# Chapter 44
2D Segment Voronoi Diagrams

Menelaos Karavelas

### Definition

CGAL provides the class CGAL::Segment_Voronoi_diagram_2<Gt,DS> for computing the 2D Voronoi diagram of segments and points. The two template parameters must be models of the SegmentVoronoiDiagramTraits_2 and SegmentVoronoiDiagramDataStructure_2 concepts. The first concept is related to the geometric objects and predicates associated with segment Voronoi diagrams, whereas the second concept refers to the data structure used to represent the dual of the segment Voronoi diagram. The classes Segment_Voronoi_diagram_traits_2<K,MTag>, Segment_Voronoi_diagram_traits_without_intersections_2<K,MTag> Segment_Voronoi_diagram_filtered_traits_2<K,MTag> Segment_Voronoi_diagram_filtered_traits_without_intersections_2<K,MTag> are models of the SegmentVoronoiDiagramTraits_2 concept, whereas the class Triangulation_data_structure_2<Vb,Fb> is a model of the SegmentVoronoiDiagramDataStructure_2 concept.

### Concepts

SegmentVoronoiDiagramSite_2
SegmentVoronoiDiagramStorageSite_2
SegmentVoronoiDiagramDataStructure_2
SegmentVoronoiDiagramVertexBase_2
SegmentVoronoiDiagramTraits_2
SegmentVoronoiDiagramHierarchyVertexBase_2

### Classes

CGAL::Segment_Voronoi_diagram_2<Gt,DS>
CGAL::Segment_Voronoi_diagram_site_2<K>
CGAL::Segment_Voronoi_diagram_storage_site_2<Gt>
CGAL::Segment_Voronoi_diagram_vertex_base_2<Gt,SSTag>
CGAL::Segment_Voronoi_diagram_traits_2<K,MTag>
CGAL::Segment_Voronoi_diagram_traits_without_intersections_2<K,MTag>
CGAL::Segment_Voronoi_diagram_filtered_traits_2<CK,CM,EK,EM,FK,FM>
CGAL::Segment_Voronoi_diagram_filtered_traits_without_intersections_2<CK,CM,EK,EM,FK,FM>
CGAL::Segment_Voronoi_diagram_hierarchy_2<Gt,STag,DS>
CGAL::Segment_Voronoi_diagram_hierarchy_vertex_base_2<Vbb>

### Links to the Reference Sections

- Segment_Voronoi_diagram_2<Gt,DS>

- SegmentVoronoiDiagramSite_2

- Segment_Voronoi_diagram_site_2<K>

- SegmentVoronoiDiagramStorageSite_2

- Segment_Voronoi_diagram_storage_site_2<Gt>

- SegmentVoronoiDiagramDataStructure_2

- SegmentVoronoiDiagramVertexBase_2

- Segment_Voronoi_diagram_vertex_base_2<Gt,SSTag>

- SegmentVoronoiDiagramTraits_2

- Segment_Voronoi_diagram_traits_2<K,MTag>

- Segment_Voronoi_diagram_traits_without_intersections_2<K,MTag>

- Segment_Voronoi_diagram_filtered_traits_2<CK,CM,EK,EM,FK,FM>

- Segment_Voronoi_diagram_filtered_traits_without_intersections_2<CK,CM,EK,EM,FK,FM>

- Segment_Voronoi_diagram_hierarchy_2<Gt,STag,DS>

- SegmentVoronoiDiagramHierarchyVertexBase_2

- Segment_Voronoi_diagram_hierarchy_vertex_base_2<Vbb>