Computes the intersection between a set of halfplanes using Bowyer-Watson algorithm. More...

#include <geogram/voronoi/convex_cell.h>

Public Member Functions
	ConvexCell (ConvexCellFlags flags=None)
	ConvexCell constructor. More...

void	use_exact_predicates (bool x)
	Specifies whether exact predicates should be used. More...

bool	has_vglobal () const
	Tests whether global vertex indices are stored. More...

bool	has_tflags () const
	Tests whether triangle flags are stored. More...

void	create_vglobal ()
	Creates vertex global indices if they are not present.

void	clear ()
	Removes all vertices and triangles from this ConvexCell. More...

void	init_with_box (double xmin, double ymin, double zmin, double xmax, double ymax, double zmax)
	Initializes this ConvexCell to an axis-aligned box. More...

void	init_with_tet (vec4 P0, vec4 P1, vec4 P2, vec4 P3)
	Initializes this ConvexCell to a tetrahedron. More...

void	init_with_tet (vec4 P0, vec4 P1, vec4 P2, vec4 P3, global_index_t P0_global_index, global_index_t P1_global_index, global_index_t P2_global_index, global_index_t P3_global_index)
	Initializes this ConvexCell to a tetrahedron. More...

void	save (const std::string &filename, double shrink=0.0) const
	Saves the computed cell in alias wavefront file format. More...

index_t	save (std::ostream &out, global_index_t v_offset=1, double shrink=0.0, bool borders_only=false) const
	Saves the computed cell in alias wavefront file format. More...

void	append_to_mesh (GEO::Mesh mesh, double shrink=0.0, bool borders_only=false, GEO::Attribute< GEO::index_t > facet_attr=nullptr) const
	Appends the computed cell to a GEO::Mesh. More...

void	for_each_Voronoi_vertex (index_t v, std::function< void(index_t)> vertex)
	Calls a user-defined function for each vertex of a Voronoi facet. More...

void	clip_by_plane (vec4 P)
	Clips this convex cell by a new plane. More...

void	clip_by_plane (vec4 P, global_index_t j)
	Clips this convex cell by a new plane and stores the corresponding global index in the newly created vertex. More...

void	clip_by_plane (vec4 P, global_index_t P_global_index, std::function< bool(ushort, ushort)> triangle_conflict_predicate)
	Clips this convex cell by a new plane, using a user-defined geometric predicate. More...

void	clip_by_plane_fast (vec4 P)
	Clips this convex cell by a new plane and stores the corresponding global index in the newly created vertex. More...

void	clip_by_plane_fast (vec4 P, global_index_t j)
	Clips this convex cell by a new plane and stores the corresponding global index in the newly created vertex. More...

index_t	nb_t () const
	Gets the number of triangles. More...

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

index_t	create_vertex (vec4 P)
	Directly creates a new vertex. More...

index_t	create_vertex (vec4 P, global_index_t v)
	Directly creates a new vertex. More...

index_t	create_triangle (index_t i, index_t j, index_t k)
	Directly creates a new triangle. More...

void	kill_vertex (index_t v)
	Replaces a vertex with the vertex at infinity in all facets. More...

bool	vertex_is_contributing (index_t v) const
	Tests whether a vertex has a corresponding facet in the cell. More...

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

void	compute_geometry ()
	Computes the geometry and some cached information. More...

double	facet_area (index_t v) const
	Gets the dual facet area of a given vertex. More...

double	volume () const
	Computes the volume of this convex cell. More...

vec3	barycenter () const
	Computes the barycenter of this convex cell. More...

void	compute_mg (double &m, vec3 &mg) const
	Computes volume and barycenter. More...

double	squared_radius (vec3 center) const
	Computes the squared radius of the smallest sphere containing the cell and centered on a point. More...

double	squared_inner_radius (vec3 center) const
	Computes the squared radius of the largest sphere contained in the cell and centered on a point. More...

bool	empty () const
	Tests whether this ConvexCell is empty. More...

global_index_t	v_global_index (index_t lv) const
	Gets the global vertex index from a local vertex index. More...

void	set_v_global_index (index_t lv, global_index_t v)
	Sets the global vertex index associated with a local vertex index. More...

bool	has_v_global_index (global_index_t v) const
	Tests whether a vertex with a given global index exists in this ConvexCell. More...

ushort	first_triangle () const
	Gets the first triangle. More...

ushort	next_triangle (ushort t) const
	Gets the successor of a triangle. More...

