Implementation of Delaunay in 2d. More...

#include <geogram/delaunay/delaunay_2d.h>

Inheritance diagram for GEO::Delaunay2d:

Public Member Functions
	Delaunay2d (coord_index_t dimension=2)
	Constructs a new Delaunay2d. More...

void	set_vertices (index_t nb_vertices, const double *vertices) override
	Sets the vertices of this Delaunay, and recomputes the cells. More...

index_t	nearest_vertex (const double *p) const override
	Computes the nearest vertex from a query point. More...

bool	has_empty_cells () const
	Tests whether the Laguerre diagram has empty cells. More...

void	abort_if_empty_cell (bool x)
	Specifies behavior if an empty cell is detected. More...

Public Member Functions inherited from GEO::Delaunay
coord_index_t	dimension () const
	Gets the dimension of this Delaunay. More...

index_t	cell_size () const
	Gets the number of vertices in each cell. More...

void	set_reorder (bool x)
	Specifies whether vertices should be reordered. More...

virtual void	set_BRIO_levels (const vector< index_t > &levels)
	Specifies the bounds of each level to be used when hierarchic ordering is specified from outside. More...

const double *	vertices_ptr () const
	Gets a pointer to the array of vertices. More...

const double *	vertex_ptr (index_t i) const
	Gets a pointer to a vertex by its global index. More...

index_t	nb_vertices () const
	Gets the number of vertices. More...

virtual bool	supports_constraints () const
	Tests whether constraints are supported by this Delaunay. More...

virtual void	set_constraints (const Mesh *mesh)
	Defines the constraints. More...

void	set_refine (bool x)
	Specifies whether the mesh should be refined. More...

bool	get_refine () const
	Tests whether mesh refinement is selected. More...

void	set_quality (double qual)
	Specifies the desired quality for mesh elements when refinement is enabled (. More...

const Mesh *	constraints () const
	Gets the constraints. More...

index_t	nb_cells () const
	Gets the number of cells. More...

index_t	nb_finite_cells () const
	Gets the number of finite cells. More...

const signed_index_t *	cell_to_v () const
	Gets a pointer to the cell-to-vertex incidence array. More...

const signed_index_t *	cell_to_cell () const
	Gets a pointer to the cell-to-cell adjacency array. More...

signed_index_t	cell_vertex (index_t c, index_t lv) const
	Gets a vertex index by cell index and local vertex index. More...

signed_index_t	cell_adjacent (index_t c, index_t lf) const
	Gets an adjacent cell index by cell index and local facet index. More...

bool	cell_is_infinite (index_t c) const
	Tests whether a cell is infinite. More...

bool	cell_is_finite (index_t c) const
	Tests whether a cell is finite. More...

index_t	index (index_t c, signed_index_t v) const
	Retrieves a local vertex index from cell index and global vertex index. More...

index_t	adjacent_index (index_t c1, index_t c2) const
	Retrieves a local facet index from two adacent cell global indices. More...

signed_index_t	vertex_cell (index_t v) const
	Gets an incident cell index by a vertex index. More...

signed_index_t	next_around_vertex (index_t c, index_t lv) const
	Traverses the list of cells incident to a vertex. More...

void	get_neighbors (index_t v, vector< index_t > &neighbors) const
	Gets the one-ring neighbors of vertex v. More...

void	save_histogram (std::ostream &out) const
	Saves the histogram of vertex degree (can be visualized with gnuplot). More...

bool	stores_neighbors () const
	Tests whether neighbors are stored. More...

void	set_stores_neighbors (bool x)
	Specifies whether neighbors should be stored. More...

bool	stores_cicl () const
	Tests whether incident tetrahedra lists are stored. More...

void	set_stores_cicl (bool x)
	Specifies whether incident tetrahedra lists should be stored. More...

bool	keeps_infinite () const
	Tests whether infinite elements are kept. More...

void	set_keeps_infinite (bool x)
	Sets whether infinite elements should be kept. More...

bool	thread_safe () const
	Tests whether thread-safe mode is active. More...

void	set_thread_safe (bool x)
	Specifies whether thread-safe mode should be used. More...

void	set_default_nb_neighbors (index_t x)
	Sets the default number of stored neighbors. More...

index_t	default_nb_neighbors () const
	Gets the default number of stored neighbors. More...

void	clear_neighbors ()
	Frees all memory used for neighbors storage.

void	set_keep_regions (bool x)
	Specifies whether all internal regions should be kept. More...

virtual index_t	region (index_t t) const
	Gets the region id associated with a tetrahedron. More...

virtual void	store_neighbors_CB (index_t i)
	Stores the neighbors of a vertex. More...

Public Member Functions inherited from GEO::Counted
void	ref () const
	Increments the reference count. More...

void	unref () const
	Decrements the reference count. More...

bool	is_shared () const
	Check if the object is shared. More...

int	nb_refs () const
	Gets the number of references that point to this object. More...

