Geometric graphs: Delaunay triangulation, Beta skeleton, Periodic graph, Euclidean minimum spanning tree, Steiner tree problem, Circle graph  (English, Paperback, LLC Books, Source Wikipedia)

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 24. Chapters: Delaunay triangulation, Beta skeleton, Periodic graph, Euclidean minimum spanning tree, Steiner tree problem, Circle graph, Interval graph, Unit distance graph, Relative neighborhood graph, Unit disk graph, Circular-arc graph, Nearest neighbor graph, Pitteway triangulation, Rectilinear Steiner tree, Visibility graph, Permutation graph, Matchstick graph, Geometric spanner, Levi graph, Polyhedral graph, Erd s-Diophantine graph, Minimum-weight triangulation, Laman graph, Urquhart graph, Planar straight-line graph, Gabriel graph, Rectilinear minimum spanning tree, Hanan grid, Constrained Delaunay triangulation. Excerpt: In mathematics and computational geometry, a Delaunay triangulation for a set P of points in the plane is a triangulation DT(P) such that no point in P is inside the circumcircle of any triangle in DT(P). Delaunay triangulations maximize the minimum angle of all the angles of the triangles in the triangulation; they tend to avoid skinny triangles. The triangulation was invented by Boris Delaunay in 1934. For a set of points on the same line there is no Delaunay triangulation (the notion of triangulation is degenerate for this case). For four or more points on the same circle (e.g., the vertices of a rectangle) the Delaunay triangulation is not unique: each of the two possible triangulations that split the quadrangle into two triangles satisfies the Delaunay condition, i.e., the requirement that the circumcircles of all triangles have empty interiors. By considering circumscribed spheres, the notion of Delaunay triangulation extends to three and higher dimensions. Generalizations are possible to metrics other than Euclidean. However in these cases a Delaunay triangulation is not guaranteed to exist or be unique. The Delaunay triangulation of a discrete point set P in general position corresponds to the ...