vec3	triangle_point (ushort t) const
	Gets the point that corresponds to a triangle. More...

global_index_t	triangle_v_global_index (ushort t, index_t llv) const
	Gets the global index of a triangle vertex. More...

index_t	triangle_v_local_index (ushort t, index_t llv) const
	Gets the local index of a triangle vertex. More...

bool	triangle_is_user_marked (ushort t)
	Tests whether a triangle is marked by the user. More...

void	triangle_user_mark (ushort t)
	Sets the user mark on a triangle. More...

void	triangle_user_unmark (ushort t)
	Resets the user mark on a triangle. More...

bool	cell_has_conflict (const vec4 &P)
	Tests whether a cell has at least one vertex in conflict with a halfspace. More...

bool	cell_is_totally_in_conflict (const vec4 &P)
	Tests whether a cell has all its vertices in conflict with a plane. More...

index_t	triangle_adjacent (index_t t, index_t le) const
	Gets a triangle adjacent to another triangle by edge local index. More...

void	set_triangle_adjacent (index_t t1, index_t le, index_t t2)
	Sets triangle to triangle adjacency. More...

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

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

index_t	triangle_find_adjacent (index_t t1, index_t t2) const
	Gets the edge on witch a triangle is adjacent to another one. More...

bool	triangle_is_infinite (index_t t) const
	Tests whether a triangle is infinite. More...

vec4	vertex_plane (index_t v) const
	Gets the equation of a plane associated with a vertex. More...

vec3	vertex_plane_normal (index_t v) const
	Gets the normal to the plane associated with a vertex. More...

bool	triangle_is_marked_as_conflict (index_t t) const
	Tests whether a triangle is marked as conflict. More...

bool	triangle_is_in_conflict (TriangleWithFlags T, const vec4 &eqn) const
	Tests whether a triangle is in conflict with a plane. More...

index_t	new_triangle (index_t i, index_t j, index_t k)
	Creates a new triangle. More...

index_t	new_triangle (index_t i, index_t j, index_t k, index_t adj0, index_t adj1, index_t adj2)
	Creates a new triangle. More...

vec4	compute_triangle_point (index_t t) const
	Computes the coordinates of the point associated with a triangle. More...

Triangle	get_triangle (index_t t) const
	Gets the three vertices of a triangle. More...

ushort	get_triangle_flags (index_t t) const
	Gets the flags associated with a triangle. More...

void	set_triangle_flags (index_t t, ushort flags)
	Sets the flags of a triangle. More...

TriangleWithFlags	get_triangle_and_flags (index_t t) const
	Gets the three vertices of a triangle and its flags. More...

bool	triangle_is_marked_as_conflict (index_t t)
	Tests whether a given triangle is in the conflict zone.

index_t	max_t () const
	Gets the maximum valid index for a triangle. More...

index_t	max_v () const
	Gets the maximum valid index for a vertex. More...

void	grow_t ()
	Allocates more space for triangles. More...

void	grow_v ()
	Allocates more space for vertices. More...

void	swap (ConvexCell &other)
	Swaps two ConvexCells. More...

vec3 &	stored_triangle_point (ushort t)
	Gets a modifiable reference to a triangle point. More...

Protected Member Functions
void	connect_triangles ()
	finds all triangle-triangle adjacency relations. More...

void	triangulate_conflict_zone (index_t lv, index_t conflict_head, index_t conflict_tail)
	Triangulates the conflict zone. More...

void	set_vertex_plane (index_t v, vec4 P)
	Changes a vertex plane equation. More...

Friends
class	GEO::PeriodicDelaunay3d

Detailed Description

Computes the intersection between a set of halfplanes using Bowyer-Watson algorithm.

Do not use with a large number of planes.

Definition at line 419 of file convex_cell.h.

Constructor & Destructor Documentation

◆ ConvexCell()

VBW::ConvexCell::ConvexCell ( ConvexCellFlags flags = None )

ConvexCell constructor.

Parameters

[in] flags a combination of WithVGlobal, WithTFlags

Member Function Documentation

◆ append_to_mesh()

void VBW::ConvexCell::append_to_mesh	(	GEO::Mesh *	mesh,
		double	shrink = `0.0`,
		bool	borders_only = `false`,
		GEO::Attribute< GEO::index_t > *	facet_attr = `nullptr`
	)		const

Appends the computed cell to a GEO::Mesh.

