How Many Triangles Are in a Convex Polygon?

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If the polygons are closed and at least one of them is compact, then there are even two parallel separator lines (with a gap between them). Inscribed triangle property: Of all triangles contained in a convex polygon, there exists a triangle with a maximal area whose vertices are all polygon vertices.

Which is a special case of a polygon triangulation?

Polygon triangulation In computational geometry, polygon triangulation is the decomposition of a polygonal area (simple polygon) P into a set of triangles, i.e., finding a set of triangles with pairwise non-intersecting interiors whose union is P. Triangulations may be viewed as special cases of planar straight-line graphs.

Is it possible to triangulate a convex polygon in linear time?

It is trivial to triangulate any convex polygon in linear time into a fan triangulation, by adding diagonals from one vertex to all other vertices. The total number of ways to triangulate a convex n -gon by non-intersecting diagonals is the ( n −2)nd Catalan number, which equals