A new algorithm, featuring overlapping domain decompositions, for the parallel construction of Delaunay and Voronoi tessellations is developed. Overlapping allows for the seamless stitching of the partial pieces of the global Delaunay tessellations constructed by individual processors. The algorithm is then modified, by the addition of stereographic projections, to handle the parallel construct...

4 We show that Delaunay triangulations and compressed quadtrees are equivalent structures. More precisely, 5 we give two algorithms: the first computes a compressed quadtree for a planar point set, given the Delaunay 6 triangulation; the second finds the Delaunay triangulation, given a compressed quadtree. Both algorithms 7 run in deterministic linear time on a pointer machine. Our work builds ...

The traditional image matching algorithms adopt more complex strategies when dealing with mismatch caused by a lot of noise. In this paper, a simple, intuitive and effective noise processing algorithm is proposed based on Delaunay triangulation in computational geometry. The algorithm extracts feature points using SIFT method, respectively establishes Delaunay triangulation in multi-spectral an...

We propose a new C++ implementation of the well-known incremental algorithm for the construction of Delaunay triangulations in any dimension. Our implementation follows the exact computing paradigm and is fully robust. Extensive comparisons have shown that our implementation outperforms the best currently available codes for convex hulls and Delaunay triangulations, and that it can be used for ...

We develop a theoretical framework for constructing guaranteed quality Delaunay meshes in parallel for general two-dimensional geometries. This paper presents a new approach for constructing graded meshes, i.e., meshes with element size controlled by a user-defined criterion. The sequential Delaunay refinement algorithms are based on inserting points at the circumcenters of triangles of poor qu...

We present an algorithm that takes as input a finite point set in R, and performs a perturbation that guarantees that the Delaunay triangulation of the resulting perturbed point set has quantifiable stability with respect to the metric and the point positions. There is also a guarantee on the quality of the simplices: they cannot be too flat. The algorithm provides an alternative tool to the we...

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 )...

In this paper we discuss a new algorithm that for any input quality constrained Delaunay triangulation with minimum interior angle greater than or equal to 30 , produces a quality nonobtuse boundary and/or interface Delaunay triangulation by the Delaunay insertion of a nite number of boundary and/or interface points. A boundary (interface) obtuse triangle is a triangle that has an obtuse angle ...

SUMMARY A ux-diierence splitting type algorithm is formulated for the steady Euler equations on un-structured grids. The polynomial ux-diierence splitting technique is used. A vertex-centered nite volume method is employed on a triangular mesh. The multigrid method is in defect-correction form. A relaxation procedure with a rst order accurate inner iteration and a second-order correction perfor...