Related papers: Differentiable Voronoi Diagrams for Simulation of …
The computation of Voronoi Diagrams, or their dual Delauney triangulations is difficult in high dimensions. In a recent publication Polianskii and Pokorny propose an iterative randomized algorithm facilitating the approximation of Voronoi…
Calculations on atomistic scale are necessary for understanding of physical phenomena occurring during advanced processing of liquids, slurries, and nano-ceramics composite materials. This paper describes some new ideas for using the…
Differential equations are a ubiquitous tool to study dynamics, ranging from physical systems to complex systems, where a large number of agents interact through a graph with non-trivial topological features. Data-driven approximations of…
Volumetric shape representations have become ubiquitous in multi-view reconstruction tasks. They often build on regular voxel grids as discrete representations of 3D shape functions, such as SDF or radiance fields, either as the full shape…
We propose a new curl-free and thermodynamically compatible finite volume scheme on Voronoi grids to solve compressible heat conducting flows written in first-order hyperbolic form. The approach is based on the definition of compatible…
The Voronoi Diagram is a geometrical structure that is widely used in scientific or technological applications where proximity is a relevant aspect to consider, and it also resembles natural phenomena such as cellular banks, rock formations…
Higher-order Voronoi diagrams and Delaunay mosaics in polygonal metrics have only recently been studied, yet no tools exist for visualizing them. We introduce a tool that fills this gap, providing dynamic interactive software for…
Probing the structure of complex astrophysical objects requires effective three-dimensional (3D) numerical simulation of the relevant radiative transfer (RT) processes. As with any numerical simulation code, the choice of an appropriate…
We present a paralell approach to discrete geometry: the first one introduces Voronoi cell complexes from statistical tessellations in order to know the mean scalar curvature in term of the mean number of edges of a cell. The second one…
Any system of bisectors (in the sense of abstract Voronoi diagrams) defines an arrangement of simple curves in the plane. We define Voronoi-like graphs on such an arrangement, which are graphs whose vertices are locally Voronoi. A vertex…
We present a new particle-merging algorithm for the particle-in-cell method. Based on the concept of the Voronoi diagram, the algorithm partitions the phase space into smaller subsets, which consist of only particles that are in close…
Image-based modeling is essential for understanding cardiovascular hemodynamics and advancing the diagnosis and treatment of cardiovascular diseases. Constructing patient-specific vascular models remains labor-intensive, error-prone, and…
In the field of data-driven 3D shape analysis and generation, the estimation of global topological features from localized representations such as point clouds, voxels, and neural implicit fields is a longstanding challenge. This paper…
Cells exhibit a wide variety of different shapes. This diversity poses a challenge for computational approaches that attempt to shed light on the role cell geometry plays in regulating cell physiology and behavior. The simulation platform…
Molecular dynamics (MD) simulation is essential for various scientific domains but computationally expensive. Learning-based force fields have made significant progress in accelerating ab-initio MD simulation but are not fast enough for…
Unlike other schemes that locally violate the essential stability properties of the analytic parabolic and elliptic problems, Voronoi finite volume methods (FVM) and boundary conforming Delaunay meshes provide good approximation of the…
Designing physical artifacts that serve a purpose - such as tools and other functional structures - is central to engineering as well as everyday human behavior. Though automating design has tremendous promise, general-purpose methods do…
We present a technique designed for parallelizing large rigid body simulations, capable of exploiting multiple CPU cores within a computer and across a network. Our approach can be applied to simulate both unilateral and bilateral…
We present a simple framework to compute hyperbolic Voronoi diagrams of finite point sets as affine diagrams. We prove that bisectors in Klein's non-conformal disk model are hyperplanes that can be interpreted as power bisectors of…
Flocking phase transitions found in models of polar active matter are paradigmatic examples of active phase transitions in soft matter. An interesting specialization of flocking models concerns a ``topological'' vs ``metric'' choice by…