We introduce the notion of generalized Delaunay triangulation of a planar straight-line graph G = (V, E) in the Euclidean plane and present some characterizations of the triangulation. It is shown that the generalized Delaunay triangulation has the property that the minimum angle of the triangles in the triangulation is maximum among all possible triangulations of the graph. A general algorithm...

We address the problem of generating 2D quality triangle meshes from a set of constraints provided as a planar straight line graph. The algorithm first computes a constrained Delaunay triangulation of the input set of constraints, then interleaves Delaunay refinement and optimization. The refinement stage inserts a subset of the Voronoi vertices and midpoints of constrained edges as Steiner poi...

In this paper we describe a generic C++ adaptor, that adapts a 2-dimensional triangulated Delaunay graph and to the corresponding a Voronoi diagram, represented as a doubly connected edge list (DCEL) data structure. Our adaptor has the ability to automatically eliminate, in a consistent manner, degenerate features of the Voronoi diagram, that are artifacts of the requirement that Delaunay graph...

Anisotropic Delaunay surfaces are surfaces of revolution with constant anisotropic mean curvature. We show how the generating curves of such surfaces can be obtained as the trace of a point held in a fixed position relative to a curve which is rolled without slipping along a line. This generalizes the classical construction for surfaces of revolution with constant mean curvature due to Delaunay...

Comparisons of five data reduction methods associated with dynamic TIN models were conducted. All methods were applied to real world Light Detection and Ranging (LIDAR) topographic data. Data reduction is based on point selection by thresholding in dynamic Delaunay triangulation together with random point selection. The triangulation criteria used include Delaunay and hybrids of Delaunay and da...

This paper establishes a Delaunay triangulation model for detecting text strings in an image. In this method, text regions are represented based on Delaunay triangles that can be extracted easily. A searching mechanism based on the left and right arms of a discrete symmetric axis is developed to locate text in an image. The discrete symmetric axis consists of a group of off-curve-edge adjacent ...

We study a problem about shortest paths in Delaunay triangulations. Given two nodes s, t in the Delaunay triangulation of a point set P , we look for a new point p that can be added, such that the shortest path from s to t, in the Delaunay triangulation of P ∪ {p}, improves as much as possible. We study several properties of the problem, and give efficient algorithms to find such point when the...

We address the problem of generating 2D quality triangle meshes from a set of constraints provided as a planar straight line graph. The algorithm first computes a constrained Delaunay triangulation of the input set of constraints, then interleaves Delaunay refinement and optimization. The refinement stage inserts a subset of the Voronoi vertices and midpoints of constrained edges as Steiner poi...

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 ...

Delaunay simplexes are very helpful instrument for analysis of computer models of atomic, molecular and granular systems. This paper illustrates their application to the current physical problems. The first one is the structure of non-crystalline packing of spheres. Recently it got the advance thanks to application of the Delaunay simplexes with quantitative measures of simplex shape. The secon...