Parameters

[out]	mesh	a pointer to the mesh.
[in]	shrink	shrinking factor to ease visualization.
[in]	borders_only	if set, only facets that correspond to vertex global index -1 are saved.
[in]	facet_attr	optional facet attribute that stores global facet (dual vertex) ids.

Note: One needs to call mesh->facets.connect() afterwards to have facets adjacencies. It is not called because one may want to append multiple cells to the same mesh.

◆ barycenter()

vec3 VBW::ConvexCell::barycenter ( ) const

Computes the barycenter of this convex cell.

compute_geometry() needs to be called before.

Returns: the barycenter.

◆ cell_has_conflict()

bool VBW::ConvexCell::cell_has_conflict ( const vec4 & P )

inline

Tests whether a cell has at least one vertex in conflict with a halfspace.

Parameters

[in] P the equation of the halfspace.

Return values

true	if there exists a triangle t such that triangle_is_in_conflict(P)
false	otherwise.

Definition at line 966 of file convex_cell.h.

◆ cell_is_totally_in_conflict()

bool VBW::ConvexCell::cell_is_totally_in_conflict ( const vec4 & P )

inline

Tests whether a cell has all its vertices in conflict with a plane.

Parameters

[in] P the equation of the halfspace.

Return values

true	if all the triangles are in conflict with P.
false	otherwise.

Definition at line 986 of file convex_cell.h.

◆ clear()

void VBW::ConvexCell::clear ( )

Removes all vertices and triangles from this ConvexCell.

Keeps allocated memory for future use.

◆ clip_by_plane() [1/3]

void VBW::ConvexCell::clip_by_plane ( vec4 P )

Clips this convex cell by a new plane.

The positive side of the plane equation corresponds to what is kept. In other words, the normal vector P.x, P.y, P.z points towards the interior of this ConvexCell.

Parameters

[in] P the plane equation.

◆ clip_by_plane() [2/3]

void VBW::ConvexCell::clip_by_plane	(	vec4	P,
		global_index_t	j
	)

Clips this convex cell by a new plane and stores the corresponding global index in the newly created vertex.

The positive side of the plane equation corresponds to what is kept. In other words, the normal vector P.x, P.y, P.z points towards the interior of this ConvexCell. This function can only be called if global indices are stored.

Parameters

[in]	P	the plane equation.
[in]	j	the global index of the plane.

◆ clip_by_plane() [3/3]

void VBW::ConvexCell::clip_by_plane	(	vec4	P,
		global_index_t	P_global_index,
		std::function< bool(ushort, ushort)>	triangle_conflict_predicate
	)

Clips this convex cell by a new plane, using a user-defined geometric predicate.

It is useful to be able to have a user-defined geometric predicates when the vertices have a symbolic representation, stored in the global indices associated with the plane. It is used by the robust mesh boolean operations. The positive side of the plane equation corresponds to what is kept. In other words, the normal vector P.x, P.y, P.z points towards the interior of this ConvexCell. If global indices are stored, then j is stored as the global index of the plane equation.

Parameters

[in]	P	the plane equation.
[in]	P_global_index	the global index of the plane.
[in]	triangle_conflict_predicate	a function that takes as arguments a local triangle index and local vertex (plane eqn) index, and that returns true if the triangle is in conflict with the vertex.

◆ clip_by_plane_fast() [1/2]

void VBW::ConvexCell::clip_by_plane_fast ( vec4 P )

Clips this convex cell by a new plane and stores the corresponding global index in the newly created vertex.

For a ConvexCell with a large number of facets, this version is faster than clip_by_plane(). However, it cannot be used with a ConvexCell that has infinite faces.

Parameters

[in] P the plane equation.

See also: clip_by_plane()

◆ clip_by_plane_fast() [2/2]

void VBW::ConvexCell::clip_by_plane_fast	(	vec4	P,
		global_index_t	j
	)

Clips this convex cell by a new plane and stores the corresponding global index in the newly created vertex.

For a ConvexCell with a large number of facets, this version is faster than clip_by_plane(). However, it cannot be used with a ConvexCell that has infinite faces.

Parameters

[in]	P	the plane equation.
[in]	j	the global index of the plane.

See also: clip_by_plane()

◆ compute_geometry()

void VBW::ConvexCell::compute_geometry ( )

Computes the geometry and some cached information.

Needs to be called before volume(), facet_area() and barycenter().

◆ compute_mg()

void VBW::ConvexCell::compute_mg	(	double &	m,
		vec3 &	mg
	)		const

Computes volume and barycenter.

