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

Wayfinding behavior and pedestrian movement pattern research relies on objective spatial configuration representation and analysis, such as space syntax, to quantify and control for the difficulty of wayfinding in multi-level buildings and…

In a containment problem, the goal is to preprocess a set of geometric objects so that, given a geometric query object, we can report all the objects containing the query object. We consider the containment problem where input objects are…

We are interested in the naive problem whether we can move a solid object in a solid box or not. We restrict move to rotation. In the case we can, the centre and the ``direction'' of rotation may be restricted. Simplifying, we consider…

As part of human core knowledge, the representation of objects is the building block of mental representation that supports high-level concepts and symbolic reasoning. While humans develop the ability of perceiving objects situated in 3D…

We discuss the scattering of photons from a three-level emitter in a one-dimensional waveguide, where the transport is governed by the interference of spontaneously emitted and directly transmitted waves. The scattering problem is solved in…

In this paper, we present an innovative technique for the path planning of flying robots in a 3D environment in Rough Mereology terms. The main goal was to construct the algorithm that would generate the mereological potential fields in…

Regions-based theories of space aim -- among others -- to define points in a geometrically appealing way. The most famous definition of this kind is probably due to Whitehead. However, to conclude that the objects defined are points indeed,…

Control architectures are often implemented in a layered fashion, combining independently designed blocks to achieve complex tasks. Providing guarantees for such hierarchical frameworks requires considering the capabilities and limitations…

The class of 2-dimensional non-integrable flat dynamical systems has a rather extensive literature with many deep results, but the methods developed for this type of problems, both the traditional approach via Teichm\"{u}ller geometry and…

Given a set of radii measured from a fixed point, the existence of a convex configuration with respect to the set of distinct radii in the two-dimensional case is proved when radii are distinct or repeated at most four points. However, we…

Most (3D) multi-object tracking methods rely on appearance-based cues for data association. By contrast, we investigate how far we can get by only encoding geometric relationships between objects in 3D space as cues for data-driven data…

Metric search is concerned with the efficient evaluation of queries in metric spaces. In general,a large space of objects is arranged in such a way that, when a further object is presented as a query, those objects most similar to the query…

Most real-world 3D sensors such as LiDARs perform fixed scans of the entire environment, while being decoupled from the recognition system that processes the sensor data. In this work, we propose a method for 3D object recognition using…

We lay out the phenomenological behavior of event-shape observables evaluated by solving optimal transport problems between collider events and reference geometries -- which we name 'manifold distances' -- to provide guidance regarding…

Bisectors are equidistant hypersurfaces between two points and are basic objects in a metric geometry. They play an important part in understanding the action of subgroups of isometries on a metric space. In many metric geometries…

Biological flyers and swimmers navigate in unsteady wake flows using limited sensory abilities and actuation energies. Understanding how vortical structures can be leveraged for energy-efficient navigation in unsteady flows is beneficial in…

Cyclic pursuit frameworks, which are built upon pursuit interactions between neighboring agents in a cycle graph, provide an efficient way to create useful global behaviors in a collective of autonomous robots. Previous work had considered…

A polyhedral friction cone is a set of reaction wrenches that an object can experience whilst in contact with its environment. This polyhedron is a powerful tool to control an object's motion and interaction with the environment. It can be…

In this note we make use of some properties of vector fields on a manifold to give an alternate proof to [3] for the equivalence between connections and parallel transport on vector bundles over manifolds. Out of the proof will emerge a new…

(Abridged) Quantitative three-dimensional (3D) position and velocity estimates obtained by passive radar will assist the Galileo Project in the detection and classification of aerial objects by providing critical measurements of range,…