Beta skeleton computational geometry (2 Ergebnisse)

Taschenbuch. Zustand: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - Please note that the content of this book primarily consists of articlesavailable from Wikipedia or other free sources online. In computationalgeometry and geometric graph theory, a ß-skeleton or beta skeleton is anundirected graph defined from a set of points in the Euclidean plane.Two points p and q are connected by an edge whenever all the angles prqare sharper than a threshold determined from the numerical parameterß.The ß-skeleton of a discrete set S of points in the plane is theundirected graph that connects two points p and q with an edge pqwhenever Rpq contains no points of S. That is, the ß-skeleton is theempty region graph defined by the regions Rpq. When S contains a point rfor which angle prq is greater than ¿, then pq is not an edge of theß-skeleton; the ß-skeleton consists of those pairs pq for which no suchpoint r exists.…

Taschenbuch. Zustand: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - Please note that the content of this book primarily consists of articlesavailable from Wikipedia or other free sources online. In mathematicsand computational geometry, a Delaunay triangulation for a set P ofpoints in the plane is a triangulation DT(P) such that no point in P isinside the circumcircle of any triangle in DT(P). Delaunaytriangulations maximize the minimum angle of all the angles of thetriangles in the triangulation; they tend to avoid skinny triangles. Thetriangulation was invented by Boris Delaunay in 1934. Based onDelaunay's definition, the circumcircle of a triangle formed by threepoints from the original point set is empty if it does not containvertices other than the three that define it. The Delaunay conditionstates that a triangle net is a Delaunay triangulation if all thecircumcircles of all the triangles in the net are empty. This is theoriginal definition for two-dimensional spaces. It is possible to use itin three-dimensional spaces by using a circumscribed sphere in place ofthe circumcircle. For a set of points on the same line there is noDelaunay triangulation.…