Θk-graphs are geometric graphs that appear in the context of graph navigation. The shortest-path metric of these graphs is known to approximate the Euclidean complete graph up to a factor depending on the cone number k and the dimension of the space. TD-Delaunay graphs, a.k.a. triangular-distance Delaunay triangulations introduced by Chew, have been shown to be plane 2-spanners of the 2D Euclid...

This review paper gives a detailed account of the development of mesh generation techniques on planar regions, over curved surfaces and within volumes for the past years. Emphasis will be on the generation of the unstructured meshes for purpose of complex industrial applications and adaptive refinement finite element analysis. Over planar domains and on curved surfaces, triangular and quadrilat...

We present two generic software projects that are part of the software library CGAL. The first part describes the design of a geometry kernel for higher-dimensional Euclidean geometry and the interaction with application programs. We describe the software structure, the interface concepts, and their models that are based on coordinate representation, number types, and memory layout. In the high...

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...

Given a set P of n points in the plane, the order-k Delaunay graph is a graph with vertex set P and an edge exists between two points p, q ∈ P when there is a circle through p and q with at most k other points of P in its interior. We provide upper and lower bounds on the number of edges in an order-k Delaunay graph. We study the combinatorial structure of the set of triangulations that can be ...

In this paper, we construct Delaunay type constant mean curvature surfaces along a nondegenerate closed geodesic in 3-dimensional Riemannian manifold.

We present an algorithm for image segmentation with irregular pyramids. Instead of starting with the original pixel grid, we rst apply some adaptive Voronoi tesselation to the image. This provides the advantage that the number of cells in the bottom level of the pyramid is already reduced as compared to the number of pixels of the original image. Furthermore the Voronoi diagram is a powerful to...