Parameters

[out]	m	the computed volume
[out]	mg	the computed volume times the barycenter

compute_geometry() needs to be called before.

◆ compute_triangle_point()

vec4 VBW::ConvexCell::compute_triangle_point ( index_t t ) const

Computes the coordinates of the point associated with a triangle.

Parameters

[in] t the triangle.

Returns: the intersection between the three planes associated with the three vertices of the triangle, in homogeneous coordinates.

◆ connect_triangles()

void VBW::ConvexCell::connect_triangles ( )

protected

finds all triangle-triangle adjacency relations.

Client code should not need to call this function. It is used by PeriodicDelaunay3d::copy_Laguerre_cell_from_Delaunay().

◆ create_triangle()

index_t VBW::ConvexCell::create_triangle	(	index_t	i,
		index_t	j,
		index_t	k
	)

inline

Directly creates a new triangle.

Parameters

[in] i,j,k the three vertices of the triangle.

The triangle is inserted into the list of valid triangles.

Returns: the index of the newly created triangle.

Definition at line 708 of file convex_cell.h.

◆ create_vertex() [1/2]

index_t VBW::ConvexCell::create_vertex ( vec4 P )

inline

Directly creates a new vertex.

Parameters

[in] P the plane equation attached to the vertex.

Returns: the index of the newly created vertex.

Definition at line 677 of file convex_cell.h.

◆ create_vertex() [2/2]

index_t VBW::ConvexCell::create_vertex	(	vec4	P,
		global_index_t	v
	)

inline

Directly creates a new vertex.

Parameters

[in]	P	the plane equation attached to the vertex.
[in]	v	the global index associated with the vertex.

Returns: the index of the newly created vertex.

Precondition: global vertex indices are stored

Definition at line 694 of file convex_cell.h.

◆ empty()

bool VBW::ConvexCell::empty ( ) const

inline

Tests whether this ConvexCell is empty.

ConvexCell can be empty if everything was clipped out.

Return values

true	if this ConvexCell is empty.
false	otherwise.

Definition at line 817 of file convex_cell.h.

◆ facet_area()

double VBW::ConvexCell::facet_area ( index_t v ) const

Gets the dual facet area of a given vertex.

compute_geometry() needs to be called before.

Parameters

[in] v the vertex.

Returns: the dual facet area associated with v.

terminate() needs to be called before calling this function.

◆ first_triangle()

ushort VBW::ConvexCell::first_triangle ( ) const

inline

Gets the first triangle.

Returns: the index of the first triangle, or END_OF_LIST if this ConvexCell is empty.

Definition at line 866 of file convex_cell.h.

◆ for_each_Voronoi_vertex()

void VBW::ConvexCell::for_each_Voronoi_vertex	(	index_t	v,
		std::function< void(index_t)>	vertex
	)

Calls a user-defined function for each vertex of a Voronoi facet.

One needs to call compute_geometry() before calling this function.

Parameters

[in]	v	the index of the (dual) Voronoi Facet, that is a (primal) vertex, in [0..nb_v()-1]
[in]	vertex	a function that takes an index_t as an argument, with the index of the triangle that corresponds to the current Voronoi vertex.

◆ get_triangle()

Triangle VBW::ConvexCell::get_triangle ( index_t t ) const

inline

Gets the three vertices of a triangle.

Parameters

[in] t the triangle.

Returns: a Triangle with the indices of the three vertices of the triangle.

Definition at line 1202 of file convex_cell.h.

◆ get_triangle_and_flags()

TriangleWithFlags VBW::ConvexCell::get_triangle_and_flags ( index_t t ) const

inline

Gets the three vertices of a triangle and its flags.

Parameters

[in] t the triangle.

Returns: a TriangleWithFlags with the indices of the three vertices of the triangle and the flags.

Definition at line 1235 of file convex_cell.h.

◆ get_triangle_flags()

ushort VBW::ConvexCell::get_triangle_flags ( index_t t ) const

inline

Gets the flags associated with a triangle.

Contains both the conflict flag and the chaining.

Parameters

[in] t the triangle.

Returns: the flags associated with t.

Definition at line 1214 of file convex_cell.h.

◆ grow_t()

void VBW::ConvexCell::grow_t ( )

Allocates more space for triangles.

Makes max_t_ twice bigger.

◆ grow_v()

void VBW::ConvexCell::grow_v ( )

Allocates more space for vertices.

Makes max_v_ twice bigger.

◆ has_tflags()

bool VBW::ConvexCell::has_tflags ( ) const

inline

Tests whether triangle flags are stored.

