Chapter 20
2D Planar Maps

Introduction

Planar maps are embeddings of topological maps into the plane. A planar map subdivides the plane into vertices, edges, and faces. The vertices, edges, and faces of a subdivision are the embeddings of their topological map counterparts into the plane, such that (1) each vertex is embedded as a planar point, (2) each edge is embedded as a bounded $$x-monotone curve, and does not contain vertices in its interior, and (3) each face is a maximal connected region of the plane that does not contain edges and vertices in its interior.

• Planar_map_2<Dcel,Traits>

• PlanarMapPointLocation_2

• Pm_trapezoid_ric_point_location<Planar_map>

• Pm_naive_point_location<Planar_map>

• Pm_walk_along_a_line_point_location<Planar_map>

• PlanarMapDcel_2

• PlanarMapDcelVertex_2

• PlanarMapDcelHalfedge_2

• Pm_dcel<V,H,F>

• PlanarMapTraits_2

• Pm_segment_traits_2<Kernel>

• PlanarMapChangeNotification_2

• File_header

• Pm_file_scanner<Planar_map>

• Pm_file_writer<Planar_map>

• write_pm

• Pm_drawer<Planar_map, Window>

• draw_pm