In this paper we describe a method for directly generating triangle strips from unstructured point clouds based on onion peeling triangulation (OPT). It is an iterative reconstruction of the convex hulls of point clouds in the 2D plane, and it uses pairs of subsequent layers to establish triangle strips. We compare the obtained triangulations with the results of Delaunay triangulations in terms...

In this paper we consider the tolerance of a geometric or combinatorial structure associated to a set of points as a measure of how much the set of points can be perturbed while leaving the (topological or combinatorial) structure essentially unchanged. We concentrate on studying the Delaunay triangulation and show that its tolerance can be computed in O(n) time if the triangulation is given as...

The restricted Delaunay triangulation can be conceived as an operator that takes as input a k-manifold (typically smooth) embedded in R and a set of points sampled with sufficient density on that manifold, and produces as output a k-dimensional triangulation of the manifold, the input points serving as its vertices. What happens if we feed that triangulation back into the operator, replacing th...

Shape Delaunay tessellations are a generalization of the classical Delaunay triangulation of a finite set of points in the plane, where the empty circle condition is replaced by emptiness of an arbitrary convex compact shape. We present some new and basic properties of shape Delaunay tessellations, concerning flipping, subgraph structures, and recognition.

This paper focuses on the application of triangulation and rubber-sheeting techniques to the problem of merging two digitized map files. The Census Bureau is currently developing a map merging procedure called conflation. Reproducibility, quality control, and a desire for mathematical consistency in conflation lead to a need for well-defined procedures. The Delaunay triangulation is well-define...

We consider a wireless ad hoc network consisting of n points randomly distributed in a two-dimensional plane. We show that, with high probability, we can locally find a path for any pair of nodes such that the length of the path is no more than a constant factor of the minimum. By assuming each node knows its position, the method decides where to forward the message purely based on the position...

Consider a wireless sensor network consisting of n wireless sensors randomly distributed in a twodimensional plane. In this paper, we show that with high probability we can locally find a path for any pair of sensors such that the length of the path is no more than a constant factor of the minimum. By assuming each sensor knows its position, our new routing method decides where to forward the m...

We consider a wireless ad hoc network consisting of points randomly distributed in a two-dimensional plane. We show that, with high probability, we can locally find a path for any pair of nodes such that the length of the path is no more than a constant factor of the minimum. By assuming each node knows its position, the method decides where to forward the message purely based on the positions ...

Several localized routing protocols guarantee the delivery of the packets when the underlying network topology is a planar graph. Typically, relative neighborhood graph (RNG) or Gabriel graph (GG) is used as such planar structure. However, it is well-known that the spanning ratios of these two graphs are not bounded by any constant (even for uniform randomly distributed points). Bose et al. [11...