Return values

true	if triangle flags are stored.
false	otherwise.

Definition at line 454 of file convex_cell.h.

◆ has_v_global_index()

bool VBW::ConvexCell::has_v_global_index ( global_index_t v ) const

Tests whether a vertex with a given global index exists in this ConvexCell.

Parameters

[in] v the global index.

Return values

true	if there exists in this ConvexCell a vertex with global index `v`.
false	otherwise.

◆ has_vglobal()

bool VBW::ConvexCell::has_vglobal ( ) const

inline

Tests whether global vertex indices are stored.

Return values

true	if global vertex indices are stored.
false	otherwise.

Definition at line 445 of file convex_cell.h.

◆ init_with_box()

void VBW::ConvexCell::init_with_box	(	double	xmin,
		double	ymin,
		double	zmin,
		double	xmax,
		double	ymax,
		double	zmax
	)

Initializes this ConvexCell to an axis-aligned box.

Previous contents of this ConvexCell are discarded. Vertex 0 is vertex at infinity.

Parameters

[in] xmin,ymin,zmin,xmax,ymax,zmax the coordinates of the box.

◆ init_with_tet() [1/2]

void VBW::ConvexCell::init_with_tet	(	vec4	P0,
		vec4	P1,
		vec4	P2,
		vec4	P3
	)

Initializes this ConvexCell to a tetrahedron.

Previous contents of this ConvexCell are discarded. Vertex 0 is vertex at infinity.

Parameters

[in] P0,P1,P2,P3 the plane equations of the four faces of the tetrahedron.

◆ init_with_tet() [2/2]

void VBW::ConvexCell::init_with_tet	(	vec4	P0,
		vec4	P1,
		vec4	P2,
		vec4	P3,
		global_index_t	P0_global_index,
		global_index_t	P1_global_index,
		global_index_t	P2_global_index,
		global_index_t	P3_global_index
	)

Initializes this ConvexCell to a tetrahedron.

Previous contents of this ConvexCell are discarded. Vertex 0 is vertex at infinity.

Parameters

[in]	P0,P1,P2,P3	the plane equations of the four faces of the tetrahedron.
[in]	P0_global_index,P1_global_index,P1_global_index,P2_global_index	the global indices associated with the plane equations.

Precondition: has_vglobal()

◆ kill_vertex()

void VBW::ConvexCell::kill_vertex ( index_t v )

Replaces a vertex with the vertex at infinity in all facets.

Parameters

[in] v the vertex to be killed.

◆ max_t()

index_t VBW::ConvexCell::max_t ( ) const

inline

Gets the maximum valid index for a triangle.

Returns: the maximum valid index of a triangle.

Definition at line 1253 of file convex_cell.h.

◆ max_v()

index_t VBW::ConvexCell::max_v ( ) const

inline

Gets the maximum valid index for a vertex.

Returns: the maximum valid index of a vertex.

Definition at line 1261 of file convex_cell.h.

◆ nb_t()

index_t VBW::ConvexCell::nb_t ( ) const

inline

Gets the number of triangles.

Returns: the number of created triangles.

The created triangles are not necessarily valid ones. To get the valid triangles, one needs to traverse the list from first_valid_.

Definition at line 657 of file convex_cell.h.

◆ nb_v()

index_t VBW::ConvexCell::nb_v ( ) const

inline

Gets the number of vertices.

Returns: the number of vertices.

Some vertices can be incident to no triangle. The first six vertices correspond to the facets of the initial axis aligned box passed to the constructor.

Definition at line 668 of file convex_cell.h.

◆ new_triangle() [1/2]

index_t VBW::ConvexCell::new_triangle	(	index_t	i,
		index_t	j,
		index_t	k
	)

inline

Creates a new triangle.

Parameters

[in] i,j,k the three vertices of the triangle.

Definition at line 1143 of file convex_cell.h.

◆ new_triangle() [2/2]

index_t VBW::ConvexCell::new_triangle	(	index_t	i,
		index_t	j,
		index_t	k,
		index_t	adj0,
		index_t	adj1,
		index_t	adj2
	)

inline

Creates a new triangle.

Adjacency information is not used (kept for reference).

Parameters

[in]	i,j,k	the three vertices of the triangle.
[in]	adj0,adj1,adj2	the three adjacent triangles (unused in this version).

Returns: the index of the new triangle.

Definition at line 1175 of file convex_cell.h.

