Largest unit rectangles inscribed in a convex polygon

Abstract

We consider an optimization problem of inscribing a unit rectangle in a convex polygon. An axis-aligned unit rectangle is an axis-aligned rectangle whose horizontal sides are of length 1. A unit rectangle of orientation B is a copy of an axis-aligned unit rectangle rotated by B in counterclockwise direction. The goal is to find a largest unit rectangle inscribed in a convex polygon over all orientations in [0, pi). This optimization problem belongs to shape analysis, classification, and simplification, and they have applications in various costoptimization problems. (c) 2024 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.