Protected Member Functions
bool	create_first_triangle (index_t &iv0, index_t &iv1, index_t &iv2)
	Finds in the pointset a set of three non-colinear points. More...

index_t	locate (const double p, index_t hint=NO_TRIANGLE, bool thread_safe=false, Sign orient=nullptr) const
	Finds the triangle that contains a point. More...

index_t	locate_inexact (const double *p, index_t hint, index_t max_iter) const
	Finds the triangle that (approximately) contains a point using inexact predicates. More...

index_t	insert (index_t v, index_t hint=NO_TRIANGLE)
	Inserts a point in the triangulation. More...

void	find_conflict_zone (index_t v, index_t t, const Sign *orient, index_t &t_bndry, index_t &e_bndry, index_t &first, index_t &last)
	Determines the list of triangles in conflict with a given point. More...

void	find_conflict_zone_iterative (const double *p, index_t t, index_t &t_bndry, index_t &e_bndry, index_t &first, index_t &last)
	This function is used to implement find_conflict_zone. More...

index_t	stellate_conflict_zone (index_t v, index_t t_bndry, index_t e_bndry)
	Creates a star of triangles filling the conflict zone. More...

index_t	max_t () const
	Maximum valid index for a triangle. More...

bool	triangle_is_in_list (index_t t) const
	Tests whether a triangle belongs to a linked list. More...

index_t	triangle_next (index_t t) const
	Gets the index of a successor of a triangle. More...

void	add_triangle_to_list (index_t t, index_t &first, index_t &last)
	Adds a triangle to a linked list. More...

void	remove_triangle_from_list (index_t t)
	Removes a triangle from the linked list it belongs to. More...

bool	triangle_is_finite (index_t t) const
	Tests whether a given triangle is a finite one. More...

bool	triangle_is_real (index_t t) const
	Tests whether a triangle is a real one. More...

bool	triangle_is_virtual (index_t t) const
	Tests whether a triangle is a virtual one. More...

bool	triangle_is_free (index_t t) const
	Tests whether a triangle is in the free list. More...

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

index_t	new_triangle (signed_index_t v1, signed_index_t v2, signed_index_t v3)
	Creates a new triangle. More...

void	set_triangle_mark_stamp (index_t stamp)
	Generates a unique stamp for marking tets. More...

bool	triangle_is_marked (index_t t) const
	Tests whether a triangle is marked. More...

void	mark_triangle (index_t t)
	Marks a triangle. More...

signed_index_t	triangle_vertex (index_t t, index_t lv) const
	Gets the index of a vertex of a triangle. More...

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

index_t	finite_triangle_vertex (index_t t, index_t lv) const
	Gets the index of a vertex of a triangle. More...

void	set_triangle_vertex (index_t t, index_t lv, signed_index_t v)
	Sets a triangle-to-vertex adjacency. More...

signed_index_t	triangle_adjacent (index_t t, index_t le) const
	Gets the index of a triangle adjacent to another one. More...

void	set_triangle_adjacent (index_t t1, index_t le1, index_t t2)
	Sets a triangle-to-triangle adjacency. More...

index_t	find_triangle_adjacent (index_t t1, index_t t2_in) const
	Finds the index of the edge accros which t1 is adjacent to t2_in. More...

void	set_tet (index_t t, signed_index_t v0, signed_index_t v1, signed_index_t v2, index_t a0, index_t a1, index_t a2)
	Sets the vertices and adjacent triangles of a triangle. More...

bool	triangle_is_conflict (index_t t, const double *p) const
	Tests whether a given triangle is in conflict with a given 3d point. More...

	~Delaunay2d () override
	Delaunay2d destructor.

void	show_triangle (index_t t) const
	For debugging purposes, displays a triangle. More...

void	show_triangle_adjacent (index_t t, index_t le) const
	For debugging purposes, displays a triangle adjacency. More...

void	show_list (index_t first, const std::string &list_name) const
	For debugging purposes, displays a triangle. More...

void	check_combinatorics (bool verbose=false) const
	For debugging purposes, tests some combinatorial properties.

void	check_geometry (bool verbose=false) const
	For debugging purposes, test some geometrical properties.

Protected Member Functions inherited from GEO::Delaunay
	Delaunay (coord_index_t dimension)
	Creates a new Delaunay triangulation. More...

	~Delaunay () override
	Delaunay destructor.

virtual void	get_neighbors_internal (index_t v, vector< index_t > &neighbors) const
	Internal implementation for get_neighbors (with vector). More...

virtual void	set_arrays (index_t nb_cells, const signed_index_t cell_to_v, const signed_index_t cell_to_cell)
	Sets the arrays that represent the combinatorics of this Delaunay. More...

virtual void	update_v_to_cell ()
	Stores for each vertex v a cell incident to v.

virtual void	update_cicl ()
	Updates the circular incident cell lists. More...

virtual void	update_neighbors ()
	Computes the stored neighbor lists.

void	set_next_around_vertex (index_t c1, index_t lv, index_t c2)
	Sets the circular incident edge list. More...

void	set_dimension (coord_index_t dim)
	Sets the dimension of this Delaunay. More...

