In the Euclidean plane, a Delaunay triangulation can be characterized by the requirement that the circumcircle of each triangle be empty of vertices of all other triangles. For triangulating a surface S in R3, the Delaunay paradigm has typically been employed in the form of the restricted Delaunay triangulation, where the empty circumcircle property is defined by using the Euclidean metric in R...

Let (X,d) be a metric space, V ⊆ X a finite set, and E ⊆ V × V . We call the graph G(E, V ) a metric graph if each edge (u, v) ∈ E has weight d(u, v). In particular edge (u, u) is in the graph and have distance 0. We call G a proximal navigation graph or PN-graph if for each edge (u, v) ∈ E either u = v or there is a node u1 such that (u, u1) ∈ E and d(u, v) > d(u1, v). In such graph it is poss...

In Euclidean 3-space endowed with a Cartesian reference system, we consider class of surfaces, called Delaunay tori, constructed by bending segments cylinders neck-size $a$ and $n$ lobes along circumferences centered at the origin. Such surfaces are complete compact, have genus one almost constant, say 1, mean curvature, when is large. Considering mappings $H\colon\mathbb{R}^{3}\to\mathbb{R}$ s...

Let P be a set of n points embedded in the plane, and let C be the complete Euclidean graph whose point-set is P. Each edge in C between two points p, q is realized as the line segment [pq], and is assigned a weight equal to the Euclidean distance |pq|. In this paper, we show how to construct inO(n lgn) time a plane spanner of C of maximum degree at most 4 and of stretch factor at most 20. This...

Cédric Delaunay, Tobias Golling, Gilad Perez, and Yotam Soreq LAPTh, Université de Savoie, CNRS, B.P. 110, F-74941 Annecy-le-Vieux, France CERN, Theory Division, CH-1211 Geneva 23, Switzerland Department of Physics, Yale University, New Haven, Connecticut 06520, USA Department of Particle Physics and Astrophysics, Weizmann Institute of Science, Rehovot 76100, Israel (Received 3 December 2013; p...

The Delaunay triangulation is generated from a points set and a structuring element of type disc. In the Delaunay triangulation definition, replacing the disc by a planar-connected region (we call a molecule), which is a union of a fixed number of discs, allows construction of what we name the molecular graphs. In a finite points set, the molecular graphs record the empty regions which are iden...

We propose an unstructured mesh redistribution method without using skewed elements for steady-state problems. The regions around solution features are indicated by a sensor function. The medial axes of the strong feature regions are calculated so that elements can be clustered around the most important solution features efficiently. Two approaches, a discrete surface-based approach using a Del...

We present an automatic algorithm to construct blocking scheme for multiblock structured meshes in 2D multiphase flow problems. Our solution is based on the concepts of medial axis and Delaunay triangulation. We show that the quality of the blocking scheme strongly depends on the quality of Delaunay triangulation. Therefore, well-known techniques and issues like Delaunay refinement and geometri...