Related papers: SurfaceVoronoi: Efficiently Computing Voronoi Diag…
Available algorithms for the initialization of volume fractions typically utilize exact functions to model fluid interfaces, or they rely on computationally costly intersections between volume meshes. Here, a new algorithm is proposed that…
The Voronoi Density Estimator (VDE) is an established density estimation technique that adapts to the local geometry of data. However, its applicability has been so far limited to problems in two and three dimensions. This is because…
Rapidly-exploring Random Trees (RRTs) are a popular technique for autonomous exploration of mobile robots. However, the random sampling used by RRTs can result in inefficient and inaccurate frontiers extraction, which affects the…
Topology optimization is able to maximally leverage the high DOFs and mechanical potentiality of porous foams but faces three fundamental challenges: conforming to free-form outer shapes, maintaining geometric connectivity between adjacent…
Probabilistic circuits (PCs) enable exact and tractable inference but employ data independent mixture weights that limit their ability to capture local geometry of the data manifold. We propose Voronoi tessellations (VT) as a natural way to…
In this paper, an efficient motion planning approach with grid-based generalized Voronoi diagrams (G$ \mathbf{^2} $VD) is newly proposed for mobile robots. Different from existing approaches, the novelty of this work is twofold: 1) a new…
Computing the Voronoi diagram of mixed geometric objects in $R^3$ is challenging due to the high cost of exact geometric predicates via Cylindrical Algebraic Decomposition (CAD). We propose an efficient exact verification framework that…
We describe the development of a new software tool, called "Pomelo", for the calculation of Set Voronoi diagrams. Voronoi diagrams are a spatial partition of the space around the particles into separate Voronoi cells, e.g. applicable to…
The Hilbert metric is a distance function defined for points lying within a convex body. It generalizes the Cayley-Klein model of hyperbolic geometry to any convex set, and it has numerous applications in the analysis and processing of…
We introduce a geometric multigrid method for solving linear systems arising from variational problems on surfaces in geometry processing, Gravo MG. Our scheme uses point clouds as a reduced representation of the levels of the multigrid…
We reprove three known algorithmic bounds for terminal-clustering problems, using a single framework that leads to simpler proofs. In this genre of problems, the input is a metric space $(X,d)$ (possibly arising from a graph) and a subset…
Angular Voronoi diagram was introduced by Asano et al. as fundamental research for a mesh generation. In an angular Voronoi diagram, the edges are curves of degree three. From view of computational robustness we need to treat the curves…
Deep learning-based multi-view stereo has emerged as a powerful paradigm for reconstructing the complete geometrically-detailed objects from multi-views. Most of the existing approaches only estimate the pixel-wise depth value by minimizing…
Voronoi and related diagrams have technological applications, for example, in motion planning and surface reconstruction, and also find significant use in materials science, molecular biology, and crystallography. Apollonius diagrams…
The use of numerical simulations in science is ever increasing and with it the computational size. In many cases single processors are no longer adequate and simulations are run on multiple core machines or supercomputers. One of the key…
In this paper, we develop a novel method for fast geodesic distance queries. The key idea is to embed the mesh into a high-dimensional space, such that the Euclidean distance in the high-dimensional space can induce the geodesic distance in…
We present an algorithm for boundary approximation in locally-linked sensor networks that communicate with a remote monitoring station. Delaunay triangulations and Voronoi diagrams are used to generate a sensor communication network and…
Given an $n$-vertex 1.5D terrain $\T$ and a set $\A$ of $m<n$ viewpoints, the Voronoi visibility map $\vorvis(\T,\A)$ is a partitioning of $\T$ into regions such that each region is assigned to the closest (in Euclidean distance) visible…
Differentiable rendering is an essential operation in modern vision, allowing inverse graphics approaches to 3D understanding to be utilized in modern machine learning frameworks. Explicit shape representations (voxels, point clouds, or…
Polygonal chains are fundamental objects in many applications like pattern recognition and protein structure alignment. A well-known measure to characterize the similarity of two polygonal chains is the famous Fr\`{e}chet distance. In this…