Protected Member Functions inherited from GEO::Counted
	Counted ()
	Creates a reference counted object. More...

virtual	~Counted ()
	Destroys a reference counted object. More...

Static Protected Member Functions
static index_t	triangle_edge_vertex (index_t e, index_t v)
	Returns the local index of a vertex by edge and by local vertex index in the edge. More...

static index_t	find_3 (const signed_index_t *T, signed_index_t v)
	Finds the index of an integer in an array of three integers. More...

Static Protected Attributes
static const index_t	NO_TRIANGLE = index_t(-1)
	Symbolic constant for uninitialized hint. More...

static const index_t	NOT_IN_LIST = index_t(~0)
	Default symbolic value of the cell_next_ field that indicates that a triangle is not in a linked list. More...

static const index_t	NOT_IN_LIST_BIT = index_t(1u << 31)
	If cell_next_[t] & NOT_IN_LIST_BIT != 0, then t is not in a linked list. More...

static const index_t	END_OF_LIST = ~(NOT_IN_LIST_BIT)
	Symbolic value of the cell_next_ field that indicates the end of list in a linked list of triangles.

static const signed_index_t	VERTEX_AT_INFINITY = -1
	Symbolic value for a vertex of a triangle that indicates a virtual triangle. More...

Additional Inherited Members
Static Public Member Functions inherited from GEO::Delaunay
static Delaunay *	create (coord_index_t dim, const std::string &name="default")
	Creates a Delaunay triangulation of the specified dimension. More...

static void	initialize ()
	This function needs to be called once before using the Delaunay class. More...

Static Public Member Functions inherited from GEO::Counted
static void	ref (const Counted *counted)
	Increments the reference count. More...

static void	unref (const Counted *counted)
	Decrements the reference count. More...

Protected Attributes inherited from GEO::Delaunay
coord_index_t	dimension_

index_t	vertex_stride_

index_t	cell_size_

index_t	cell_v_stride_

index_t	cell_neigh_stride_

const double *	vertices_

index_t	nb_vertices_

index_t	nb_cells_

const signed_index_t *	cell_to_v_

const signed_index_t *	cell_to_cell_

vector< signed_index_t >	v_to_cell_

vector< signed_index_t >	cicl_

bool	is_locked_

PackedArrays	neighbors_

bool	store_neighbors_

index_t	default_nb_neighbors_

bool	do_reorder_
	If true, uses BRIO reordering (in some implementations)

const Mesh *	constraints_

bool	refine_

double	quality_

bool	store_cicl_
	It true, circular incident tet lists are stored.

bool	keep_infinite_
	If true, infinite vertex and infinite simplices are kept.

index_t	nb_finite_cells_
	If keep_infinite_ is true, then finite cells are 0..nb_finite_cells_-1 and infinite cells are nb_finite_cells_ ... nb_cells_.

bool	keep_regions_

Related Functions inherited from GEO::Delaunay
typedef SmartPointer< Delaunay >	Delaunay_var
	Smart pointer that refers to a Delaunay object.

typedef Factory1< Delaunay, coord_index_t >	DelaunayFactory
	Delaunay Factory. More...

Detailed Description

Implementation of Delaunay in 2d.

This package uses concepts inspired by two triangulation softwares, CGAL and tetgen, described in the following references. This package follows the idea used in CGAL of traversing the cavity from inside, since it traverses less triangles than when traversing from outside.

Jean-Daniel Boissonnat, Olivier Devillers, Monique Teillaud, and Mariette Yvinec. Triangulations in CGAL. In Proc. 16th Annu. ACM Sympos. Comput. Geom., pages 11-18, 2000.
Hang Si, Constrained Delaunay trianglesl mesh generation and refinement. Finite elements in Analysis and Design, 46 (1-2):33–46, 2010.

Note that the algorithm here does not support vertex deletion nor degenerate input with all coplanar or all colinear points (use CGAL instead if you have these requirements).

The core algorithm used in this code, CGAL and tetgen was independently and simultaneously discovered by Bowyer and Watson:

Adrian Bowyer, "Computing Dirichlet tessellations", Comput. J., vol. 24, no 2, 1981, p. 162-166
David F. Watson, "Computing the n-dimensional Delaunay tessellation with application to Voronoi polytopes", Comput. J., vol. 24, no 2, 1981, p. 167-172

The spatial reordering method, that dramatically increases the performances, also used in this code, CGAL and tetgen was introduced in the following references. The second one is a smart implementation based on the std::nth_element() function of the STL, that inspired the compute_BRIO_ordering() function of this package.

Nina Amenta, Sunghee Choi and Gunter Rote, "Incremental constructions con brio", ACM Symposium on Computational Geometry 2003.
Christophe Delage and Olivier Devillers. Spatial Sorting. In CGAL User and Reference Manual. CGAL Editorial Board, 3.9 edition, 2011

The locate() function is based on the following two references. The first one randomizes the choice of the next triangle. The second one uses an inexact locate() function to initialize the exact one (it is called "structural filtering"). The first idea is used in both CGAL and tetgen, and the second one is used in CGAL.

