CGAL 5.0.2 - 2D Arrangements
OverlayTraits Concept Reference

## Definition

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.

Has Models:

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 end-vertices are created, (and the corresponding create_vertex() methods were invoked). In all cases, the edge is represented by a halfedge e directed in lexicographic decreasing order (from right to left). The create_edge() method should attach auxiliary data to the twin halfedge (namely to e->twin()) as well:

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.