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Planar straight-line graph

In computational geometry and geometric graph theory, a planar straight-line graph (PSLG), also called a straight-line plane graph or plane straight-line graph, is an embedding of a planar graph in the plane such that its edges are mapped into straight-line segments. Fáry's theorem (1948) states that every planar graph has this kind of embedding.

Representations
There exist three well-known data structures for representing PSLGs, these are the Winged-edge data structure, Halfedge, and Quadedge. The winged-edge data structure is the oldest of the three, but manipulating it often requires complicated case distinctions. This is because edge references do not store the edge direction, and the directions of edges around a face need not be consistent. The halfedge data structure stores both orientations of an edge and links them properly, simplifying operations and the storage scheme. The Quadedge data structure stores both the planar subdivision and its dual simultaneously. Its records consist explicitly only of edge records, four for each edge, and in a simplified form it is suitable for storing PSLGs. ==Problems in terms of PSLG==
Problems in terms of PSLG
Point location. For a query point, find which face of the PSLG it belongs to. • Map overlay. Find the overlay of two PSLGs (maps), which is the subdivision of the plane by the two simultaneously embedded PSLGs. In GIS this problem is known as "thematic map overlay". ==See also==
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