Walking in a triangulation, O Devillers, S Pion, M Teillaud 17th Annual Symposium on Computational geometry, 106-114
Stefan Funke , Kurt Mehlhorn and Stefan Naher, "Structural filtering, a paradigm for efficient and exact geometric programs", Comput. Geom., 1999

Definition at line 106 of file delaunay_2d.h.

Constructor & Destructor Documentation

◆ Delaunay2d()

GEO::Delaunay2d::Delaunay2d ( coord_index_t dimension = 2 )

Constructs a new Delaunay2d.

Parameters

[in]

dimension

dimension of the triangulation (2 or 3). If dimension = 3, this creates a regular triangulation (dual of a power diagram). In this case:

the input points are 3d points, were the third coordinate of point $ i $ is $ \sqrt{W - w_i} $ where $ W $ is the maximum of the weights of all the points and \d$ w_i $ is the weight associated with vertex $ i $.
the constructed combinatorics is a triangulated surface (2d and not 3d although dimension() returns 3). This triangulated surface corresponds to the regular triangulation of the weighted points.

Member Function Documentation

◆ abort_if_empty_cell()

void GEO::Delaunay2d::abort_if_empty_cell ( bool x )

inline

Specifies behavior if an empty cell is detected.

Parameters

[in] x if set, then computation is aborted as soon as an empty cell is detected.

only happens in RegularTriangulation/Laguerre diagram.

Definition at line 155 of file delaunay_2d.h.

◆ add_triangle_to_list()

void GEO::Delaunay2d::add_triangle_to_list	(	index_t	t,
		index_t &	first,
		index_t &	last
	)

inlineprotected

Adds a triangle to a linked list.

Triangles can be linked, it is used to manage the free list that recycles deleted triangles.

Parameters

[in]	t	the index of the triangle
[in,out]	first	first item of the list or END_OF_LIST if the list is empty
[in,out]	last	last item of the list or END_OF_LIST if the list is empty

Definition at line 415 of file delaunay_2d.h.

◆ create_first_triangle()

bool GEO::Delaunay2d::create_first_triangle	(	index_t &	iv0,
		index_t &	iv1,
		index_t &	iv2
	)

protected

Finds in the pointset a set of three non-colinear points.

This function is used to initiate the incremental Delaunay construction.

Parameters

[out]	iv0	index of the first vertex
[out]	iv1	index of the second vertex
[out]	iv2	index of the third vertex

Return values

true	if a set of three non-colinear points was found
false	if all the points are colinear

◆ find_3()

static index_t GEO::Delaunay2d::find_3	(	const signed_index_t *	T,
		signed_index_t	v
	)

inlinestaticprotected

Finds the index of an integer in an array of three integers.

Parameters

[in]	T	a const pointer to an array of three integers
[in]	v	the integer to retrieve in `T`

Returns: the index (0,1 or 2) of v in T

Precondition: The three entries of T are different and one of them is equal to v.

Definition at line 873 of file delaunay_2d.h.

◆ find_conflict_zone()

void GEO::Delaunay2d::find_conflict_zone	(	index_t	v,
		index_t	t,
		const Sign *	orient,
		index_t &	t_bndry,
		index_t &	e_bndry,
		index_t &	first,
		index_t &	last
	)

protected

Determines the list of triangles in conflict with a given point.

Parameters

[in]	v	the index of the point to be inserted
[in]	t	the index of a triangle that contains `p`, as returned by locate()
[in]	orient	an array of three signs indicating the orientation of `p` with respect to the three edges of `t`, as returned by locate()
[out]	t_bndry	a triangle adjacent to the boundary of the conflict zone
[out]	e_bndry	the edge along which t_bndry is adjacent to the boundary of the conflict zone
[out]	first	the index of the first triangle in conflict
[out]	last	the index of the last triangle in conflict The other triangles are linked, and can be traversed from `first` by using triangle_next() until `last` or END_OF_LIST is reached. The conflict zone can be empty under two circumstances: the vertex `v` already exists in the triangulation the triangulation is weighted and `v` is not visible in either cases, both `first` and `last` contain END_OF_LIST

◆ find_conflict_zone_iterative()

void GEO::Delaunay2d::find_conflict_zone_iterative	(	const double *	p,
		index_t	t,
		index_t &	t_bndry,
		index_t &	e_bndry,
		index_t &	first,
		index_t &	last
	)

protected

This function is used to implement find_conflict_zone.

This function detects the neighbors of t that are in the conflict zone and calls itself recursively on them.

