Plane-Sweep Incremental Algorithm: Computing Delaunay Tessellations of Large Datasets
نویسندگان
چکیده
We present the plane-sweep incremental algorithm, a hybrid approach for computing Delaunay tessellations of large point sets whose size exceeds the computer’s main memory. This approach unites the simplicity of the incremental algorithms with the comparatively low memory requirements of plane-sweep approaches. The procedure is to first sort the point set along the first principal component and then to sequentially insert the points into the tessellation, essentially simulating a sweeping plane. The part of the tessellation that has been passed by the sweeping plane can be evicted from memory and written to disk, limiting the memory requirement of the program to the ”thickness” of the data set along its first principal component. We implemented the algorithm and used it to compute the Delaunay tessellation and Voronoi partition of the Sloan Digital Sky Survey magnitude space consisting of 287 million points. ∗[email protected] 1 ar X iv :1 21 0. 35 95 v1 [ cs .C G ] 1 2 O ct 2 01 2
منابع مشابه
A Comparison of Plane Sweep Delaunay Triangulation Algorithms
This paper presents a survey as well as a new sweep-circle algorithm, on plane sweep algorithms for computing the Delaunay triangulation. The algorithms examined are: Fortune’s sweep-line algorithm, Zalik’s sweep-line algorithm, and a sweep-circle algorithm proposed by Adam, Kauffmann, Schmitt, and Spehner. We test implementations of these algorithms on a number of uniform and none-uniform dist...
متن کاملSweep Line Algorithm for Convex Hull Revisited
Convex hull of some given points is the intersection of all convex sets containing them. It is used as primary structure in many other problems in computational geometry and other areas like image processing, model identification, geographical data systems, and triangular computation of a set of points and so on. Computing the convex hull of a set of point is one of the most fundamental and imp...
متن کاملOn shape Delaunay tessellations
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.
متن کاملParallel algorithms for planar and spherical Delaunay construction with an application to centroidal Voronoi tessellations
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...
متن کاملMeshing the Universe: Identifying Voids in Cosmological Simulations Through In Situ Parallel Voronoi Tessellation
Mesh tessellations are effective constructs for the visualization and analysis of point data, because they transform sparse discrete samples into dense and continuous functions. We present a prototype method for computing a Voronoi tessellation in parallel from large particle datasets; the same method, in principle, is applicable to the Delaunay. Computing large tessellations is computationally...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- CoRR
دوره abs/1210.3595 شماره
صفحات -
تاریخ انتشار 2012