Ready, Set, Go! The Voronoi diagram of moving points that start from a line

It is an outstanding open problem of computational geometry to prove a near-quadratic upper bound on the number of combinatorial changes in the Voronoi diagram of points moving at a common constant speed along linear trajectories in the plane. In this note we observe that this quantity is Θ(n²) if the points start their movement from a common line.     

Polygonal extrusion

A sweeping operation called polygonal extrusion is defined to improve the modeling power of CSG-based modeling. It is assumed that a 2D cross-sectional polygon (sweeping polygon) moves in space while its containing plane is kept orthogonal to the tangent direction of the trajectory curve, a planar polygonal chain having no self-intersections. The objective of the paper is to compute the boundary of the swept volume of the sweeping polygon as a set of polygons (or triangles). The most significant challenge to accomplishing this objective is the problem of trimming the swept volume. To solve the trimming problem, 2D-curve offsetting methods are employed. Two algorithms are presented for polygonal extrusion that are based on different offsetting methods, the Voronoi diagram and PWID offset. The proposed algorithms have been implemented and tested with various examples. Published online: 28 January 2003     

A faster divide-and-conquer algorithm for constructing delaunay triangulations

An easily implemented modification to the divide-and-conquer algorithm for computing the Delaunay triangulation ofn sites in the plane is presented. The change reduces its (n logn) expected running time toO(n log logn) for a large class of distributions that includes the uniform distribution in the unit square. Experimental evidence presented demonstrates that the modified algorithm performs very well forn2¹⁶, the range of the experiments. It is conjectured that the average number of edges it creates—a good measure of its efficiency—is no more than twice optimal forn less than seven trillion. The improvement is shown to extend to the computation of the Delaunay triangulation in theL _p metric for 1<p.This research was supported by National Science Foundation Grants DCR-8352081 and DCR-8416190.     

Simulation of polycrystalline aluminum tensile test with crystal plasticity finite element method

The crystal plasticity was implemented in the finite element method（FEM） software ABAQUS through the user subroutine UMAT. By means of discretizing the space at the grain level with the Voronoi diagram method, a polycrystal model was built and used in the FEM analysis. The initial orientation of each grain was generated based on the orientation distribution function（ODF）. The developed model was successfully applied in simulation of polycrystalline aluminium samples deformed by the tensile tests. The theoretical strain--stress relation was in good agreement with the experimental result. The simulation results show that the grain size has significant effect on the deformation behavior. The initial plastic deformation usually occurs at grain boundaries, and multiple slip often results in an enhanced local hardening at grain boundaries.     

An alignment-free fingerprint bio-cryptosystem based on modified Voronoi neighbor structures

Bio-cryptography is an emerging security technology which combines cryptography with biometrics. A good bio-cryptosystem is required to protect the privacy of the relevant biometric data as well as achieving high recognition accuracy. Fingerprints have been widely used in bio-cryptosystem design. However, fingerprint uncertainty caused by distortion and rotation during the image capturing process makes it difficult to achieve a high recognition rate in most bio-cryptographic systems. Moreover, most existing bio-cryptosystems rely on the accurate detection of singular points for fingerprint image pre-alignment, which is very hard to achieve, and the image rotation transformation during the alignment process can cause significant singular point deviation and minutiae changes. In this paper, by taking full advantage of local Voronoi neighbor structures (VNSs), e.g. local structural stability and distortion insensitivity, we propose an alignment-free bio-cryptosystem based on fixed-length bit-string representations extracted from modified VNSs, which are rotation- and translation-invariant and distortion robust. The proposed alignment-free bio-cryptosystem is able to provide strong security while achieving good recognition performance. Experimental results in comparison with most existing alignment-free bio-cryptosystems using the publicly-available databases show the validity of the proposed scheme.     

基于Voronoi图的连续反向最近邻查询

为解决动态环境中移动点的连续反向最近邻查询问题,将连续反向最近邻查询分为单色和双色2种情况进行研究。利用移动点Voronoi图,分别给出单色连续反向最近邻查询算法、双色连续反向最近邻查询算法以及相关定理,对算法正确性和可终止性进行证明,分析算法时间复杂性。按照移动点Voronoi图的拓扑结构是否改变分为2种情况,分析每种情况下候选所在区域的变化,在变化区域内进行Voronoi图的重构,得到对应的解决方法。在多数情况下,该算法只需生成局部移动点的Voronoi图即可找到结果,减小了连续反向最近邻查询的代价。     

动态受限区域内的单纯型连续近邻链查询方法

受限区域内的单纯型连续近邻链查询在空间数据挖掘、数据的相似分析和推理、空间数据库等方面具有重要的作用。为了弥补已有方法的不足,详细研究了动态受限区域内的单纯型连续近邻链查询方法。基于计算几何中的Voronoi图给出了VOR_IN_CRSCNNC算法、VOR_EX_CRSCNNC算法和VOR_DE_CRSCNNC算法。进一步进行了实验比较和分析。理论研究和实验分析表明,所提出的算法在查询过程中减少了数据逐一筛选和判断的冗余计算,在处理空间数据量较大、初始受限区域数据量较多、受限区域形状较为复杂的单纯型连续近邻链查询方面具有较大的优势。     

空间数据库中一种自适应的缓存替换策略

随着近年来空间数据库研究和应用的不断深入,针对空间数据库中数据组织和查询的特征来设计缓存页面替换策略成为一个新的研究问题.Voronoi图是一种重要的空间数据库组织技术,在处理kNN查询时具有非常好的性能.针对Voronoi图组织的空间数据库,首先利用空间局部性提出了一种基于欧氏距离的替换策略,在发生页面失效时选择距离上一次访问页面欧氏距离最远的页面进行替换;进一步,针对不同kNN查询的搜索空间大小差异非常大的特点,在LIRS替换策略基础上提出一种自适应替换策略,通过对HIR页面占缓存比例自动调整来适应不同的查询.综合两者,形成基于欧氏距离的自适应缓存页面替换算法AELIRS.大量实验表明,在缓存大小与搜索空间大范围变动中,AELIRS始终优于其他替换策略.     

2-Covered paths by a set of antennas with minimum power transmission range

In this paper we describe and solve the following geometric optimisation problem: given a set S of n points on the plane (antennas) and two points A and B, find the smallest radial range r∈^ℜ+ (power transmission range of the antennas) so that a path with endpoints A and B exists in which all points are within the range of at least two antennas. The solution to the problem has several applications (e.g., in the planning of safe routes). We present an O(nlogn) time solution, which is based on the second order Voronoi diagram. We also show how to obtain a path with such characteristics.     

Slice coherence in a query-based architecture for 3D heterogeneous printing

We report on 3D printing of artifacts with a structured, inhomogeneous interior. The interior is decomposed into cells defined by a 3D Voronoi diagram and their sites. When printing such objects, most slices the printer deposits are topologically the same and change only locally in the interior. The slicing algorithm capitalizes on this coherence and minimizes print head moves that do not deposit material. This approach has been implemented on a client/server architecture that computes the slices on the geometry side. The slices are printed by fused deposition, and are communicated upon demand.