Parameters

[in]	p	the point to be inserted
[in]	t	index of a triangle in the fonflict zone
[out]	t_bndry	a triangle adjacent to the boundary of the conflict zone
[out]	e_bndry	the edge along which t_bndry is adjacent to the boundary of the conflict zone
[out]	first	the index of the first triangle in conflict
[out]	last	the index of the last triangle in conflict

Precondition: The triangle t was already marked as conflict (triangle_is_in_list(t))

◆ find_triangle_adjacent()

index_t GEO::Delaunay2d::find_triangle_adjacent	(	index_t	t1,
		index_t	t2_in
	)		const

inlineprotected

Finds the index of the edge accros which t1 is adjacent to t2_in.

Parameters

[in]	t1	first triangle
[in]	t2_in	second triangle

Returns: e such that triangle_adjacent(t1,e)==t2_in

Precondition: t1 and t2_in are adjacent

Definition at line 728 of file delaunay_2d.h.

◆ find_triangle_vertex()

index_t GEO::Delaunay2d::find_triangle_vertex	(	index_t	t,
		signed_index_t	v
	)		const

inlineprotected

Finds the index of the vertex in a triangle.

Parameters

[in]	t	the triangle
[in]	v	the vertex

Returns: iv such that triangle_vertex(t,v)==iv

Precondition: t is incident to v

Definition at line 658 of file delaunay_2d.h.

◆ finite_triangle_vertex()

index_t GEO::Delaunay2d::finite_triangle_vertex	(	index_t	t,
		index_t	lv
	)		const

inlineprotected

Gets the index of a vertex of a triangle.

Parameters

[in]	t	index of the triangle
[in]	lv	local vertex (0,1,2) index in `t`

Returns: the global index of the lvth vertex of triangle t

Precondition: Vertex lv of triangle t is not at infinity

Definition at line 673 of file delaunay_2d.h.

◆ has_empty_cells()

bool GEO::Delaunay2d::has_empty_cells ( ) const

inline

Tests whether the Laguerre diagram has empty cells.

If the Laguerre diagram has empty cells and abort_if_empty_cell is set, then computation is stopped, and all the queries on the Laguerre diagram will not work (including the non-empty cells).

Return values

true	if the Laguerre diagram has empty cells.
false	otherwise.

Definition at line 144 of file delaunay_2d.h.

◆ insert()

index_t GEO::Delaunay2d::insert	(	index_t	v,
		index_t	hint = `NO_TRIANGLE`
	)

protected

Inserts a point in the triangulation.

Parameters

[in]	v	the index of the point to be inserted
[in]	hint	the index of a triangle as near as possible to `v`, or -1 if unspecified

Returns: the index of one of the triangles incident to point v

◆ locate()

index_t GEO::Delaunay2d::locate	(	const double *	p,
		index_t	hint = `NO_TRIANGLE`,
		bool	thread_safe = `false`,
		Sign *	orient = `nullptr`
	)		const

protected

Finds the triangle that contains a point.

If the point is on an edge or vertex, the function returns one of the triangles incident to that edge or vertex.

Parameters

[in]	p	a pointer to the coordinates of the point
[in]	thread_safe	if true, a global spinlock is used to protect the calls to random(), this is necessary if multiple threads use locate() simultaneously
[out]	orient	a pointer to an array of three Signs or nullptr. If non-nullptr, returns the orientation with respect to the three edges of the triangle that contains `p`.

Returns: the index of a triangle that contains p. If the point is outside the convex hull of the inserted so-far points, then the returned triangle is a virtual one (first vertex is the "vertex at infinity" of index -1) or NO_TRIANGLE if the virtual triangles were previously removed.

◆ locate_inexact()

index_t GEO::Delaunay2d::locate_inexact	(	const double *	p,
		index_t	hint,
		index_t	max_iter
	)		const

protected

Finds the triangle that (approximately) contains a point using inexact predicates.

The result of this function can be used as a hint for locate(). It accelerates locate as compared to calling it directly. This technique is referred to as "structural filtering".

Parameters

[in]	p	a pointer to the coordinates of the point
[in]	max_iter	maximum number of traversed tets

Returns: the index of a triangle that (approximately) contains p. If the point is outside the convex hull of the inserted so-far points, then the returned triangle is a virtual one (first vertex is the "vertex at infinity" of index -1) or NO_TRIANGLE if the virtual triangles were previously removed.

◆ mark_triangle()

void GEO::Delaunay2d::mark_triangle ( index_t t )

inlineprotected

Marks a triangle.

A triangle is marked whenever it is detected as non-conflict. The same space is used for marking and for chaining the conflict list. The index of the point being inserted is used as a time-stamp for marking triangles. A triangle can be in the following states:

in list
not in list and marked
not in list and not marked
Parameters

[in] t index of the triangle to be marked

Definition at line 610 of file delaunay_2d.h.

◆ max_t()

index_t GEO::Delaunay2d::max_t ( ) const

inlineprotected

Maximum valid index for a triangle.

This includes not only real triangles, but also the virtual ones on the border, the conflict list and the free list.

Returns: the maximum valid index for a triangle.

Definition at line 320 of file delaunay_2d.h.