◆ next_triangle()

ushort VBW::ConvexCell::next_triangle ( ushort t ) const

inline

Gets the successor of a triangle.

Parameters

[in] t the index of a valid triangle.

Returns: the index of the successor of t, or END_OF_LIST if t is the last triangle.

Definition at line 876 of file convex_cell.h.

◆ save() [1/2]

void VBW::ConvexCell::save	(	const std::string &	filename,
		double	shrink = `0.0`
	)		const

Saves the computed cell in alias wavefront file format.

Parameters

[in]	filename	the name of the file where to save the cell.
[in]	shrink	shrinking factor to ease visualization.

◆ save() [2/2]

index_t VBW::ConvexCell::save	(	std::ostream &	out,
		global_index_t	v_offset = `1`,
		double	shrink = `0.0`,
		bool	borders_only = `false`
	)		const

Saves the computed cell in alias wavefront file format.

Parameters

[out]	out	a stream where to save the output.
[in]	v_offset	offset applied to vertex indices.
[in]	shrink	shrinking factor to ease visualization.
[in]	borders_only	if set, only facets that correspond to vertex global index -1 are saved.

Returns: the number of created vertices.

◆ set_triangle_adjacent()

void VBW::ConvexCell::set_triangle_adjacent	(	index_t	t1,
		index_t	le,
		index_t	t2
	)

inline

Sets triangle to triangle adjacency.

Parameters

[in]	t1	a triangle.
[in]	le	local index of an edge of `t` (in 0..2).
[in]	t2	triangle to be made adjacent to `t1` along edge `le`.

Definition at line 1019 of file convex_cell.h.

◆ set_triangle_flags()

void VBW::ConvexCell::set_triangle_flags	(	index_t	t,
		ushort	flags
	)

inline

Sets the flags of a triangle.

Parameters

[in]	t	the triangle.
[in]	flags	the flags to be set.

Definition at line 1224 of file convex_cell.h.

◆ set_v_global_index()

void VBW::ConvexCell::set_v_global_index	(	index_t	lv,
		global_index_t	v
	)

inline

Sets the global vertex index associated with a local vertex index.

Vertex indices correspond to planes (remember, we are in dual form).

Parameters

[in]	lv	the local vertex index
[in]	v	the global vertex index that corresponds to lv.

Definition at line 845 of file convex_cell.h.

◆ set_vertex_plane()

void VBW::ConvexCell::set_vertex_plane	(	index_t	v,
		vec4	P
	)

inlineprotected

Changes a vertex plane equation.

Parameters

[in]	v	the vertex.
[in]	P	the plane equation.

Does not update combinatorics.

Note: Use with care, for experts only.

Definition at line 1343 of file convex_cell.h.

◆ squared_inner_radius()

double VBW::ConvexCell::squared_inner_radius ( vec3 center ) const

Computes the squared radius of the largest sphere contained in the cell and centered on a point.

Returns: the minimum squared distance between center and all facets of the cell.

◆ squared_radius()

double VBW::ConvexCell::squared_radius ( vec3 center ) const

Computes the squared radius of the smallest sphere containing the cell and centered on a point.

Returns: the maximum squared distance between center and all the vertices of the cell.

◆ stored_triangle_point()

vec3& VBW::ConvexCell::stored_triangle_point ( ushort t )

inline

Gets a modifiable reference to a triangle point.

Parameters

[in] t the index

Returns: a modifiable reference to the stored point

Definition at line 1311 of file convex_cell.h.

◆ swap()

void VBW::ConvexCell::swap ( ConvexCell & other )

inline

Swaps two ConvexCells.

Parameters

[in] other the ConvexCell to be exchanged with this ConvexCell.

Definition at line 1283 of file convex_cell.h.

◆ triangle_adjacent()

index_t VBW::ConvexCell::triangle_adjacent	(	index_t	t,
		index_t	le
	)		const

inline

Gets a triangle adjacent to another triangle by edge local index.

Parameters

[in]	t	a triangle.
[in]	le	local index of an edge of `t` (in 0..2).

Returns: the triangle adjacent to t along \ p e.

Definition at line 1006 of file convex_cell.h.

◆ triangle_find_adjacent()

index_t VBW::ConvexCell::triangle_find_adjacent	(	index_t	t1,
		index_t	t2
	)		const

inline

Gets the edge on witch a triangle is adjacent to another one.

Parameters

[in]	t1	a triangle.
[in]	t2	a triangle adjacent to t1

Returns: the edge index e such that triangle_adjacent(t1,e)=t2

Definition at line 1061 of file convex_cell.h.

