Equal-area locus-based convex polygon decomposition

Finding the Maximum Area Centrosymmetric Polygon in a Convex Polygon

Maximal Area Triangles in a Convex Polygon

In [12], the widely known linear time algorithm for computing the maximum area triangle in a convex polygon was found incorrect, and whether it can still be solved in linear time was proposed as an open problem. We resolved it affirmatively by presenting a new linear time algorithm. Our algorithm is simple and easy to implement, and it computes all the locally maximal triangles. 1998 ACM Subjec...

Equal Area Polygons in Convex Bodies

In this paper, we consider the problem of packing two or more equal area polygons with disjoint interiors into a convex body K in E such that each of them has at most a given number of sides. We show that for a convex quadrilateral K of area 1, there exist n internally disjoint triangles of equal area such that the sum of their areas is at least 4n 4n+1 . We also prove results for other types o...

Finding the Maximum Area Parallelogram 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(n2) time. Achieving this running time requires proving several new structural properties of the MAP, and combining them with a rotating technique of Toussaint [10]. We also discuss applications of our result to th...

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...