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 sweep-hull (sequentially created from the radially sorted set of 2D points, giving a non-overlapping triangulation), paired with a final triangle flipping step to give the Delaunay triangluation. In empirical tests the algorithm runs ...

When a triangulation of a set of points and edges is required, the constrained Delaunay triangulation is often the preferred choice because of its well-shaped triangles. However, in applications like terrain modeling, it is sometimes necessary to have flexibility to optimize some other aspect of the triangulation, while still having nicely-shaped triangles and including a set of constraints. Hi...

We propose a new C++ implementation of the well-known incremental algorithm for the construction of Delaunay triangulations in any dimension. Our implementation follows the exact computing paradigm and is fully robust. Extensive comparisons have shown that our implementation outperforms the best currently available codes for convex hulls and Delaunay triangulations, and that it can be used for ...

We introduce a parametrized notion of genericity for Delaunay triangulations which, in particular, implies that the Delaunay simplices of δ-generic point sets are thick. Equipped with this notion, we study the stability of Delaunay triangulations under perturbations of the metric and of the vertex positions. We quantify the magnitude of the perturbations under which the Delaunay triangulation r...

Delaunay flip is an elegant, simple tool to convert a triangulation of a point set to its Delaunay triangulation. The technique has been researched extensively for full dimensional triangulations of point sets. However, an important case of triangulations which are not full dimensional is surface triangulations in three dimensions. In this paper we address the question of converting a surface t...

Given a set P of n points in the plane, we show how to compute in O(n logn) time a subgraph of their Delaunay triangulation that has maximum degree 7 and is a strong planar t-spanner of P with t = (1 + √ 2) ∗ δ, where δ is the spanning ratio of the Delaunay triangulation. Furthermore, given a Delaunay triangulation, we show a distributed algorithm that computes the same bounded degree planar sp...

One of most famous theorems in computational geometry is the duality between Voronoi diagram and Delaunay triangulation in Euclidean space. This paper proposes an extension of that theorem to the Voronoi diagram and Delaunay-type triangulation in dually at space. In that space, the Voronoi diagram and the triangulation can be computed e ciently by using potential functions. We also propose high...

I Given a finite point set X ⊂ Rd . Then there exists simplicial a complex called Delaunay triangulation of this point set such that I X is the set of vertices of the triangulation I The union of all its simplices is the convex hull of X . I (Delaunay property): For any given d-simplex Σ ⊂ Ω belonging to the triangulation, the interior of its circumsphere does not contain any vertex xk ∈ X . I ...

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.