◆ triangle_find_vertex()

index_t VBW::ConvexCell::triangle_find_vertex	(	index_t	t,
		index_t	v
	)		const

inline

Gets the local index of a vertex in a triangle.

Parameters

[in]	t	a triangle.
[in]	v	a vertex index.

Returns: the local index of v in t (in 0..2).

Definition at line 1047 of file convex_cell.h.

◆ triangle_is_in_conflict()

bool VBW::ConvexCell::triangle_is_in_conflict	(	TriangleWithFlags	T,
		const vec4 &	eqn
	)		const

Tests whether a triangle is in conflict with a plane.

A triangle is in conflict with a plane if feeding the point associated with the triangle in the equation of the plane yields a negative number.

Parameters

[in]	T	a triangle.
[in]	eqn	the four coefficients of the equation of the plane.

Return values

true	if `t` is in conflict with `eqn`.
false	otherwise.

◆ triangle_is_infinite()

bool VBW::ConvexCell::triangle_is_infinite ( index_t t ) const

inline

Tests whether a triangle is infinite.

Parameters

[in] t the triangle

Return values

true	if t is incident to the vertex at infinity.
false	otherwise.

Definition at line 1077 of file convex_cell.h.

◆ triangle_is_marked_as_conflict()

bool VBW::ConvexCell::triangle_is_marked_as_conflict ( index_t t ) const

inline

Tests whether a triangle is marked as conflict.

Parameters

[in] t a triangle.

Return values

true	if `t` is marked as conflict.
false	otherwise.

Definition at line 1120 of file convex_cell.h.

◆ triangle_is_user_marked()

bool VBW::ConvexCell::triangle_is_user_marked ( ushort t )

inline

Tests whether a triangle is marked by the user.

Parameters

[in] t the triangle.

Return values

true	if the triangle is marked.
false	otherwise.

Precondition: triangle flags are stored.

Definition at line 930 of file convex_cell.h.

◆ triangle_point()

vec3 VBW::ConvexCell::triangle_point ( ushort t ) const

inline

Gets the point that corresponds to a triangle.

If compute_geometry() was called, this gets the previously computed point, else it is computed and returned.

Parameters

[in] t the index of the triangle.

Returns: the point that corresponds to triangle t.

Definition at line 888 of file convex_cell.h.

◆ triangle_user_mark()

void VBW::ConvexCell::triangle_user_mark ( ushort t )

inline

Sets the user mark on a triangle.

Parameters

[in] t the triangle.

Precondition: triangle flags are stored.

Definition at line 941 of file convex_cell.h.

◆ triangle_user_unmark()

void VBW::ConvexCell::triangle_user_unmark ( ushort t )

inline

Resets the user mark on a triangle.

Parameters

[in] t the triangle.

Precondition: triangle flags are stored.

Definition at line 952 of file convex_cell.h.

◆ triangle_v_global_index()

global_index_t VBW::ConvexCell::triangle_v_global_index	(	ushort	t,
		index_t	llv
	)		const

inline

Gets the global index of a triangle vertex.

Parameters

[in]	t	the triangle.
[in]	llv	one of 0,1,2.

Returns: the global index of the vertex.

Precondition: global indices are stored.

Definition at line 906 of file convex_cell.h.

◆ triangle_v_local_index()

index_t VBW::ConvexCell::triangle_v_local_index	(	ushort	t,
		index_t	llv
	)		const

inline

Gets the local index of a triangle vertex.

Parameters

[in]	t	the triangle.
[in]	llv	one of 0,1,2.

Returns: the local index of the vertex, in 0..nb_v()-1

Definition at line 918 of file convex_cell.h.

◆ triangle_vertex()

index_t VBW::ConvexCell::triangle_vertex	(	index_t	t,
		index_t	lv
	)		const

inline

Gets a triangle vertex.

Parameters

[in]	t	a triangle.
[in]	lv	local index of a vertex of `t` (in 0..2).

Returns: the vertex

Definition at line 1034 of file convex_cell.h.

◆ triangulate_conflict_zone()

void VBW::ConvexCell::triangulate_conflict_zone	(	index_t	lv,
		index_t	conflict_head,
		index_t	conflict_tail
	)

protected

Triangulates the conflict zone.

Parameters

[in]	lv	the local index of the new vertex
[in]	conflict_head,conflict	tail the first and last triangle of the conflict zone stored as a linked list.

