CGAL 5.5.2  2D Arrangements

A model for the OverlayTraits
should be able to operate on records (namely, vertices, halfedges and faces) of two input DCEL classes, named Dcel_A
and Dcel_B
, and construct the records of an output DCEL class, referred to as Dcel_R
.
Models for the concept are used by the global overlay()
function to maintain the auxiliary data stored with the DCEL records of the resulting overlaid arrangement, based on the contents of the input records.
CGAL::Arr_default_overlay_traits<Arrangement>
CGAL::Arr_face_overlay_traits<Arr1,Arr2,ResArr,OvlFaceData>
overlay
Types  
typedef unspecified_type  Vertex_handle_A 
a constant handle a vertex in Dcel_A .  
typedef unspecified_type  Halfedge_handle_A 
a constant handle to a halfedge in Dcel_A .  
typedef unspecified_type  Face_handle_A 
a constant handle to a face Dcel_A .  
typedef unspecified_type  Vertex_handle_B 
a constant handle to a vertex in Dcel_B .  
typedef unspecified_type  Halfedge_handle_B 
a constant handle to a halfedge in Dcel_B .  
typedef unspecified_type  Face_handle_B 
a constant handle to a face in Dcel_B .  
typedef unspecified_type  Vertex_handle_R 
a handle to a vertex in Dcel_R .  
typedef unspecified_type  Halfedge_handle_R 
a handle to a halfedge in Dcel_R .  
typedef unspecified_type  Face_handle_R 
a handle to a faces in Dcel_R .  
Vertex Creation  
Whenever a vertex in the overlaid arrangement is created, one of the following functions is called in order to attach the appropriate auxiliary data to this vertex:  
void  create_vertex (Vertex_handle_A v1, Vertex_handle_B v2, Vertex_handle_R v) const 
constructs the vertex v induced by the coinciding vertices v1 and v2 .  
void  create_vertex (Vertex_handle_A v1, Halfedge_handle_B e2, Vertex_handle_R v) const 
constructs the vertex v induced by the vertex v1 that lies on the halfedge e2 .  
void  create_vertex (Vertex_handle_A v1, Face_handle_B f2, Vertex_handle_R v) const 
constructs the vertex v induced by the vertex v1 that lies inside the face f2 .  
void  create_vertex (Halfedge_handle_A e1, Vertex_handle_B v2, Vertex_handle_R v) const 
constructs the vertex v induced by the vertex v2 that lies on the halfedge e1 .  
void  create_vertex (Face_handle_A f1, Vertex_handle_B v2, Vertex_handle_R v) const 
constructs the vertex v induced by the vertex v2 that lies inside the face f1 .  
void  create_vertex (Halfedge_handle_A e1, Halfedge_handle_B e2, Vertex_handle_R v) const 
constructs the vertex v induced by the intersection of the halfedges e1 and e2 .  
Edge Creation  
Whenever an edge in the overlaid arrangement is created, one of the following functions is called in order to attach the appropriate auxiliary data to this vertex. Note that an edge is created after both its endvertices are created, (and the corresponding  
void  create_edge (Halfedge_handle_A e1, Halfedge_handle_B e2, Halfedge_handle_R e) const 
constructs the halfedge e induced by an overlap between the halfedges e1 and e2 .  
void  create_edge (Halfedge_handle_A e1, Face_handle_B f2, Halfedge_handle_R e) const 
constructs the halfedge e induced by the halfedge e1 that lies inside the face f2 .  
void  create_edge (Face_handle_A f1, Halfedge_handle_B e2, Halfedge_handle_R e) const 
constructs the halfedge e induced by the halfedge e2 that lies inside the face f1 .  
Face Creation  
The following function is invoked whenever a new face is created. It is guaranteed that all halfedges along the face boundary have already been created an have their auxiliary data fields attached to them:  
void  create_face (Face_handle_A f1, Face_handle_B f2, Face_handle_R f) const 
constructs the face f induced by the an overlap between the faces f1 and f2 .  