Related papers: SurfaceVoronoi: Efficiently Computing Voronoi Diag…
Given a countable set of points in a continuous space, Voronoi tessellation is an intuitive way of partitioning the space according to the distance to the individual points. As a powerful approach to obtain structural information, it has a…
In this paper, we develop constructive algorithms for generating quasi-uniform point sets and sequences over arbitrary two-dimensional triangular domains. Our proposed method, called the \emph{Voronoi-guided greedy packing} algorithm,…
The Voronoi diagram is a certain geometric data structure which has numerous applications in various scientific and technological fields. The theory of algorithms for computing 2D Euclidean Voronoi diagrams of point sites is rich and…
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…
Computational technologies for the approximate solution of multidimensional boundary value problems often rely on irregular computational meshes and finite-volume approximations. In this framework, the discrete problem represents the…
Triangle meshes remain the most popular data representation for surface geometry. This ubiquitous representation is essentially a hybrid one that decouples continuous vertex locations from the discrete topological triangulation.…
We present an algorithm to compute the geodesic $L_1$ farthest-point Voronoi diagram of $m$ point sites in the presence of $n$ rectangular obstacles in the plane. It takes $O(nm+n \log n + m\log m)$ construction time using $O(nm)$ space.…
We study algorithms and combinatorial complexity bounds for \emph{stable-matching Voronoi diagrams}, where a set, $S$, of $n$ point sites in the plane determines a stable matching between the points in $\mathbb{R}^2$ and the sites in $S$…
A Voronoi diagram partitions the plane into convex cells, each containing the points closest to a single generator. Given such a tessellation, the inverse Voronoi problem seeks the generator set \( S \) that produced it. Our algorithm…
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 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…
We consider the following variant of the Monge-Kantorovich transportation problem. Let S be a finite set of point sites in d dimensions. A bounded set C in d-dimensional space is to be distributed among the sites p in S such that (i) each p…
This paper presents a new approach to obtaining nearly complete coverage paths (CP) with low overlapping on 3D general surfaces using mesh models. The CP is obtained by segmenting the mesh model into a given number of clusters using…
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…
We present a simple wavefront-like approach for computing multiplicatively weighted Voronoi diagrams of points and straight-line segments in the Euclidean plane. If the input sites may be assumed to be randomly weighted points then the use…
We investigate the problem of image retrieval based on visual queries when the latter comprise arbitrary regions-of-interest (ROI) rather than entire images. Our proposal is a compact image descriptor that combines the state-of-the-art in…
This work concerns adaptive refinement procedures for meshes of polygonal virtual elements. Specifically, refinement procedures previously proposed by the authors for structured meshes are generalized for the challenging case of arbitrary…
We investigate the combinatorial complexity of geodesic Voronoi diagrams on polyhedral terrains using a probabilistic analysis. Aronov etal [ABT08] prove that, if one makes certain realistic input assumptions on the terrain, this complexity…
The area query, to find all elements contained in a specified area from a certain set of spatial objects, is a very important spatial query widely required in various fields. A number of approaches have been proposed to implement this…
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…