◆ nearest_vertex()

index_t GEO::Delaunay2d::nearest_vertex ( const double * p ) const

overridevirtual

Computes the nearest vertex from a query point.

Parameters

[in] p query point

Returns: the index of the nearest vertex

Reimplemented from GEO::Delaunay.

◆ new_triangle() [1/2]

index_t GEO::Delaunay2d::new_triangle ( )

inlineprotected

Creates a new triangle.

Uses either a triangle recycled from the free list, or creates a new one by expanding the two indices arrays.

Returns: the index of the newly created triangle

Definition at line 522 of file delaunay_2d.h.

◆ new_triangle() [2/2]

index_t GEO::Delaunay2d::new_triangle	(	signed_index_t	v1,
		signed_index_t	v2,
		signed_index_t	v3
	)

inlineprotected

Creates a new triangle.

Sets the vertices. Adjacent triangles index are left uninitialized. Uses either a triangle recycled from the free list, or creates a new one by expanding the two indices arrays.

Parameters

[in]	v1	index of the first vertex
[in]	v2	index of the second vertex
[in]	v3	index of the third vertex

Returns: the index of the newly created triangle

Definition at line 556 of file delaunay_2d.h.

◆ remove_triangle_from_list()

void GEO::Delaunay2d::remove_triangle_from_list ( index_t t )

inlineprotected

Removes a triangle from the linked list it belongs to.

Triangles can be linked, it is used to manage both the free list that recycles deleted triangles and the list of triangles in conflict with the inserted point.

Parameters

[in] t the index of the triangle

Definition at line 437 of file delaunay_2d.h.

◆ set_tet()

void GEO::Delaunay2d::set_tet	(	index_t	t,
		signed_index_t	v0,
		signed_index_t	v1,
		signed_index_t	v2,
		index_t	a0,
		index_t	a1,
		index_t	a2
	)

inlineprotected

Sets the vertices and adjacent triangles of a triangle.

Parameters

[in]	t	index of the triangle
[in]	v0	index of the first vertex
[in]	v1	index of the second vertex
[in]	v2	index of the third vertex
[in]	a0	index of the adjacent triangle opposite to `v0`
[in]	a1	index of the adjacent triangle opposite to `v1`
[in]	a2	index of the adjacent triangle opposite to `v2`

Definition at line 761 of file delaunay_2d.h.

◆ set_triangle_adjacent()

void GEO::Delaunay2d::set_triangle_adjacent	(	index_t	t1,
		index_t	le1,
		index_t	t2
	)

inlineprotected

Sets a triangle-to-triangle adjacency.

Parameters

[in]	t1	index of the first triangle
[in]	le1	local facet index (0,1,2) in t1
[in]	t2	index of the triangle adjacent to `t1` accros `lf1`

Definition at line 712 of file delaunay_2d.h.

◆ set_triangle_mark_stamp()

void GEO::Delaunay2d::set_triangle_mark_stamp ( index_t stamp )

inlineprotected

Generates a unique stamp for marking tets.

Storage is shared for list-chaining and stamp-marking (both are mutually exclusive), therefore the stamp has the NOT_IN_LIST_BIT set.

Parameters

[in] stamp the unique stamp for marking tets

Definition at line 574 of file delaunay_2d.h.

◆ set_triangle_vertex()

void GEO::Delaunay2d::set_triangle_vertex	(	index_t	t,
		index_t	lv,
		signed_index_t	v
	)

inlineprotected

Sets a triangle-to-vertex adjacency.

Parameters

[in]	t	index of the triangle
[in]	lv	local vertex index (0,1,2) in `t`
[in]	v	global index of the vertex

Definition at line 686 of file delaunay_2d.h.

◆ set_vertices()

void GEO::Delaunay2d::set_vertices	(	index_t	nb_vertices,
		const double *	vertices
	)

overridevirtual

Sets the vertices of this Delaunay, and recomputes the cells.

Parameters

[in]	nb_vertices	number of vertices
[in]	vertices	a pointer to the coordinates of the vertices, as a contiguous array of doubles

Reimplemented from GEO::Delaunay.

◆ show_list()

void GEO::Delaunay2d::show_list	(	index_t	first,
		const std::string &	list_name
	)		const

protected

For debugging purposes, displays a triangle.

Parameters

[in]	first	index of the first triangle in the list
[in]	list_name	name of the list, will be displayed as well

◆ show_triangle()

void GEO::Delaunay2d::show_triangle ( index_t t ) const

protected

For debugging purposes, displays a triangle.

Parameters

[in] t index of the triangle to display.

◆ show_triangle_adjacent()

void GEO::Delaunay2d::show_triangle_adjacent	(	index_t	t,
		index_t	le
	)		const

protected

For debugging purposes, displays a triangle adjacency.

Parameters

[in]	t	index of the triangle to display.
[in]	le	local index (0,1,2) of the triangle facet adjacenty to display.

