Relations To Other Structures
The Delaunay triangulation of a point set and its dual, the Voronoi Diagram, are mathematically related to convex hulls: the Delaunay triangulation of a point set in Rn can be viewed as the projection of a convex hull in Rn+1.
Topologically, the convex hull of an open set is always itself open, and the convex hull of a compact set is always itself compact; however, there exist closed sets that do not have closed convex hulls. For instance, the closed set
has the open upper half-plane as its convex hull.
Read more about this topic: Convex Hull
Famous quotes containing the words relations to, relations and/or structures:
“Actually, the laboring man has not leisure for a true integrity day by day; he cannot afford to sustain the manliest relations to men; his labor would be depreciated in the market.
He has no time to be anything but a machine.”
—Henry David Thoreau (1817–1862)
“She has problems with separation; he has trouble with unity—problems that make themselves felt in our relationships with our children just as they do in our relations with each other. She pulls for connection; he pushes for separateness. She tends to feel shut out; he tends to feel overwhelmed and intruded upon. It’s one of the reasons why she turns so eagerly to children—especially when they’re very young.”
—Lillian Breslow Rubin (20th century)
“The philosopher believes that the value of his philosophy lies in its totality, in its structure: posterity discovers it in the stones with which he built and with which other structures are subsequently built that are frequently better—and so, in the fact that that structure can be demolished and yet still possess value as material.”
—Friedrich Nietzsche (1844–1900)