Affine Properties of Convex Equal-Area Polygons

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...

Affine invariants of convex polygons

In this correspondence, we prove that the affine invariants, for image registration and object recognition, proposed recently by Yang and Cohen (see ibid., vol.8, no.7, p.934-46, July 1999) are algebraically dependent. We show how to select an independent and complete set of the invariants. The use of this new set leads to a significant reduction of the computing complexity without decreasing t...

Polygons Whose Vertex Triangles Have Equal Area

Convex lattice polygons of fixed area with perimeter-dependent weights.

We study fully convex polygons with a given area, and variable perimeter length on square and hexagonal lattices. We attach a weight tm to a convex polygon of perimeter m and show that the sum of weights of all polygons with a fixed area s varies as s(-theta(conv))eK(t)square root(s) for large s and t less than a critical threshold tc, where K(t) is a t-dependent constant, and theta(conv) is a ...

New Results on Optimal Area Triangulations of Convex Polygons

We consider the problems of finding two optimal triangulations of convex polygon: MaxMin area and MinMax area. These are the triangulations that maximize the area of the smallest area triangle in a triangulation, and respectively minimize the area of the largest area triangle in a triangulation, over all possible triangulations. The problem was originally solved by Klincsek by dynamic programmi...