Related papers: SurfaceVoronoi: Efficiently Computing Voronoi Diag…

In this work we study the minimization problem for the total distance in a cloud computing network on the sphere. We give a solution to this problem in terms of hyperbolic Voronoi diagrams on the sphere. We present results of computer…

A hybrid map representation, which consists of a modified generalized Voronoi Diagram (GVD)-based topological map and a grid-based metric map, is proposed to facilitate a new frontier-driven exploration strategy. Exploration frontiers are…

This paper overviews work on the use of simple chemical reactions to calculate Voronoi diagrams and undertake other related geometric calculations. This work highlights that this type of specialised chemical processor is a model example of…

Let $P$ be a set of $n$ points and $Q$ a convex $k$-gon in ${\mathbb R}^2$. We analyze in detail the topological (or discrete) changes in the structure of the Voronoi diagram and the Delaunay triangulation of $P$, under the convex distance…

Solving Partially Observable Markov Decision Processes (POMDPs) with continuous actions is challenging, particularly for high-dimensional action spaces. To alleviate this difficulty, we propose a new sampling-based online POMDP solver,…

The anticipated widespread use of unmanned aerial vehicles (UAVs) raises significant safety and security concerns, including trespassing in restricted areas, colliding with other UAVs, and disrupting high-traffic airspaces. To mitigate…

Many methods for modelling spatial processes assume global smoothness properties; such assumptions are often violated in practice. We introduce a method for modelling spatial processes that display heterogeneity or contain discontinuities.…

We propose a weakly-supervised multi-view learning approach to learn category-specific surface mapping without dense annotations. We learn the underlying surface geometry of common categories, such as human faces, cars, and airplanes, given…

This paper presents a new curved layer volume decomposition method for multi-axis support-free printing of freeform solid parts. Given a solid model to be printed that is represented as a tetrahedral mesh, we first establish a geodesic…

In the realm of household robotics, the Zero-Shot Object Navigation (ZSON) task empowers agents to adeptly traverse unfamiliar environments and locate objects from novel categories without prior explicit training. This paper introduces…

Characterizing the spacing of primary dendrite arms in directionally-solidified microstructures is an important step for developing process-structure-property relationships by enabling the quantification of (i) the influence of processing…

Approximating PDEs on surfaces by the diffuse interface approach allows us to use standard numerical tools to solve these problems. This makes it an attractive numerical approach. We extend this approach to vector-valued surface PDEs and…

This work addresses the collaborative multi-robot autonomous online exploration problem, particularly focusing on distributed exploration planning for dynamically balanced exploration area partition and task allocation among a team of…

We consider offsets of a union of convex objects. We aim for a filtration, a sequence of nested cell complexes, that captures the topological evolution of the offsets for increasing radii. We describe methods to compute a filtration based…

The goal of this study is to provide a method for computing the following: Given a network of curves in 3d (satisfying a condition at the intersection points), compute efficiently a smooth surface such that the curves are geodesics on it.…

Improving on the Voronoi cell based techniques of Micciancio and Voulgaris (SIAM J. Comp. 13), and Sommer, Feder and Shalvi (SIAM J. Disc. Math. 09), we give a Las Vegas $\tilde{O}(2^n)$ expected time and space algorithm for CVPP (the…

This paper considers several approximate operators used in a particle method based on a Voronoi diagram. We introduce and study our approximate operators on gradient and Laplace operators. We derive error estimates for these approximate…

For a given set of points $U$ on a sphere $S$, the order $k$ spherical Voronoi diagram $SV_k(U)$ decomposes the surface of $S$ into regions whose points have the same $k$ nearest points of $U$. Hyeon-Suk Na, Chung-Nim Lee, and Otfried…

In this paper, we introduce novel methods for computing middle surfaces between various 3D data sets such as point clouds and/or discrete surfaces. Traditionally the middle surface is obtained by detecting singularities in computed distance…

Neural Surface Reconstruction learns a Signed Distance Field~(SDF) to reconstruct the 3D model from multi-view images. Previous works adopt voxel-based explicit representation to improve efficiency. However, they ignored the gradient…