◆ stellate_conflict_zone()

index_t GEO::Delaunay2d::stellate_conflict_zone	(	index_t	v,
		index_t	t_bndry,
		index_t	e_bndry
	)

protected

Creates a star of triangles filling the conflict zone.

For each triangle edge on the border of the conflict zone, a new triangle is created, resting on the edge and incident to vertex v. The function is called recursively until the entire conflict zone is filled.

Parameters

[in]	v	the index of the point to be inserted
[in]	t_bndry	index of a triangle on the border of the conflict zone.
[in]	e_bndry	index of the facet along which `t_bndry` is incident to the border of the conflict zone

Returns: the index of one the newly created triangles

◆ triangle_adjacent()

signed_index_t GEO::Delaunay2d::triangle_adjacent	(	index_t	t,
		index_t	le
	)		const

inlineprotected

Gets the index of a triangle adjacent to another one.

Parameters

[in]	t	index of the triangle
[in]	le	local edge (0,1,2) index in `t`

Returns: the triangle adjacent to t accros edge le

Definition at line 698 of file delaunay_2d.h.

◆ triangle_edge_vertex()

static index_t GEO::Delaunay2d::triangle_edge_vertex	(	index_t	e,
		index_t	v
	)

inlinestaticprotected

Returns the local index of a vertex by edge and by local vertex index in the edge.

tri edge vertex is such that the triangle formed with:

vertex lv
triangle_edge_vertex(lv,0)
triangle_edge_vertex(lv,1) has the same orientation as the original triangle for any vertex lv.
Parameters

[in] e local facet index, in (0,1,2)

[in] v local vertex index, in (0,1)

Returns
the local triangle vertex index of vertex v in edge f

Definition at line 632 of file delaunay_2d.h.

◆ triangle_is_conflict()

bool GEO::Delaunay2d::triangle_is_conflict	(	index_t	t,
		const double *	p
	)		const

inlineprotected

Tests whether a given triangle is in conflict with a given 3d point.

A real triangle is in conflict with a point whenever the point is contained by its circumscribed sphere, and a virtual triangle is in conflict with a point whenever the triangle formed by its real face and with the point has positive orientation.

Parameters

[in]	t	the index of the triangle
[in]	p	a pointer to the coordinates of the point

Return values

true	if point `p` is in conflict with triangle `t`
false	otherwise

Definition at line 791 of file delaunay_2d.h.

◆ triangle_is_finite()

bool GEO::Delaunay2d::triangle_is_finite ( index_t t ) const

inlineprotected

Tests whether a given triangle is a finite one.

Infinite triangles are the ones that are incident to the infinite vertex (index -1)

Parameters

[in] t the index of the triangle

Return values

true	if `t` is finite
false	otherwise

Definition at line 461 of file delaunay_2d.h.

◆ triangle_is_free()

bool GEO::Delaunay2d::triangle_is_free ( index_t t ) const

inlineprotected

Tests whether a triangle is in the free list.

Deleted triangles are recycled in a free list.

Parameters

[in] t index of the triangle

Return values

true	if triangle `t` is in the free list
false	otherwise

Definition at line 511 of file delaunay_2d.h.

◆ triangle_is_in_list()

bool GEO::Delaunay2d::triangle_is_in_list ( index_t t ) const

inlineprotected

Tests whether a triangle belongs to a linked list.

Triangles can be linked, it is used to manage both the free list that recycles deleted triangles, the conflict region and the list of newly created triangles. In addition, a triangle that is not in a list can be marked. The same space is used for marking and chaining triangles in lists. A triangle can be in the following states:

in list
not in list and marked
not in list and not marked
Parameters

[in] t the index of the triangle

Return values

true if triangle t belongs to a linked list

false otherwise

Definition at line 384 of file delaunay_2d.h.

◆ triangle_is_marked()

bool GEO::Delaunay2d::triangle_is_marked ( index_t t ) const

inlineprotected

Tests whether a triangle is marked.

A triangle is marked whenever it is detected as non-conflict. The index of the point being inserted is used as a time-stamp for marking triangles. The same space is used for marking and for chaining the conflict list. A triangle can be in the following states:

in list
not in list and marked
not in list and not marked
Parameters

[in] t index of the triangle

Return values

true if triangle t is marked

false otherwise

Definition at line 593 of file delaunay_2d.h.

◆ triangle_is_real()

bool GEO::Delaunay2d::triangle_is_real ( index_t t ) const

inlineprotected

Tests whether a triangle is a real one.

Real triangles are incident to three user-specified vertices (there are also virtual triangles that are incident to the vertex at infinity, with index -1)

Parameters

[in] t index of the triangle

Return values

true	if triangle `t` is a real one
false	otherwise

Definition at line 479 of file delaunay_2d.h.

◆ triangle_is_virtual()

bool GEO::Delaunay2d::triangle_is_virtual ( index_t t ) const

inlineprotected

Tests whether a triangle is a virtual one.

Virtual triangles are triangles incident to the vertex at infinity.

