Related papers: Cellular Topology Optimization on Differentiable V…
We introduce a differentiable 3D representation that unifies the ray tracing capabilities of foam-based ray tracing with the efficiency of modern rasterization pipelines. While prior foam representations enable constant-time ray traversal…
Given two sets of training samples, general method is to estimate the density function and classify the test sample according to higher values of estimated densities. Natural way to estimate the density should be histogram tending to…
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…
Voronoi diagrams are essential geometrical structures with numerous applications, particularly astrophysics-driven finite volume methods. While serial algorithms for constructing these entities are well-established, parallel construction…
Computing offsets of curves on parametric surfaces is a fundamental yet challenging operation in computer aided design and manufacturing. Traditional analytical approaches suffer from time-consuming geodesic distance queries and complex…
Given a set of $n$ sites from $\mathbb{R}^d$, each having some positive weight factor, the Multiplicatively Weighted Voronoi Diagram is a subdivision of space that associates each cell to the site whose weighted Euclidean distance is…
Photonic topology optimization is a technique used to find the electric permittivity distribution of a device that optimizes an electromagnetic figure-of-merit. Two common techniques are used: continuous density-based optimizations that…
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…
Spinodoid architected materials have drawn significant attention due to their unique nature in stochasticity, aperiodicity, and bi-continuity. Compared to classic periodic truss-, beam- and plate-based lattice architectures, spinodoids are…
In the current industry, the development of optimized mechanical components able to satisfy the customer requirements evolves quickly. Therefore, companies are asked for efficient solutions to improve their products in terms of stiffness…
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…
We present an analytically explicit study of optimal discrete quantization on spherical geometries equipped with the geodesic metric, focusing on highly symmetric configurations on the unit sphere $\mathbb S^2$. Three discrete uniform…
Mimicking natural tessellation patterns is a fascinating multi-disciplinary problem. Geometric methods aiming at reproducing such partitions on surface meshes are commonly based on the Voronoi model and its variants, and are often faced…
Topological Deep Learning seeks to enhance the predictive performance of neural network models by harnessing topological structures in input data. Topological neural networks operate on spaces such as cell complexes and hypergraphs, that…
Many physical systems can be studied as collections of particles embedded in space, evolving through deterministic evolution equations. Natural questions arise concerning how to characterize these arrangements - are they ordered or…
We study Voronoi diagrams for distance functions that add together two convex functions, each taking as its argument the difference between Cartesian coordinates of two planar points. When the functions do not grow too quickly, then the…
Every real algebraic variety determines a Voronoi decomposition of its ambient Euclidean space. Each Voronoi cell is a convex semialgebraic set in the normal space of the variety at a point. We compute the algebraic boundaries of these…
I present a regression algorithm that provides a continuous, piecewise-smooth function approximating scattered data. It is based on composing and blending linear functions over Voronoi cells, and it scales to high dimensions. The algorithm…
For the analysis of systems consisting of small, regular objects, the methods of mathematical morphology applied to images of these systems are well-suited. One of these methods is the use of Voronoi polygons. It was found that the Voronoi…
In this paper, we present a topology optimization (TO) framework to simultaneously optimize the matrix topology and fiber distribution of functionally graded continuous fiber-reinforced composites (FRC). Current approaches in density-based…