The concept SurfaceMeshTriangulation_3 describes the triangulation type used by the surface mesher make_surface_mesh to represent the three dimensional triangulation embedding the surface mesh. Thus, this concept describes the requirements for the triangulation type SurfaceMeshC2T3::Triangulation nested in the model of SurfaceMeshComplex2InTriangulation3 plugged as the template parameter SurfaceMeshC2T3 of make_surface_mesh. It also describes the requirements for the triangulation type plugged in the class Surface_mesh_complex_2_in_triangulation_3<Tr>.
 
The point type. It must be DefaultConstructible, CopyConstructible and
Assignable.

Vertices and cells of the triangulation are manipulated via handles, which support the two dereference operators operator* and operator>.
 
Handle to a data representing a vertex. Vertex_handle must be
a model of Handle and its value type must be model of
TriangulationDataStructure_3::Vertex.
 
 
Handle to a data representing a cell. Cell_handle must be a
model of Handle and its value type must be model of
TriangulationDataStructure_3::Cell.

 
 The edge type.  
 
 The facet type. 
The following iterators allow one to visit all finite vertices, edges and facets of the triangulation.
 
Iterator over finite vertices
 
 
Iterator over finite edges
 
 
Iterator over finite facets
 
 
The geometric traits class. Must be a model of
DelaunayTriangulationTraits_3.

 
default constructor.
 
 
Copy constructor. All vertices and faces are duplicated.


 The triangulation tr is duplicated, and modifying the copy after the duplication does not modify the original. The previous triangulation held by t is deleted. 

 Deletes all finite vertices and all cells of t. 

 Returns the dimension of the affine hull. 

 Returns a const reference to a model of DelaunayTriangulationTraits_3. 


Returns the dual of facet f, which is in dimension 3: either a segment, if the two cells incident to f are finite, or a ray, if one of them is infinite; in dimension 2: a point. 
A point p is said to be in conflict with a cell c in dimension 3 (resp. a facet f in dimension 2) iff t.side_of_sphere(c, p) (resp. t.side_of_circle(f, p)) returns ON_BOUNDED_SIDE. The set of cells (resp. facets in dimension 2) which are in conflict with p is connected, and it forms a hole.
 
 
 
Computes the conflict hole induced by p. The starting cell
(resp. facet) c must be in conflict.
Then this function returns respectively in the output iterators:  cit: the cells (resp. facets) in conflict.  bfit: the facets (resp. edges) on the boundary, that is, the facets (resp. edges) (t, i) where the cell (resp. facet) t is in conflict, but t>neighbor(i) is not.  ifit: the facets (resp. edges) inside the hole, that is, delimiting two cells (resp facets) in conflict. Returns the Triple composed of the resulting output iterators. 
The following iterators allow the user to visit facets, edges and vertices of the triangulation.

 Starts at an arbitrary finite vertex. Then ++ and  will iterate over finite vertices. Returns finite_vertices_end() when t.number_of_vertices() $$=0.  

 Pasttheend iterator  

 Starts at an arbitrary finite edge. Then ++ and  will iterate over finite edges. Returns finite_edges_end() when t.dimension() $$<1.  

 Pasttheend iterator  

 Starts at an arbitrary finite facet. Then ++ and  will iterate over finite facets. Returns finite_facets_end() when t.dimension() $$<2.  

 Pasttheend iterator  
 

 
Copies the Cell_handles of all cells incident to v to the output
iterator cells. If t.dimension() $$<3, then do nothing.
Returns the resulting output iterator.
 
 

 
Copies the Cell_handles of all cells incident to v to the output iterator cells. If t.dimension() $$<3, then do nothing. Returns the resulting output iterator.  

 
Tests whether p is a vertex of t by locating p in the triangulation. If p is found, the associated vertex v is given.  

 
Tests whether (u,v) is an edge of t. If the edge is found,
it gives a cell c having this edge and the indices i
and j of the vertices u and v in c, in this order.
 

 
true, iff vertex v is the infinite vertex.  

 
true, iff c is incident to the infinite vertex.
 

 Returns the same facet viewed from the other adjacent cell.  

 
Return the indexes of the jth vertex of the facet of a cell opposite to vertex i. 

 
If the point query lies inside the convex hull of the points, the cell
that contains the query in its interior is returned. If query lies on a
facet, an edge or on a vertex, one of the cells having query on
its boundary is returned. If the point query lies outside the convex hull of the points, an infinite cell with vertices $${ p, q, r, } is returned such that the tetrahedron $$( p, q, r, query ) is positively oriented (the rest of the triangulation lies on the other side of facet $$( p, q, r )). Note that locate works even in degenerate dimensions: in dimension 2 (resp. 1, 0) the Cell_handle returned is the one that represents the facet (resp. edge, vertex) containing the query point. The optional argument start is used as a starting place for the search.  

 
If query lies inside the affine hull of the points, the $$kface
(finite or infinite) that contains query in its interior is
returned, by means of the cell returned together with lt, which
is set to the locate type of the query (VERTEX, EDGE, FACET, CELL, or OUTSIDE_CONVEX_HULL if the cell is infinite and query
lies strictly in it) and two indices li and lj that
specify the $$kface of the cell containing query. If the $$kface is a cell, li and lj have no meaning; if it is a facet (resp. vertex), li gives the index of the facet (resp. vertex) and lj has no meaning; if it is and edge, li and lj give the indices of its vertices. If the point query lies outside the affine hull of the points, which can happen in case of degenerate dimensions, lt is set to OUTSIDE_AFFINE_HULL, and the cell returned has no meaning. As a particular case, if there is no finite vertex yet in the triangulation, lt is set to OUTSIDE_AFFINE_HULL and locate returns the default constructed handle. The optional argument start is used as a starting place for the search.  
 

 
Creates a new vertex by starring a hole. It takes an iterator range
[cell_begin; cell_end[ of Cell_handles which specifies
a hole: a set of connected cells (resp. facets in dimension 2) which is
starshaped wrt p.
(begin, i) is a facet (resp. an edge) on the boundary of the hole,
that is, begin belongs to the set of cells (resp. facets) previously
described, and begin>neighbor(i) does not. Then this function deletes
all the cells (resp. facets) describing the hole, creates a new vertex
v, and for each facet (resp. edge) on the boundary of the hole, creates
a new cell (resp. facet) with v as vertex. Then v>set_point(p)
is called and v is returned.

Any 3D Delaunay triangulation class of CGAL