We show that the combinatorial complexity of the Euclidean Voronoi diagram of n lines in R3 that have at most c distinct orientations is O(c3n2+ε) for any ε > 0. This result is a step toward proving the long-standing conjecture that the Euclidean Voronoi diagram of lines in three dimensions has near-quadratic complexity. It provides the first natural instance in which this conjecture is shown t...

In this paper we will extend the concept of Voronoi diagrams to parameterized surfuces where distance between two points is defined as infimum over the lengths of surface paths connecting these points. We will present a method to compute Voronoi diagrams on these surfuces.

Voronoi Diagrams Revisited Rolf Klein∗ Elmar Langetepe∗ Zahra Nilforoushan† Abstract Abstract Voronoi diagrams [21] were designed as a unifying concept that should include as many concrete types of diagrams as possible. To ensure that abstract Voronoi diagrams, built from given sets of bisecting curves, are finite graphs, it was required that any two bisecting curves intersect only finitely oft...

We present a method for finding the boundaries between adjacent regions in an image, where “seed” areas have already been identified in the individual regions to be segmented. This method was motivated by the problem of finding the borders of cells in microscopy images, given a labelling of the nuclei in the images. The method finds the Voronoi region of each seed on a manifold with a metric co...

The effect of approximately homogeneous isotropic turbulence on the dynamics an axisymmetric turbulent jet (Re = 10 600 and 5800) in ambient with a negligible mean flow is interpreted from statistics passive scalar field. generated by random array concentrations are measured orthogonal cross sections using planar laser-induced fluorescence. Statistics field compared to those quiescent ambient, ...

Abstract The simulation of complex deformation problems often requires enrichment techniques that introduce local high‐resolution detail on a generally coarse discretization. use cases include spatial or temporal refinement the discretization, composite materials with phenomena occurring at different scales, even codimensional simulation. We present an efficient method for both discretization a...

Voronoi treemaps represent hierarchies as nested polygons. We here show that, contrary to the apparent popular belief, utilization of an algorithm for weighted Voronoi diagrams is not only feasible, but also more efficient than previous low-resolution approximations, even when the latter are implemented on graphics hardware. More precisely, we propose an instantiation of Lloyd’s method for cent...

This paper overviews the whole-body force control framework implemented on the iCub humanoid robot. This framework consists in a hierarchy of two tasks, where the highest priority task is a force control task, and the lowest one a postural task. Forces are regulated to stabilize a desired centroidal dynamics, i.e., a desired linear and angular momentum of the rigid body system. In turn, these f...