In this thesis, we study three problems related to geometric algorithms of reconfigurable
structures. In the first problem, strip folding, we present two universal hinge patterns for a …

We present two universal hinge patterns that enable a strip of material to fold into any
connected surface made up of unit squares on the 3D cube grid—for example, the surface of …

This thesis addressed the three-dimensional Art Gallery Problem (3D-AGP), a version of the
art gallery problem, which aims to determine the number of guards required to cover the …

Abstract 2D-representations of 3D digital objects find versatile applications to computer
vision, robotics, medical imaging, and in discrete geometry. This work presents an algorithm …

The core of this thesis is the wireless localization or internet café problem, a relatively new
problem which evolved within the field of art gallery problems: An internet café wants to …

In the wireless localization problem, given a polygon P⊂ R2, we have to place guards and
fix their angular range such that P can be described using these guards. The guards …

A famous theorem by Cauchy states that the dihedral angles of a convex polyhedron are
determined by the incidence structure and face-polygons alone. In this paper, we prove the …

Let V be a set of n points in R d. We study the question whether there exists an orientation
such that V is the vertex set of a connected rectilinear graph in that orientation. A graph is …

We present two universal hinge patterns that enable a strip of material to fold into any
connected surface made up of unit squares on the 3D cube grid—for example, the surface of …