Related papers: Convex Hull Formation for Programmable Matter

We present a novel method for predicting binary phase diagrams through the automatic construction of a minimal basis set of representative templates. The core assumption is that any materials space can be divided into a small number of…

The self-assembly of polyhedral shells, each constructed from 60 trapezoidal particles, is simulated using molecular dynamics. The spatial organization of the component particles in this shell is similar to the capsomer proteins forming the…

Mutually repelling particles form spontaneously ordered clusters when forced into confinement. The clusters may adopt similar spatial arrangements even if the underlying particle interactions are contrastingly different. Here we demonstrate…

Users frequently seek to fabricate objects whose outer surfaces consist of regions with different surface attributes, such as color or material. Manufacturing such objects in a single piece is often challenging or even impossible. The…

At the cutting edge of materials science, matter is designed to self-organize into structures that perform a wide range of functions. The past two decades have witnessed major innovations in the versatility of building blocks, ranging from…

We reexamine fundamental problems from computational geometry in the word RAM model, where input coordinates are integers that fit in a machine word. We develop a new algorithm for offline point location, a two-dimensional analog of sorting…

CAT(0) metric spaces and hyperbolic spaces play an important role in combinatorial and geometric group theory. In this paper, we present efficient algorithms for distance problems in CAT(0) planar complexes. First of all, we present an…

A model of a geometric algorithm is introduced and methodology of its operation is presented for the dynamic partitioning of data spaces.

Active matter physics and swarm robotics have provided powerful tools for the study and control of ensembles driven by internal sources. At the macroscale, controlling swarms typically utilizes significant memory, processing power, and…

For a given point set $S$ in a plane, we develop a distributed algorithm to compute the $\alpha-$shape of $S$. $\alpha-$shapes are well known geometric objects which generalize the idea of a convex hull, and provide a good definition for…

In this paper, we study the computation of shortest paths within the \emph{geometric amoebot model}, a commonly used model for programmable matter. Shortest paths are essential for various tasks and therefore have been heavily investigated…

Convex hulls are fundamental geometric tools used in a number of algorithms. This paper presents a fast, simple to implement and robust Smart Convex Hull (S-CH) algorithm for computing the convex hull of a set of points in E3. This…

In this article, we determine the amortized computational complexity of the planar dynamic convex hull problem by querying. We present a data structure that maintains a set of n points in the plane under the insertion and deletion of points…

We present a geometric design rule for size-controlled clustering of self-propelled particles. We show that active particles that tend to rotate under an external force have an intrinsic, signed parameter with units of curvature which we…

Convex hulls are a fundamental geometric tool used in a number of algorithms. As a side-effect of exhaustive tests for an algorithm for which a convex hull computation was the first step, interesting experimental results were found and are…

Convex hull data structures are fundamental in computational geometry. We study insertion-only data structures, supporting various containment and intersection queries. When $P$ is sorted by $x$- or $y$-coordinate, convex hulls can be…

Finding the coordinate-wise maxima and the convex hull of a planar point set are probably the most classic problems in computational geometry. We consider these problems in the self-improving setting. Here, we have $n$ distributions…

We present algorithmic results for the parallel assembly of many micro-scale objects in two and three dimensions from tiny particles, which has been proposed in the context of programmable matter and self-assembly for building high-yield…

Within simulations of molecules deposited on a surface we show that neuroevolutionary learning can design particles and time-dependent protocols to promote self-assembly, without input from physical concepts such as thermal equilibrium or…

We investigate algorithmic control of a large swarm of mobile particles (such as robots, sensors, or building material) that move in a 2D workspace using a global input signal (such as gravity or a magnetic field). We show that a maze of…