Constrained Delaunay triangulation. More...

#include <geogram/delaunay/CDT_2d.h>

Inheritance diagram for GEO::CDT2d:

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

void	create_enclosing_triangle (const vec2 &p1, const vec2 &p2, const vec2 &p3)
	Creates a first large enclosing triangle. More...

void	create_enclosing_quad (const vec2 &p1, const vec2 &p2, const vec2 &p3, const vec2 &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...

index_t	insert (const vec2 &p, index_t hint=index_t(-1))
	Inserts a point. More...

void	insert (index_t nb_points, const double points, index_t indices=nullptr, bool remove_unreferenced_vertices=false)
	Batch-inserts a set of point. More...

void	save (const std::string &filename) const override
	Saves this CDT to a geogram mesh file. More...

const vec2	point (index_t v) const
	Gets a point by index. More...

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
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
virtual void	begin_insert_transaction ()

virtual void	commit_insert_transaction ()

virtual void	rollback_insert_transaction ()

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< vec2 >	point_

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.

Example:

CDT cdt;
vec2 p1(.,.), p2(.,.), p3(.,.);
cdt.create_enclosing_triangle(p1,p2,p3);
     // or create_enclosing_quad() or create_enclosing_rect()
// insert points
for(...) {
  vec2 p(.,.);
  index_t v = cdt.insert(p);
  ...
}
// insert constraints
for(...) {
   index_t v1=..., v2=...;
   cdt.insert_constraint(v1,v2);
}
// get triangles
for(index_t t=0; t<cdt.nT(); ++t) {
   index_t v1 = cdt.Tv(t,0);
   index_t v2 = cdt.Tv(t,1);
   index_t v3 = cdt.Tv(t,2);
   ... do something with v1,v2,v3
}

If some constraints are intersecting, new vertices are generated. They can be accessed using the function vec2 CDT::point(index_t v). Vertices coming from an intersection are between indices nv1 and CDT::nv(), where nv1 is the value of CDT::nv() before inserting the constraints (nv1 corresponds to the number of times CDT::insert() was called plus the number of points in the enclosing polygon). Note that like input points, constraint intersections are represented using double-precision floating point numbers, which is not always sufficient to ensure robustness. If the input has intersecting constraints and bullet-proof guarantees are needed, one can use ExactCDT2d instead.

If you want only a constrained triangulation (not Delaunay), you can call CDT::set_Delaunay(false) before inserting the points.

If you have many points to insert, you can use the function:

void CDT::insert(index_t nb_points, const double* points);

It is much much faster than inserting the points one by one. Internally it uses Amenta et.al's BRIO method (multi-resolution spatial sort).

Definition at line 1381 of file CDT_2d.h.

Member Function Documentation

◆ clear()

void GEO::CDT2d::clear ( )

overridevirtual

Removes everything from this triangulation.

Reimplemented from GEO::CDTBase2d.

◆ create_enclosing_quad()

void GEO::CDT2d::create_enclosing_quad	(	const vec2 &	p1,
		const vec2 &	p2,
		const vec2 &	p3,
		const vec2 &	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_triangle(), create_enclosing_rectangle() or create_enclosing_quad() need to be called before anything else

◆ create_enclosing_rectangle()

void GEO::CDT2d::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 1421 of file CDT_2d.h.

◆ create_enclosing_triangle()

void GEO::CDT2d::create_enclosing_triangle	(	const vec2 &	p1,
		const vec2 &	p2,
		const vec2 &	p3
	)

Creates a first large enclosing triangle.

Parameters

[in] p1,p2,p3 the three vertices of the first triangle

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

◆ create_intersection()

index_t GEO::CDT2d::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::CDT2d::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() [1/2]

index_t GEO::CDT2d::insert	(	const vec2 &	p,
		index_t	hint = `index_t(-1)`
	)

inline

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

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

Definition at line 1440 of file CDT_2d.h.

◆ insert() [2/2]

void GEO::CDT2d::insert	(	index_t	nb_points,
		const double *	points,
		index_t *	indices = `nullptr`,
		bool	remove_unreferenced_vertices = `false`
	)

Batch-inserts a set of point.

In general, it is much faster than calling insert() multiple times. Internally it uses a spatial sort (Amenta et.al's BRIO method). On exit, the optional indices array contains the index mapping. indices[i] may be different from i if there were duplicated points. If there may be duplicated points and if one wants to insert constraint using CDTBase2d::insert_constraint(), one needs to call insert_constraint(indices[i],indices[j]) to get the correct translation of the indices

Parameters

[in]	points	a contiguous array of all point coordinates
[in]	nb_points	number of points
[out]	indices	an optional pointer to an array of size `nb_points` of indices. On exit, indices[i] contains the index of the mesh vertex that corresponds to the i-th point. If there are duplicated points or if `remove_unreferenced_vertices` is set, then indices[i] may be different from i
[in]	remove_unreferenced_vertices	if set, then duplicated vertices are not stored in the vertices array. Internally, this systematically changes the order of the points. For this reason, if this flag is set, then one needs to do index mapping with `indices`, even when there is no duplicated point

◆ orient2d()

Sign GEO::CDT2d::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 vec2 GEO::CDT2d::point ( index_t v ) const

inline

Gets a point by index.

Parameters

[in] v point index

Returns: the point at index v

Definition at line 1493 of file CDT_2d.h.

◆ save()

void GEO::CDT2d::save ( const std::string & filename ) const

overridevirtual

Saves this CDT to a geogram mesh file.

Parameters

[in] filename where to save this CDT

Implements GEO::CDTBase2d.

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

geogram/delaunay/CDT_2d.h

Public Member Functions

Protected Member Functions

Protected Attributes

Additional Inherited Members

Detailed Description

Member Function Documentation

◆ clear()

◆ create_enclosing_quad()

◆ create_enclosing_rectangle()

◆ create_enclosing_triangle()

◆ create_intersection()

◆ incircle()

◆ insert() [1/2]

◆ insert() [2/2]

◆ orient2d()

◆ point()

◆ save()