Application-layer multicast supports group applications without the need for a network-layer multicast protocol. Here, applications arrange themselves in a logical overlay network and transfer data within the overlay. In this paper, we present an application-layer multicast solution that uses a Delaunay triangulation as an overlay network topology. An advantage of using a Delaunay triangulation...

This paper presents a Delaunay-based region-growing (DBRG) surface reconstruction algorithm that holds the advantages of both Delaunay-based and region-growing approaches. The proposed DBRG algorithm takes a set of unorganized sample points from the boundary surface of a threedimensional object and produces an orientable manifold triangulated model with a correct geometry and topology that is f...

We propose a new algorithm that preprocess a set of n disjoint unit disks to be able to compute the Delaunay triangulation in O(n) expected time. Conversely to previous similar results, our algorithm is actually faster than a direct computation in O(n log n) time. Key-words: Delaunay triangulation, uncertainties, randomization This work is partly supported by ANR grant Triangles (ANR-07-BLAN-03...

Let S be a finite set of points in the Euclidean plane, and let E be the complete graph whose point-set is S. Chew, in 1986, proved a lower bound of π/2 on the stretch factor of the Delaunay triangulation of S (with respect to E), and conjectured that this bound is tight. Dobkin, Friedman, and Supowit, in 1987, showed that the stretch factor of the Delaunay triangulation of S is at most π( √ 5 ...

This paper presents a technique of incorporating anisotropic metric into the Delaunay triangulation algorithm for unstructured mesh generation on 3D parametric surfaces. Both empty circumcircle and inner angles criteria of Delaunay retriangulation can be successfully used with the developed method of coordinate transformation with little adjustments. We investigate the efficiency of mesh genera...

Over 20 years ago, Dillencourt [1] showed that all outerplanar graphs can be realized as Delaunay triangulations of points in convex position. His proof is elementary, constructive and leads to a simple algorithm for obtaining a concrete Delaunay realization. In this note, we provide two new, alternate, also quite elementary proofs.

We introduce the restricted constrained Delaunay triangulation (restricted CDT). The restricted CDT generalizes the restricted Delaunay triangulation, allowing us to define a triangulation of a surface that includes a set of constraining segments. Under certain sampling conditions, the restricted CDT includes every constrained segment and suggests an algorithm that produces a triangulation of t...

The problem of determining whether a polyhedron has a constrained Delaunay tetrahedralization is NP-complete. However, if no five vertices of the polyhedron lie on a common sphere, the problem has a polynomial-time solution. Constrained Delaunay tetrahedralization has the unusual status (for a small-dimensional problem) of being NP-hard only for degenerate inputs.

In this paper, we propose a method for solving the problem triangulation of a domain between convex polyhedrons in ddimensional space using Delaunay triangulation in O(N) time. Novelty of our work is in using a modified Delaunay triangulation algorithm with constraints.

In this paper we determine the stretch factor of the L1-Delaunay and L∞-Delaunay triangulations, and we show that this stretch is √ 4 + 2 √ 2 ≈ 2.61. Between any two points x, y of such triangulations, we construct a path whose length is no more than