D CSG, indicating on which primitive boundaries the constraint is. Each bit set corresponds to a primitive. It is used by the classify() function.

See also: CDTBase::insert_constraint() and classify()

Definition at line 1580 of file CDT_2d.h.

◆ orient2d()

Sign GEO::ExactCDT2d::orient2d	(	index_t	i,
		index_t	j,
		index_t	k
	)		const

overrideprotectedvirtual

Computes the orientation predicate in 2d.

Computes the sign of the signed area of the triangle p0, p1, p2.

Parameters

[in] p0,p1,p2 vertices of the triangle as 2d vectors with homogeneous coordinates stored as expansion_nt (arbitrary precision).

Return values

POSITIVE	if the triangle is oriented counter-clockwise
ZERO	if the triangle is flat
NEGATIVE	if the triangle is oriented clockwise

Implements GEO::CDTBase2d.

◆ point()

const ExactPoint& GEO::ExactCDT2d::point ( index_t v ) const

inline

Gets a point by vertex index.

Parameters

[in] v vertex index

Returns: the point at index v

Definition at line 1620 of file CDT_2d.h.

◆ save()

void GEO::ExactCDT2d::save ( const std::string & filename ) const

overridevirtual

See also: CDTBase2d::save()

Implements GEO::CDTBase2d.

◆ set_vertex_id()

void GEO::ExactCDT2d::set_vertex_id	(	index_t	v,
		index_t	id
	)

inline

Sets a vertex id by vertex index.

Parameters

[in]	v	vertex index
[in]	id	vertex id

Definition at line 1640 of file CDT_2d.h.

◆ vertex_id()

index_t GEO::ExactCDT2d::vertex_id ( index_t v ) const

inline

Gets a vertex id by vertex index.

Parameters

[in] v vertex index

Returns: the point at index v

Definition at line 1630 of file CDT_2d.h.

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

geogram/delaunay/CDT_2d.h

Public Types

Public Member Functions

Protected Member Functions

Protected Attributes

Additional Inherited Members

Detailed Description

Member Function Documentation

◆ classify_triangles()

◆ clear()

◆ create_enclosing_quad()

◆ create_enclosing_rectangle()

◆ create_intersection()

◆ incircle()

◆ insert()

◆ insert_constraint()

◆ orient2d()

◆ point()

◆ save()

◆ set_vertex_id()

◆ vertex_id()