◆ use_exact_predicates()

void VBW::ConvexCell::use_exact_predicates ( bool x )

inline

Specifies whether exact predicates should be used.

Parameters

[in] x true if exact predicates should be used.

Not supported if ConvexCell distributed as standalone file.

Definition at line 435 of file convex_cell.h.

◆ v_global_index()

global_index_t VBW::ConvexCell::v_global_index ( index_t lv ) const

inline

Gets the global vertex index from a local vertex index.

Vertex indices correspond to planes (remember, we are in dual form).

Parameters

[in] lv the local vertex index

Returns: the global vertex index that corresponds to lv.

Definition at line 830 of file convex_cell.h.

◆ vertex_is_contributing()

bool VBW::ConvexCell::vertex_is_contributing ( index_t v ) const

inline

Tests whether a vertex has a corresponding facet in the cell.

Calling compute_geometry() before makes this function faster.

Definition at line 728 of file convex_cell.h.

◆ vertex_plane()

vec4 VBW::ConvexCell::vertex_plane ( index_t v ) const

inline

Gets the equation of a plane associated with a vertex.

The first six equations correspond to the six facets of a cube.

Parameters

[in] v the local index of the vertex.

Definition at line 1093 of file convex_cell.h.

◆ vertex_plane_normal()

vec3 VBW::ConvexCell::vertex_plane_normal ( index_t v ) const

inline

Gets the normal to the plane associated with a vertex.

The first six equations correspond to the six facets of a cube.

Parameters

[in] v the local index of the vertex.

Definition at line 1104 of file convex_cell.h.

◆ vertex_triangle()

index_t VBW::ConvexCell::vertex_triangle ( index_t v ) const

inline

Gets a triangle incident to a vertex.

Parameters

[in] v vertex index.

Returns: a triangle incident to v.

Definition at line 748 of file convex_cell.h.

◆ volume()

double VBW::ConvexCell::volume ( ) const

Computes the volume of this convex cell.

compute_geometry() needs to be called before.

Returns: the volume.

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

geogram/voronoi/convex_cell.h

Public Member Functions

Protected Member Functions

Friends

Detailed Description

Constructor & Destructor Documentation

◆ ConvexCell()

Member Function Documentation

◆ append_to_mesh()

◆ barycenter()

◆ cell_has_conflict()

◆ cell_is_totally_in_conflict()

◆ clear()

◆ clip_by_plane() [1/3]

◆ clip_by_plane() [2/3]

◆ clip_by_plane() [3/3]

◆ clip_by_plane_fast() [1/2]

◆ clip_by_plane_fast() [2/2]

◆ compute_geometry()

◆ compute_mg()

◆ compute_triangle_point()

◆ connect_triangles()

◆ create_triangle()

◆ create_vertex() [1/2]

◆ create_vertex() [2/2]

◆ empty()

◆ facet_area()

◆ first_triangle()

◆ for_each_Voronoi_vertex()

◆ get_triangle()

◆ get_triangle_and_flags()

◆ get_triangle_flags()

◆ grow_t()

◆ grow_v()

◆ has_tflags()

◆ has_v_global_index()

◆ has_vglobal()

◆ init_with_box()

◆ init_with_tet() [1/2]

◆ init_with_tet() [2/2]

◆ kill_vertex()

◆ max_t()

◆ max_v()

◆ nb_t()

◆ nb_v()

◆ new_triangle() [1/2]

◆ new_triangle() [2/2]

◆ next_triangle()

◆ save() [1/2]

◆ save() [2/2]

◆ set_triangle_adjacent()

◆ set_triangle_flags()

◆ set_v_global_index()

◆ set_vertex_plane()

◆ squared_inner_radius()

◆ squared_radius()

◆ stored_triangle_point()

◆ swap()

◆ triangle_adjacent()

◆ triangle_find_adjacent()

◆ triangle_find_vertex()

◆ triangle_is_in_conflict()

◆ triangle_is_infinite()

◆ triangle_is_marked_as_conflict()

◆ triangle_is_user_marked()

◆ triangle_point()

◆ triangle_user_mark()

◆ triangle_user_unmark()

◆ triangle_v_global_index()

◆ triangle_v_local_index()

◆ triangle_vertex()

◆ triangulate_conflict_zone()

◆ use_exact_predicates()

◆ v_global_index()

◆ vertex_is_contributing()

◆ vertex_plane()

◆ vertex_plane_normal()

◆ vertex_triangle()

◆ volume()