Box underapproximation

[schillic]

Inside connected union of boxes

Finding a largest rectangle inside a digital object and rectangularization

Inside convex polytopes

Largest Inscribed Rectangles in Geometric Convex Sets

• Underapproximation of polygon with box #3011: axis-aligned box with largest area inside a 2D polygon
  The method and paper have room for future extensions:
  • non-polytopic constraints (ellipsiodal constraints also work)
  • 1D case (trivial, does not require a solver)
  • alternative optimization objective (here: the area), e.g., the perimeter (requires only a linear program instead)
  • higher dimensions
  • non-axis-aligned rectangles

Inner and outer approximations of polytopes using boxes

On the computation of invariant sets for constrained nonlinear systems: An interval arithmetic approach

Computing the largest orthogonal rectangle in a convex polygon

Inside nonconvex polygons

Finding the Maximum Area Axis-Parallel Rectangle in a Polygon

Finding the Axis Aligned Largest Interior Rectangle in a simple polygon

Approximation and randomized algorithms

Largest inscribed rectangles in convex polygons