Related papers: Constructing Two-Dimensional Voronoi Diagrams via …

Voronoi diagrams are highly compact representations that are used in various Graphics applications. In this work, we show how to embed a differentiable version of it -- via a novel deep architecture -- into a generative deep network. By…

We use Lie sphere geometry to describe two large categories of generalized Voronoi diagrams that can be encoded in terms of the Lie quadric, the Lie inner product, and polyhedra. The first class consists of diagrams defined in terms of…

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…

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…

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…

The Voronoi diagram-based dual-front active contour models are known as a powerful and efficient way for addressing the image segmentation and domain partitioning problems. In the basic formulation of the dual-front models, the evolving…

In this article, we investigate vacuum leakage detection problems in composite manufacturing. Our approach uses Voronoi diagrams, a well-known structure in discrete geometry. The Voronoi diagram of the vacuum connection positions partitions…

Voronoi diagrams appear in many areas in science and technology and have numerous applications. They have been the subject of extensive investigation during the last decades. Roughly speaking, they are a certain decomposition of a given…

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…

In this article, we propose a numerical method to solve semi-discrete optimal transport problems for gigantic pointsets (108 points and more). By pushing the limits by several orders of magnitude, it opens the path to new applications in…

Recently, the construction of 2D empirical wavelets based on partitioning the Fourier domain with the watershed transform has been proposed. If such approach can build partitions of completely arbitrary shapes, for some applications, it is…

In stark contrast to the case of images, finding a concise, learnable discrete representation of 3D surfaces remains a challenge. In particular, while polygon meshes are arguably the most common surface representation used in geometry…

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…

Recent work has demonstrated that the interior material layout of a 3D model can be designed to make a fabricated replica satisfy application-specific demands on its physical properties such as resistance to external loads. A widely used…

Given two point sets in the plane, we study the minimization of the bottleneck distance between a point set B and an equally-sized subset of a point set A under translations. We relate this problem to a Voronoi-type diagram and derive…

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…

This article presents an algorithm to compute digital images of Voronoi, Johnson-Mehl or Laguerre diagrams of a set of punctual sites, in a domain of a Euclidean space of any dimension. The principle of the algorithm is, in a first step, to…

In quantum information theory, a geometric approach, known as "quantum information geometry," has been considered as a powerful method. In this thesis, we give a computational geometric interpretation to the geometric structure of a quantum…

Navigating topological transitions in cellular mechanical systems is a significant challenge for existing simulation methods. While abstract models lack predictive capabilities at the cellular level, explicit network representations…

We introduce a novel method for acquiring boundary representations (B-Reps) of 3D CAD models which involves a two-step process: it first applies a spatial partitioning, referred to as the ``split``, followed by a ``fit`` operation to derive…