Related papers: Combinatorics of Beacon-based Routing in Three Dim…

Motivated by results on the mobility of mechanical devices called pentapods, this paper deals with a mathematically freestanding problem, which we call M\"obius Photogrammetry. Unlike traditional photogrammetry, which tries to recover a set…

It is well known that the description of topological and geometric properties of bisectors in normed spaces is a non-trivial subject. In this paper we introduce the concept of bounded representation of bisectors in finite dimensional real…

Let a polyhedral convex set be given by a finite number of linear inequalities and consider the problem to project this set onto a subspace. This problem, called polyhedral projection problem, is shown to be equivalent to multiple objective…

Planes are familiar mathematical objects which lie at the subtle boundary between continuous geometry and discrete combinatorics. A plane is geometrical, certainly, but the ways that two planes can interact break cleanly into discrete sets:…

Rendering articulated objects while controlling their poses is critical to applications such as virtual reality or animation for movies. Manipulating the pose of an object, however, requires the understanding of its underlying structure,…

Bounding volumes are an established concept in computer graphics and vision tasks but have seen little change since their early inception. In this work, we study the use of neural networks as bounding volumes. Our key observation is that…

Dimensional metrology and positioning operations are used in many fields of particle accelerator projects. This lecture gives the basic tools to designers in the field of measure by analysing the spatial layout of measurement systems since…

With the field of rigid-body robotics having matured in the last fifty years, routing, planning, and manipulation of deformable objects have recently emerged as a more untouched research area in many fields ranging from surgical robotics to…

A novel object detection method is presented that handles freely rotated objects of arbitrary sizes, including tiny objects as small as $2\times 2$ pixels. Such tiny objects appear frequently in remotely sensed images, and present a…

We have pioneered the Where-You-Look-Is Where-You-Go approach to controlling mobility platforms by decoding how the user looks at the environment to understand where they want to navigate their mobility device. However, many natural…

The study of the graph diameter of polytopes is a classical open problem in polyhedral geometry and the theory of linear optimization. In this paper we continue the investigation initiated in [4] by introducing a vast hierarchy of…

This paper will extend a known relationship between the circumradius and dihedral angles of a tetrahedron in three-dimensional Euclidean space to three-dimensional affine space over a general field not of characteristic two, using only the…

Atkinson [2] found a sequence of three-dimensional hyperbolic polyhedra whose dihedral angles are $\pi /3$. In this paper, we construct another sequence of such polyhedra. We also determine the volumes of some of these polyhedra.

It is well known that the trajectory of a light beam can curve if the medium in which the beam propagates is inhomogeneous or if the local spacetime is curved. In this paper we present a third possibility and show that a properly-prepared…

There has been significant progress made in the field of autonomous vehicles. Object detection and tracking are the primary tasks for any autonomous vehicle. The task of object detection in autonomous vehicles relies on a variety of sensors…

A completely well-centered tetrahedral mesh is a triangulation of a three dimensional domain in which every tetrahedron and every triangle contains its circumcenter in its interior. Such meshes have applications in scientific computing and…

In ground-view object change detection, the recently emerging mapless navigation has great potential to navigate a robot to objects distantly detected (e.g., books, cups, clothes) and acquire high-resolution object images, to identify their…

Most wireless terrestrial networks are designed based on the assumption that the nodes are deployed on a two-dimensional (2D) plane. However, this 2D assumption is not valid in underwater, atmospheric, or space communications. In fact,…

Optical resonators are structures that utilize wave interference and feedback to confine light in all three dimensions. Depending on the feedback mechanism, resonators can support either standing- or traveling-wave modes. Over the years,…

We consider a discrete random walk on a diagonal lattice in two and three dimensions and obtain explicit solutions of absorption probabilities and probabilities of return in several domains. In three dimensions we consider both the cube and…