Panagiotis Cheilaris, Sandeep Kumar Dey, and Evanthia Papadopoulou

Algorithms and geometric traits for computing the dual of the Voronoi diagram of a set of points and segments under the \(L_{\infty}\) metric.

Introduced in: CGAL 4.7
Depends on: 2D Segment Delaunay Graphs
BibTeX: cgal:cdp-sdglinf2-24b
License: GPL

CGAL provides algorithms for computing the segment Delaunay graph, i.e., the dual of the Voronoi diagram of segments, under the \( L_{\infty}\) metric. The algorithms are implemented in the classes CGAL::Segment_Delaunay_graph_Linf_2<Gt> and CGAL::Segment_Delaunay_graph_Linf_hierarchy_2<Gt>. The template parameter Gt must be a model of the SegmentDelaunayGraphLinfTraits_2 concept, which is related to the geometric objects and predicates associated with computing segment Delaunay graphs, under the \( L_{\infty}\) distance. The classes CGAL::Segment_Delaunay_graph_Linf_traits_2<K,MTag>, CGAL::Segment_Delaunay_graph_Linf_traits_without_intersections_2<K,MTag> CGAL::Segment_Delaunay_graph_Linf_filtered_traits_2<K,MTag> CGAL::Segment_Delaunay_graph_Linf_filtered_traits_without_intersections_2<K,MTag> are models of the SegmentDelaunayGraphLinfTraits_2 concept.

Classified Reference Pages

Concepts

Classes
class	CGAL::Segment_Delaunay_graph_Linf_2< Gt, DS >
	The class `Segment_Delaunay_graph_Linf_2` represents the segment Delaunay graph under the \( L_{\infty} \) metric (which is the dual graph of the 2D segment Voronoi diagram under the \( L_{\infty} \) metric). More...

struct	CGAL::Segment_Delaunay_graph_Linf_filtered_traits_2< CK, CM, EK, EM, FK, FM >
	The class `Segment_Delaunay_graph_Linf_filtered_traits_2` provides a model for the `SegmentDelaunayGraphLinfTraits_2` concept. More...

struct	CGAL::Segment_Delaunay_graph_Linf_filtered_traits_without_intersections_2< CK, CM, EK, EM, FK, FM >
	The class `Segment_Delaunay_graph_Linf_filtered_traits_without_intersections_2` provides a model for the `SegmentDelaunayGraphLinfTraits_2` concept. More...

class	CGAL::Segment_Delaunay_graph_Linf_hierarchy_2< Gt, STag, DS >
	This class is equivalent to the `Segment_Delaunay_graph_hierarchy_2` class, but it uses `Segment_Delaunay_graph_Linf_2<Gt,DS>` at every level of the hierarchy (instead of `Segment_Delaunay_graph_2<Gt,DS>` at each level of `Segment_Delaunay_graph_hierarchy_2`). More...

struct	CGAL::Segment_Delaunay_graph_Linf_traits_2< K, MTag >
	The class `Segment_Delaunay_graph_Linf_traits_2` provides a model for the `SegmentDelaunayGraphLinfTraits_2` concept. More...

struct	CGAL::Segment_Delaunay_graph_Linf_traits_without_intersections_2< K, MTag >
	The class `Segment_Delaunay_graph_Linf_traits_without_intersections_2` provides a model for the `SegmentDelaunayGraphLinfTraits_2` concept. More...