Point Set Triangulation
A triangulation of a set of points P in the plane is a triangulation of the convex hull of P, with all points from P being among the vertices of the triangulation. Triangulations are special cases of planar straight-line graphs.
There are special triangulations like the Delaunay triangulation which is the geometric dual of the Voronoi diagram. Subsets of the Delaunay triangulation are the Gabriel graph, nearest neighbor graph and the minimal spanning tree.
Triangulations have a number of applications, and there is an interest to find a "good" triangulation for a given point set under some criteria. One of them is a minimum-weight triangulation. Sometimes it is desirable to have a triangulation with special properties, e.g., in which all triangles have large angles (long and narrow ("splinter") triangles are avoided).
Given a set of edges that connect some pairs of the points, the problem to determine whether they contain a triangulation is NP-complete (Lloyd, 1977).
Read more about Point Set Triangulation: Triangulation and Convex Hull
Famous quotes containing the words point and/or set:
“The whole point of Camp is to dethrone the serious. Camp is playful, anti-serious. More precisely, Camp involves a new, more complex relation to “the serious.” One can be serious about the frivolous, frivolous about the serious.”
—Susan Sontag (b. 1933)
“This is God’s country—Why set it on fire and make it look like hell?”
—For the State of Maine, U.S. public relief program (1935-1943)