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Voronoi treemaps are used to depict nodes and their hierarchical relationships simultaneously. However, in addition to the hierarchical structure, data attributes, such as co-occurring features or similarities, frequently exist. Examples…
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…
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…
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…
Late-interaction models such as ColBERT offer competitive performance across various retrieval tasks but require storing a dense embedding for each document token, leading to a substantial index storage overhead. Past works address this by…
In this paper, we propose a novel space partitioning strategy for implicit hierarchy visualization such that the new plot not only has a tidy layout similar to the treemap, but also is flexible to data changes similar to the Voronoi…
VORO++ is a software library written in C++ for computing the Voronoi tessellation, a technique in computational geometry that is widely used for analyzing systems of particles. VORO++ was released in 2009 and is based on computing the…
In this work we introduce a differential rendering module which allows neural networks to efficiently process cluttered data. The module is composed of continuous piecewise differentiable functions defined as a sensor array of cells…
Poisson Voronoi tessellations have been used in modeling many types of systems across different sciences, from geography and astronomy to telecommunications. The existing literature on the statistical properties of Poisson Voronoi cells is…
We introduce VoroFields, a hierarchical neural-field framework for approximating generalized Voronoi diagrams of finite geometric site sets in low-dimensional domains under arbitrary evaluable point-to-site distances. Instead of…
We consider problem of constructing purely Voronoi mesh where the union of uncut Voronoi cells approximates the planar computational domain with piecewise-smooth boundary. Smooth boundary fragments are approximated by the Voronoi edges and…
We use a simple fragmentation model to describe the statistical behavior of the Voronoi cell patterns generated by a set of points in 1D and in 2D. In particular, we are interested in the distribution of sizes of these Voronoi cells. Our…
A method based on orthogonal function series interpolation of the square root probability density to analyze higher dimensional scattered data is presented. The method is targeted for the use-case when the model and/or data are available…
We propose a novel meshless method to achieve super resolution from scattered data obtained from sparse, randomly positioned sensors such as the particle tracers of particle tracking velocimetry. The method combines K Nearest Neighbor…
A novel algorithm to detect coherent structures with sparse Lagrangian particle tracking data, using Voronoi tessellation and techniques from spectral graph theory, is tested. Neighbouring tracer particles are naturally identified through…
Poisson point processes provide a versatile framework for modeling the distributions of random points in space. When the space is partitioned into cells, each associated with a single generating point from the Poisson process, there appears…
Polyhedral meshes are increasingly becoming an attractive option with particular advantages over traditional meshes for certain applications. What has been missing is a robust polyhedral meshing algorithm that can handle broad classes of…
In this paper, we address a way to reduce the total computational cost of meshless approximation by reducing the required stencil size through spatially varying computational node regularity. Rather than covering the entire domain with…
We introduce an end-to-end deep learning architecture called the wide-band butterfly network (WideBNet) for approximating the inverse scattering map from wide-band scattering data. This architecture incorporates tools from computational…
We propose a self-improving algorithm for computing Voronoi diagrams under a given convex distance function with constant description complexity. The $n$ input points are drawn from a hidden mixture of product distributions; we are only…