Finding the Maximum Area Parallelogram in a Convex Polygon

Finding all Maximal Area Parallelograms in a Convex Polygon

We consider the problem of finding the maximum area parallelogram (MAP) inside a given convex polygon. Our main result is an algorithm for computing the MAP in an n-sided polygon in O(n) time. Achieving this running time requires proving several new structural properties of the MAP. Our algorithm actually computes all the locally maximal area parallelograms (LMAPs). In addition to the algorithm...

Algorithm for finding the largest inscribed rectangle in polygon

In many industrial and non-industrial applications, it is necessary to identify the largest inscribed rectangle in a certain shape. The problem is studied for convex and non-convex polygons. Another criterion is the direction of the rectangle: axis aligned or general. In this paper a heuristic algorithm is presented for finding the largest axis aligned inscribed rectangle in a general polygon. ...

Maximal Parallelograms in Convex Polygons

Given a convex polygon P of n vertices in the plane, we consider the problem of finding the maximum area parallelogram (MAP) inside P. Previously, the best algorithm for this problem runs in time O(n2), and this was achieved by utilizing some nontrivial properties of the MAP. In this paper, we exhibit an algorithm for finding the MAP in time O(n log2 n), greatly improving the previous result. T...

Finding the Maximum Area Centrosymmetric Polygon in a Convex Polygon

Maximum-Area Triangle in a Convex Polygon, Revisited

We revisit the following problem: Given a convex polygon P , find the largest-area inscribed triangle. We show by example that the linear-time algorithm presented in 1979 by Dobkin and Snyder [1] for solving this problem fails. We then proceed to show that with a small adaptation, their approach does lead to a quadratic-time algorithm. We also present a more involved O(n logn) time divide-and-c...