The perimeter centroid of a convex polygon

The Sum of Distances between Vertices of a Convex Polygon with Unit Perimeter

On implementation of the minimal perimeter triangle enclosing a convex polygon algorithm

A high-level description of an algorithm which computes the minimum perimeter triangle enclosing a convex polygon in linear time exists in the literature. Besides that an implementation of the algorithm is given in the subsequent work. However, that implementation is incomplete and omits certain common cases. This note’s contribution consist of a modern treatment of the algorithm and its conseq...

Exact solution of the staircase and row-convex polygon perimeter and area generating function

An explicit expression is obtained for the perimeter and area generating function G(y, z) = ∑ n>=2 ∑ m>=1 cn,my z, where cn,m is the number of row-convex polygons with area m and perimeter n. A similar expression is obtained for the area-perimeter generating function for staircase polygons. Both expressions contain q-series.

Finding the Maximum Area Centrosymmetric Polygon in a Convex Polygon

An Implementation of a linear time algorithm for computing the minimum perimeter triangle enclosing a convex polygon

In this paper, we discuss an efficient and robust implementation of a linear time algorithm due to [1] for computing the minimum perimeter triangle that circumscribes a convex n-gon. Our implementation is in C++, and utilizes the OpenGL graphics library for visualization and animation. The proposed implementation is efficient in the sense that it complies with the algorithm’s linear time comple...