Related papers: Kinetic Geodesic Voronoi Diagrams in a Simple Poly…
The dynamic analysis of structural change in the organization of the sciences requires methodologically the integration of multivariate and time-series analysis. Structural change--e.g., interdisciplinary development--is often an objective…
We investigate higher-order Voronoi diagrams in the city metric. This metric is induced by quickest paths in the L1 metric in the presence of an accelerating transportation network of axis-parallel line segments. For the structural…
We present a simple randomized scheme for triangulating a set $P$ of $n$ points in the plane, and construct a kinetic data structure which maintains the triangulation as the points of $P$ move continuously along piecewise algebraic…
The Voronoi model is a popular tool for studying confluent living tissues. It exhibits an anomalous glassy behavior even at very low temperatures or weak active self-propulsion, and at zero temperature the model exhibits a disordered solid…
Chaotic dynamics can be quite heterogeneous in the sense that in some regions the dynamics are unstable in more directions than in other regions. When trajectories wander between these regions, the dynamics is complicated. We say a chaotic…
Experiments under laboratory conditions were carried out to study the ordering in bidirectional pedestrian streams and its influence on the fundamental diagram (density-speed-flow relation). The Voronoi method is used to resolve the fine…
We describe the implementation of algorithms to construct and maintain three-dimensional dynamic Delaunay triangulations with kinetic vertices using a three-simplex data structure. The code is capable of constructing the geometric dual, the…
Given two point sets in the plane, we study the minimization of the bottleneck distance between a point set B and an equally-sized subset of a point set A under translations. We relate this problem to a Voronoi-type diagram and derive…
We describe a technique for improving the performance of hydrodynamics codes which employ a moving Voronoi mesh. Currently, such codes are susceptible to high-frequency noise produced by rapid adjustments in the grid topology on the…
In four-dimensional symplectic maps complex instability of periodic orbits is possible, which cannot occur in the two-dimensional case. We investigate the transition from stable to complex unstable dynamics of a fixed point under parameter…
Coherent structures are spatially varying regions which disperse minimally over time and organise motion in non-autonomous systems. This work develops and implements algorithms providing multilayered descriptions of time-dependent systems…
We develop a class of new kinetic data structures for collision detection between moving convex polytopes; the performance of these structures is sensitive to the separation of the polytopes during their motion. For two convex polygons in…
The simple cubic lattice defines a set of points at regular distances. The volume of the Voronoi cells around each point may serve as a weight for integration over the entire space. We add interstitial points to this grid according to the…
In this article the dynamics of pedestrian streams in four different scenarios are compared empirically to investigate the influence of boundary conditions on it. The Voronoi method, which allows high resolution and small fluctuations of…
We address the problem of replicating a Voronoi diagram $V(S)$ of a planar point set $S$ by making proximity queries, which are of three possible (in decreasing order of information content): 1. the exact location of the nearest site(s) in…
Networks embedded in space can display all sorts of transitions when their structure is modified. The nature of these transitions (and in some cases crossovers) can differ from the usual appearance of a giant component as observed for the…
The geodesic edge center of a polygon is a point c inside the polygon that minimizes the maximum geodesic distance from c to any edge of the polygon, where geodesic distance is the shortest path distance inside the polygon. We give a…
In this article, I argue that the concept of the standard Voronoi diagram is incorrect for the calculation of dominance area in soccer. The correct region that should replace the polygonal Voronoi region controlled by a player emerges…
We present an explicit and efficient construction of additively weighted Voronoi diagrams on planar graphs. Let $G$ be a planar graph with $n$ vertices and $b$ sites that lie on a constant number of faces. We show how to preprocess $G$ in…
We consider the problem of maintaining the Euclidean Delaunay triangulation $\DT$ of a set $P$ of $n$ moving points in the plane, along algebraic trajectories of constant description complexity. Since the best known upper bound on the…