COMPUTING TRIANGULATIONS OF THE CONVEX POLYGON IN PHP/MYSQL ENVIRONMENT

Counting Triangulations of a Convex Polygon

In a 1751 letter to Christian Goldbach (1690–1764), Leonhard Euler (1707–1783) discusses the problem of counting the number of triangulations of a convex polygon. Euler, one of the most prolific mathematicians of all times, and Goldbach, who was a Professor of Mathematics and historian at St. Petersburg and later served as a tutor for Tsar Peter II, carried out extensive correspondence, mostly ...

Algorithms for optimal area triangulations of a convex polygon

Given a convex polygon with n vertices in the plane, we are interested in triangulations of its interior, i.e., maximal sets of nonintersecting diagonals that subdivide the interior of the polygon into triangles. The MaxMin area triangulation is the triangulation of the polygon that maximizes the area of the smallest triangle in the triangulation. Similarly, the MinMax area triangulation is the...

Computing Two Centers of a Convex Polygon

Computing the Center of Area of a Convex Polygon∗

The center of area of a convex planar set is the point for which the minimum area of intersected by any halfplane containing is maximized. We describe a simple randomized linear-time algorithm for computing the center of area of a convex -gon.

Computing the convex hull of a simple polygon

An algorithm for computing the convex hull of a simple polygon is presented. Its correctness and complexity are also shown. Computational geometry Convex hull Simple polygon Algorithm