Related papers: Delaunay Edge Flips in Dense Surface Triangulation…
A new O(nlog(n)) algorithm is presented for performing Delaunay triangulation of sets of 2D points. The novel component of the algorithm is a radially propagating \emph{sweep-hull} (sequentially created from the radially sorted set of 2D…
Strata of translation surfaces are covered by the closures of finitely many iso-Delaunay regions: open subspaces parametrizing surfaces whose Delaunay triangulations are combinatorially equivalent. We prove that the iso-Delaunay regions for…
In this short paper, we consider the functional density on sets of uniformly bounded triangulations with fixed sets of vertices. We prove that if a functional attains its minimum on the Delaunay triangulation, for every finite set in the…
We present a new and simple randomized algorithm for constructing the Delaunay triangulation using nearest neighbor graphs for point location. Under suitable assumptions, it runs in linear expected time for points in the plane with…
We investigate a type of distance between triangulations on finite type surfaces where one moves between triangulations by performing simultaneous flips. We consider triangulations up to homeomorphism and our main results are upper bounds…
We consider whether any two triangulations of a polygon or a point set on a non-planar surface with a given metric can be transformed into each other by a sequence of edge flips. The answer is negative in general with some remarkable…
A Frontal-Delaunay refinement algorithm for mesh generation in piecewise smooth domains is described. Built using a restricted Delaunay framework, this new algorithm combines a number of novel features, including: (i) an unweighted,…
An ideal triangulation of a singular flat surface is a geodesic triangulation such that its vertex set is equal to the set of singular points of the surface. Using the fact that each pair of points in a surface has a finite number of…
Dense random sampling and surfacing of shapes encoded via implicit occupancy functions (OFs) are critical elements of many applications. Existing methods largely provide either one or the other of random sampling or mesh surfaces: ray…
Given a finite set of points $P$ sampling an unknown smooth surface $\mathcal{M} \subseteq \mathbb{R}^3$, our goal is to triangulate $\mathcal{M}$ based solely on $P$. Assuming $\mathcal{M}$ is a smooth orientable submanifold of codimension…
Delaunay has shown that the Delaunay complex of a finite set of points $P$ of Euclidean space $\mathbb{R}^m$ triangulates the convex hull of $P$, provided that $P$ satisfies a mild genericity property. Voronoi diagrams and Delaunay…
I present a 3D advancing-front mesh refinement algorithm that generates a constrained Delaunay mesh for any piecewise linear complex (PLC) and extend this algorithm to produce truly Delaunay meshes for any PLC. First, as in my recently…
We investigate algorithms with predictions in computational geometry, specifically focusing on the basic problem of computing 2D Delaunay triangulations. Given a set $P$ of $n$ points in the plane and a triangulation $G$ that serves as a…
A main result in this paper is the proof that proximal Delaunay triangulation regions are convex polygons. In addition, it is proved that every Delaunay triangulation region has a local Leader uniform topology.
We propose an algorithm to create a 3-colorable Delaunay Triangulation. The input of the problem we are trying to solve is a set X of n twodimensional points. The output is a 3-colorable two-dimensional Delaunay triangulation T for X U Y ,…
The Delaunay-Rips filtration is a lighter and faster alternative to the well-known Rips filtration for low-dimensional Euclidean point clouds. Despite these advantages, it has seldom been studied. In this paper, we aim to bridge this gap by…
It is important that a spatial network's construction algorithm reproduces the structural properties of the original physical embedding. Here, we assess the Delaunay triangulation as a spatial network construction algorithm for seven…
We show that $O(n^2)$ exchanging flips suffice to transform any edge-labelled pointed pseudo-triangulation into any other with the same set of labels. By using insertion, deletion and exchanging flips, we can transform any edge-labelled…
In this paper a new connection between the discrete conformal geometry problem of disk pattern construction and the continuous conformal geometry problem of metric uniformization is presented. In a nutshell, we discuss how to construct disk…
We show how a filtration of Delaunay complexes can be used to approximate the persistence diagram of the distance to a point set in $R^d$. Whereas the full Delaunay complex can be used to compute this persistence diagram exactly, it may…