Finding extremal polygons

Abstract

Given n points in the plane, we present algorithms for finding maximum perimeter or area convex k-gons with vertices k of the given n points. Our algorithms work in linear space and time O(knlgn-I-nlg 2 n).For the special case k : 3 we give O(nlgn) algorithms for these problems. Several related issues are discussed.

Triangles of Extremal Area or Perimeter in a Finite Planar Point Set

“…They use an alternation property that was already discovered in algorithmic studies of the same question: to determine the maximum area (or maximum perimeter) k-gon inscribed in a convex n-gon. This can be done in O(n) time [3], [6], [7]. This algorithmic question was also studied without the convexity assumption (finding the maximum area triangle contained in a simple n-gon), where it becomes much harder [17].…”

“…3). The proof of Theorems 1 and 2 uses a special case of Lemma 2.2 from [3], which captures the geometric content of the problem. For the sake of completeness, we prove this lemma at the end of the section.…”

Scandinavian Thins on Top of Cake: New and Improved Algorithms for Stacking and Packing

“…It appears in various domains ranging from computer graphics to pattern recognition to robotics. The enclosure problem has a rich history of research [18,25,26,29,30,35,36,49,50,54,55,59]. Our rectangular-suitcase problems are extensions of the minimum enclosing rectangle problem.…”

Optimized color gamuts for tiled displays

“…Intersect the chromaticity diagrams of the projectors, and find a large triangle within this intersection. Stone does not specify how this triangle is selected, but efficient algorithms are known for finding large triangles within convex polygons [3,6]. 2.…”