We describe an algorithm to construct an intrinsic Delaunay triangulation of a smooth closed submanifold of Euclidean space. Using results established in a companion paper on the stability of Delaunay triangulations on δ-generic point sets, we establish sampling criteria which ensure that the intrinsic Delaunay complex coincides with the restricted Delaunay complex and also with the recently in...

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...

Computing the Delaunay triangulation of n points requires usually a minimum of (n log n) operations, but in some special cases where some additional knowledge is provided, faster algorithms can be designed. Given two sets of points, we prove that, if the Delaunay triangulation of all the points is known, the Delaunay triangulation of each set can be computed in randomized expected linear time.

Aiming at Delaunay triangulation with islets constrains in terrain simulation. A general Delaunay triangulation algorithm for constrained data set with islets is proposed. The algorithm firstly constructs Constrained Delaunay Triangulation with constraint polygons which are inner boundary of islets, then according to topological relations within edge, surface, arc segment, applies bidirectional...

Given a triangulation T of n points in the plane, we are interested in the minimal set of edges in T such that T can be reconstructed from this set (and the vertices of T ) using constrained Delaunay triangulation. We show that this minimal set consists of the non locally Delaunay edges of T , and that its cardinality is less than or equal to n+ i=2 (if i is the number of interior points in T )...

We show that, given a set of randomly distributed wireless nodes with density n, when the transmission range rn of wireless nodes satis£es πr n ≥ 3 log n+c(n) n , the localized Delaunay triangulation (LDel) [1] is the same as the Delaunay triangulation with high probability, where c(n) → ∞ as n goes in£nity. Our experiments show that the delivery rates of existing localized routing protocols ar...

We characterize the conditions under which completing a Delaunay tessellation produces a connguration that is a nondegenerate Delaunay triangulation of an arbitrarily small perturbation of the original sites. One consequence of this result is a simple postpro-cessing step for resolving degeneracies in Delaunay triangulations that does not require symbolic perturbation of the data. We also give ...

A wireless sensor network can be represented by a graph. While the network graph is extremely useful, it often exhibits undesired irregularity. Therefore, special treatment of the graph is required by a variety of network algorithms and protocols. In particular, many geometry-oriented algorithms depend on a type of subgraph called Delaunay triangulation. However, when location information is un...

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 introduce the restricted constrained Delaunay triangulation (restricted CDT). The restricted CDT generalizes the restricted Delaunay triangulation, allowing us to define a triangulation of a surface that includes a set of constraining segments. Under certain sampling conditions, the restricted CDT includes every constrained segment and suggests an algorithm that produces a triangulation of t...