Delaunay triangulationhas beenmuch used in such applicationsas volume rendering, shape representation, terrain modeling and so on. The main disadvantage of Delaunay triangulation is large computation time required to obtain the triangulation on an input points set. This time can be reduced by using more than one processor, and several parallel algorithms for Delaunay triangulation have been pro...

An algorithm for constructing almost regular triangulations (ARTs) for three-dimensional polygonal domains is described. Ideally such triangulations consist entirely of congruent tetrahedra with nearly equal edges. The new feature of this method is that the position of the vertices is adjusted, before any connecting edges are assigned. This leads to grids with very few irregular vertices, i.e. ...

We give an expected-case analysis of Delaunay triangulations. To avoid edge effects we consider a unit-intensity Poisson process in Euclidean d-space, and then limit attention to the portion of the triangulation within a cube of side n1/d. For d equal to two, we calculate the expected maximum edge length, the expected minimum and maximum angles, and the average aspect ratio of a triangle. We al...

Interpolation error estimates in terms of geometric quality measures are established for harmonic coordinates on polytopes in two and three dimensions. First we derive interpolation error estimates over convex polygons that depend on the geometric quality of the triangles in the constrained Delaunay triangulation of the polygon. This characterization is sharp in the sense that families of polyg...

We show that it is possible to route locally and competitively on two bounded-degree plane 6-spanners, one with maximum degree 12 and the other with maximum degree 9. Both spanners are subgraphs of the empty equilateral triangle Delaunay triangulation. First, in a weak routing model where the only information stored at each vertex is its neighbourhood, we show how to find a path between any two...

We study fundamental characteristics for the connectivity of multi-hop D2D networks. Devices are randomly distributed on street systems and are able to communicate with each other whenever their separation is smaller than some connectivity threshold. We model the street systems as PoissonVoronoi or Poisson-Delaunay tessellations with varying street lengths. We interpret the existence of adequat...

Let S be a set of n points in the plane, let E be the complete Euclidean graph whose point-set is S, and let G be the Delaunay triangulation of S. We present a very simple local algorithm that, given G, constructs a subgraph of G of degree at most 11 that is a geometric spanner of G with stretch factor 2.86, and hence a geometric spanner of E with stretch factor < 7. This algorithm gives an O(n...

Datasets producedbydifferent countries or organisations are seldomproperly aligned and contain several discrepancies (eg gaps and overlaps). This problem has been so far almost exclusively tackled by snapping vertices based on a user-defined threshold. However, as we argue in this paper, this leads to invalid geometries, is error-prone, and leaves several discrepancies along the boundaries. We ...

The concept of the categorical gradient field is introduced to encompass spatially continuous fields of probabilities or membership values in a fixed number of categories. Three models for implementing categorical gradient fields are examined: raster grids, epsilon bands and gradient polygons. Of these, the gradient polygon model shows promise but has not been fully specified. A specification o...

An animation manifold encapsulates an animation sequence of surfaces contained within a higher dimensional manifold with one dimension being time. An iso–surface extracted from this structure is a frame of the animation sequence. In this dissertation I make an argument for the use of animation manifolds as a representation of complex animation sequences. In particular animation manifolds can re...