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41.
Planar graph navigation is an important problem with significant implications to both point location in geometric data structures and routing in networks. However, whilst a number of algorithms and existence proofs have been proposed, very little analysis is available for the properties of the paths generated and the computational resources required to generate them under a random distribution hypothesis for the input. In this paper we analyse a new deterministic planar navigation algorithm with constant spanning ratio (w.r.t the Euclidean distance) which follows vertex adjacencies in the Delaunay triangulation. We call this strategy cone walk. We prove that given n uniform points in a smooth convex domain of unit area, and for any start point z and query point q; cone walk applied to z and q will access at most sites with complexity with probability tending to 1 as n goes to infinity. We additionally show that in this model, cone walk is ‐memoryless with high probability for any pair of start and query point in the domain, for any positive ξ. We take special care throughout to ensure our bounds are valid even when the query points are arbitrarily close to the border. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 49, 95–136, 2016 相似文献
42.
空间编码与灰度投影相结合实现高效3-D形貌测量的研究 总被引:2,自引:1,他引:1
介绍了一种结合空间编码与灰度投影来实现高效三维形貌测量的方法。用空间编码完成对被测空间的粗略编码,用灰度投影完成精确编码,将它们结合起来得到被测物体表面丰富的编码信息,作为一种基于三角法的三维形貌测量方法,能够在物体表面非常不连续和外部光照造成的背景光强分布不确定的情况下工作良好。同时,与传统的空间编码方法相比,它大大提高了空间编码的效率。实验表明,该方法用5 幅图像取得了与灰度码10幅图像相当的测量结果。 相似文献
43.
44.
Investigating the minimum weight triangulation of a point set with constraint is an important approach for seeking the ultimate solution of the minimum weight triangulation problem. In this paper, we consider the minimum weight triangulation of a sparse point set, and present an O(n
4) algorithm to compute a triangulation of such a set. The property of sparse point set can be converted into a new sufficient condition for finding subgraphs of the minimum weight triangulation. A special point set is exhibited to show that our new subgraph of minimum weight triangulation cannot be found by any currently known methods. 相似文献
45.
Three new ideas for anisotropic adaption of unstructured triangular grids are presented, with particular emphasis on fluid flow computations. © 1997 John Wiley & Sons, Ltd. 相似文献
46.
47.
Jean-Daniel Boissonnat Leonidas J. Guibas Steve Y. Oudot 《Discrete and Computational Geometry》2009,42(1):37-70
It is a well-established fact that the witness complex is closely related to the restricted Delaunay triangulation in low
dimensions. Specifically, it has been proved that the witness complex coincides with the restricted Delaunay triangulation
on curves, and is still a subset of it on surfaces, under mild sampling conditions. In this paper, we prove that these results
do not extend to higher-dimensional manifolds, even under strong sampling conditions such as uniform point density. On the
positive side, we show how the sets of witnesses and landmarks can be enriched, so that the nice relations that exist between
restricted Delaunay triangulation and witness complex hold on higher-dimensional manifolds as well. We derive from our structural
results an algorithm that reconstructs manifolds of any arbitrary dimension or co-dimension at different scales. The algorithm
combines a farthest-point refinement scheme with a vertex pumping strategy. It is very simple conceptually, and it does not
require the input point sample to be sparse. Its running time is bounded by c(d)n
2, where n is the size of the input point cloud, and c(d) is a constant depending solely (yet exponentially) on the dimension d of the ambient space. Although this running time makes our reconstruction algorithm rather theoretical, recent work has shown
that a variant of our approach can be made tractable in arbitrary dimensions, by building upon the results of this paper.
This work was done while S.Y. Oudot was a post-doctoral fellow at Stanford University. His email there is no longer valid. 相似文献
48.
Matching Points with Squares 总被引:1,自引:0,他引:1
Bernardo M. Ábrego Esther M. Arkin Silvia Fernández-Merchant Ferran Hurtado Mikio Kano Joseph S. B. Mitchell Jorge Urrutia 《Discrete and Computational Geometry》2009,41(1):77-95
Given a class
of geometric objects and a point set P, a
-matching of P is a set
of elements of
such that each C
i
contains exactly two elements of P and each element of P lies in at most one C
i
. If all of the elements of P belong to some C
i
, M is called a perfect matching. If, in addition, all of the elements of M are pairwise disjoint, we say that this matching M is strong. In this paper we study the existence and characteristics of
-matchings for point sets in the plane when
is the set of isothetic squares in the plane. A consequence of our results is a proof that the Delaunay triangulations for
the L
∞ metric and the L
1 metric always admit a Hamiltonian path. 相似文献
49.
In this paper, we shall prove that a projective‐planar (resp., toroidal) triangulation G has K6 as a minor if and only if G has no quadrangulation isomorphic to K4 (resp., K5 ) as a subgraph. As an application of the theorems, we can prove that Hadwiger's conjecture is true for projective‐planar and toroidal triangulations. © 2009 Wiley Periodicals, Inc. J Graph Theory 60: 302‐312, 2009 相似文献
50.
Medvedev NN Voloshin VP Luchnikov VA Gavrilova ML 《Journal of computational chemistry》2006,27(14):1676-1692
The paper presents an algorithm for calculating the three-dimensional Voronoi-Delaunay tessellation for an ensemble of spheres of different radii (additively-weighted Voronoi diagram). Data structure and output of the algorithm is oriented toward the exploration of the voids between the spheres. The main geometric construct that we develop is the Voronoi S-network (the network of vertices and edges of the Voronoi regions determined in relation to the surfaces of the spheres). General scheme of the algorithm and the key points of its realization are discussed. The principle of the algorithm is that for each determined site of the network we find its neighbor sites. Thus, starting from a known site of the network, we sequentially find the whole network. The starting site of the network is easily determined based on certain considerations. Geometric properties of ensembles of spheres of different radii are discussed, the conditions of applicability and limitations of the algorithm are indicated. The algorithm is capable of working with a wide variety of physical models, which may be represented as sets of spheres, including computer models of complex molecular systems. Emphasis was placed on the issue of increasing the efficiency of algorithm to work with large models (tens of thousands of atoms). It was demonstrated that the experimental CPU time increases linearly with the number of atoms in the system, O(n). 相似文献