The auxiliary class Polyhedron_incremental_builder_3<HDS> supports the incremental construction of polyhedral surfaces, which is for example convenient when constructing polyhedral surfaces from file formats, such as the Object File Format (OFF) [Phi96], OpenInventor [Wer94] or VRML [BPP95, VRM96]. Polyhedron_incremental_builder_3<HDS> needs access to the internal halfedge data structure of type HDS of the polyhedral surface. It is intended to be used within a modifier, see CGAL::Modifier_base in the Support Library Reference Manual.

The incremental builder might be of broader interest for other uses of the halfedge data structures, but it is specifically bound to the definition of polyhedral surfaces given here. During construction all conditions of polyhedral surfaces are checked and in case of violation an error status is set. A diagnostic message will be issued to cerr if the verbose flag has been set at construction time.

The incremental construction starts with a list of all point coordinates and concludes with a list of all facet polygons. Edges are not explicitly specified. They are derived from the vertex incidence information provided from the facet polygons. The polygons are given as a sequence of vertex indices. The halfedge data structure HDS must support vertices (i.e., Supports_halfedge_vertex CGAL::Tag_true). Vertices and facets can be added in arbitrary order as long as a call to add_vertex_to_facet() refers only to a vertex index that is already known. Some methods return already handles to vertices, facets, and halfedges newly constructed. They can be used to initialize additional fields, however, the incidences in the halfedge-data structure are not stable and are not allowed to be changed.

The incremental builder can work in two modes: RELATIVE_INDEXING (the default), in which a polyhedral surface already contained in the halfedge data structure is ignored and all indices are relative to the newly added surface, or ABSOLUTE_INDEXING, in which all indices are absolute indices including an already existing polyhedral surface. The former mode allows to create easily independent connected components, while the latter mode allows to to continue the construction of an existing surface, the absolute indexing allows to address existing vertices when creating new facets.

#include <CGAL/Polyhedron_incremental_builder_3.h>


halfedge data structure HDS.

point type of the vertex.

size type.

typedef typename HalfedgeDS::Vertex_handle
typedef typename HalfedgeDS::Halfedge_handle
typedef typename HalfedgeDS::Face_handle


two different indexing modes.


Polyhedron_incremental_builder_3<HDS> B ( HDS& hds, bool verbose = false);
stores a reference to the halfedge data structure hds of a polyhedral surface in its internal state. An existing polyhedral surface in hds remains unchanged. The incremental builder appends the new polyhedral surface. If verbose is true, diagnostic messages will be printed to cerr in case of malformed input data.

Surface Creation

To build a polyhedral surface, the following regular expression gives the correct and allowed order and nesting of method calls from this section:

begin_surface (add_vertex | (begin_facet add_vertex_to_facet* end_facet))* end_surface

B.begin_surface ( size_type v,
size_type f,
size_type h = 0,
starts the construction. v is the number of new vertices to expect, f the number of new facets, and h the number of new halfedges. If h is unspecified (== 0) it is estimated using Euler's equation (plus 5% for the so far unknown holes and genus of the object). These values are used to reserve space in the halfedge data structure hds. If the representation supports insertion these values do not restrict the class of constructible polyhedra. If the representation does not support insertion the object must fit into the reserved sizes.
If mode is set to ABSOLUTE_INDEXING the incremental builder uses absolute indexing and the vertices of the old polyhedral surface can be used in new facets (needs preprocessing time linear in the size of the old surface). Otherwise relative indexing is used starting with new indices for the new construction.

Vertex_handle B.add_vertex ( Point_3 p)
adds a new vertex for p and returns its handle.

Facet_handle B.begin_facet () starts a new facet and returns its handle.

void B.add_vertex_to_facet ( size_type i)
adds a vertex with index i to the current facet. The first point added with add_vertex() has the index 0 if mode was set to RELATIVE_INDEXING, otherwise the first vertex in the referenced hds has the index 0.

Halfedge_handle B.end_facet () ends a newly constructed facet. Returns the handle to the halfedge incident to the new facet that points to the vertex added first. The halfedge can be safely used to traverse the halfedge cycle around the new facet.

void B.end_surface () ends the construction.

Additional Operations

template <class InputIterator>
B.add_facet ( InputIterator first,
InputIterator beyond)
is a synonym for begin_facet(), a call to add_facet() for each value in the range [first,beyond), and a call to end_facet(). Returns the return value of end_facet().
Precondition: The value type of InputIterator is std::size_t. All indices must refer to vertices already added.

template <class InputIterator>
B.test_facet ( InputIterator first,
InputIterator beyond)
returns true if a facet described by the vertex indices in the range [first,beyond) can be successfully inserted, e.g., with add_facet(first,beyond).
Precondition: The value type of InputIterator is std::size_t. All indices must refer to vertices already added.

Vertex_handle B.vertex ( std::size_t i)
returns handle for the vertex of index i, or Vertex_handle if there is no i-th vertex.

bool B.error () returns error status of the builder.

void B.rollback () undoes all changes made to the halfedge data structure since the last begin_surface() in relative indexing, and deletes the whole surface in absolute indexing. It needs a new call to begin_surface() to start inserting again.

bool B.check_unconnected_vertices ()
returns true if unconnected vertices are detected. If verbose was set to true (see the constructor above) debug information about the unconnected vertices is printed.

bool B.remove_unconnected_vertices ()
returns true if all unconnected vertices could be removed successfully. This happens either if no unconnected vertices had appeared or if the halfedge data structure supports the removal of individual elements.

See Also

CGAL::Modifier_base in the Support Library Reference Manual.


A modifier class creates a new triangle in the halfedge data structure using the incremental builder.

// file: examples/Polyhedron/polyhedron_prog_incr_builder.C

#include <CGAL/Simple_cartesian.h>
#include <CGAL/Polyhedron_incremental_builder_3.h>
#include <CGAL/Polyhedron_3.h>

// A modifier creating a triangle with the incremental builder.
template <class HDS>
class Build_triangle : public CGAL::Modifier_base<HDS> {
    Build_triangle() {}
    void operator()( HDS& hds) {
        // Postcondition: `hds' is a valid polyhedral surface.
        CGAL::Polyhedron_incremental_builder_3<HDS> B( hds, true);
        B.begin_surface( 3, 1, 6);
        typedef typename HDS::Vertex   Vertex;
        typedef typename Vertex::Point Point;
        B.add_vertex( Point( 0, 0, 0));
        B.add_vertex( Point( 1, 0, 0));
        B.add_vertex( Point( 0, 1, 0));
        B.add_vertex_to_facet( 0);
        B.add_vertex_to_facet( 1);
        B.add_vertex_to_facet( 2);

typedef CGAL::Simple_cartesian<double>     Kernel;
typedef CGAL::Polyhedron_3<Kernel>         Polyhedron;
typedef Polyhedron::HalfedgeDS             HalfedgeDS;

int main() {
    Polyhedron P;
    Build_triangle<HalfedgeDS> triangle;
    P.delegate( triangle);
    CGAL_assertion( P.is_triangle( P.halfedges_begin()));
    return 0;