Parameters

[in] t index of the triangle

Return values

true	if triangle `t` is virtual
false	otherwise

Definition at line 492 of file delaunay_2d.h.

◆ triangle_next()

index_t GEO::Delaunay2d::triangle_next ( index_t t ) const

inlineprotected

Gets the index of a successor of a triangle.

Triangles can be linked, it is used to manage both the free list that recycles deleted triangles.

Parameters

[in] t the index of the triangle

Return values

END_OF_LIST	if the end of the list is reached
the	index of the successor of triangle \t otherwise

Precondition: triangle_is_in_list(t)

Definition at line 399 of file delaunay_2d.h.

◆ triangle_vertex()

signed_index_t GEO::Delaunay2d::triangle_vertex	(	index_t	t,
		index_t	lv
	)		const

inlineprotected

Gets the index of a vertex of a triangle.

Parameters

[in]	t	index of the triangle
[in]	lv	local vertex (0,1,2) index in `t`

Returns: the global index of the lvth vertex of triangle t or -1 if the vertex is at infinity

Definition at line 645 of file delaunay_2d.h.

Member Data Documentation

◆ NO_TRIANGLE

const index_t GEO::Delaunay2d::NO_TRIANGLE = index_t(-1)

staticprotected

Symbolic constant for uninitialized hint.

Locate functions can be accelerated by specifying a hint. This constant indicates that no hint is given.

Definition at line 167 of file delaunay_2d.h.

◆ NOT_IN_LIST

const index_t GEO::Delaunay2d::NOT_IN_LIST = index_t(~0)

staticprotected

Default symbolic value of the cell_next_ field that indicates that a triangle is not in a linked list.

This is the default value. Note that it suffices that NOT_IN_LIST_BIT is set for a triangle to be not in any list. A triangle can be:

in a list (cell_next_[t] & NOT_IN_LIST_BIT == 0)
not in a list and not marked (cell_next_[t] & NOT_IN_LIST_BIT != 0) && (cell_next_[t] != cur_stamp_)
not in a list and marked (cell_next_[t] == cur_stamp_)

Definition at line 340 of file delaunay_2d.h.

◆ NOT_IN_LIST_BIT

const index_t GEO::Delaunay2d::NOT_IN_LIST_BIT = index_t(1u << 31)

staticprotected

If cell_next_[t] & NOT_IN_LIST_BIT != 0, then t is not in a linked list.

The other bits of cell_next_[t] are used to store the stamp (i.e. index of the current point being inserted). The stamp is used for marking triangles that were detected as non-conflict when inserting a point. A triangle can be:

in a list (cell_next_[t] & NOT_IN_LIST_BIT == 0)
not in a list and not marked (cell_next_[t] & NOT_IN_LIST_BIT != 0) && (cell_next_[t] != cur_stamp_)
not in a list and marked (cell_next_[t] == cur_stamp_)

Definition at line 357 of file delaunay_2d.h.

◆ VERTEX_AT_INFINITY

const signed_index_t GEO::Delaunay2d::VERTEX_AT_INFINITY = -1

staticprotected

Symbolic value for a vertex of a triangle that indicates a virtual triangle.

The three other vertices then correspond to a facet on the convex hull of the points.

Definition at line 449 of file delaunay_2d.h.

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

geogram/delaunay/delaunay_2d.h

[in]	e	local facet index, in (0,1,2)
[in]	v	local vertex index, in (0,1)

Public Member Functions

Protected Member Functions

Static Protected Member Functions

Static Protected Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ Delaunay2d()

Member Function Documentation

◆ abort_if_empty_cell()

◆ add_triangle_to_list()

◆ create_first_triangle()

◆ find_3()

◆ find_conflict_zone()

◆ find_conflict_zone_iterative()

◆ find_triangle_adjacent()

◆ find_triangle_vertex()

◆ finite_triangle_vertex()

◆ has_empty_cells()

◆ insert()

◆ locate()

◆ locate_inexact()

◆ mark_triangle()

◆ max_t()

◆ nearest_vertex()

◆ new_triangle() [1/2]

◆ new_triangle() [2/2]

◆ remove_triangle_from_list()

◆ set_tet()

◆ set_triangle_adjacent()

◆ set_triangle_mark_stamp()

◆ set_triangle_vertex()

◆ set_vertices()

◆ show_list()

◆ show_triangle()

◆ show_triangle_adjacent()

◆ stellate_conflict_zone()

◆ triangle_adjacent()

◆ triangle_edge_vertex()

◆ triangle_is_conflict()

◆ triangle_is_finite()

◆ triangle_is_free()

◆ triangle_is_in_list()

◆ triangle_is_marked()

◆ triangle_is_real()

◆ triangle_is_virtual()

◆ triangle_next()

◆ triangle_vertex()

Member Data Documentation

◆ NO_TRIANGLE

◆ NOT_IN_LIST

◆ NOT_IN_LIST_BIT

◆ VERTEX_AT_INFINITY