A pseudotriangle is a planar polygon with exactly three convex vertices. Each pair of convex vertices is connected by a reflex chain, which may be just one segment. (Thus, a triangle is a pseudotriangle.) A pseudotriangulation of a set S of n points in the plane is a partition of the convex hull of S into pseudotriangles using S as a vertex set. A minimum pseudotriangulation, or pointed pseudotriangulation, has the fewest possible number of edges for a given set S of points.
See [Str00,KKM+01,O'R02a] for examples, explanation of the term ``pointed,'' and further details.