线段加权的Voronoi图

本文将点上加权的Ｖｏｒｏｎｏｉ图推广到线段上加权的Ｖｏｒｏｎｏｉ图，证明了该图的两线段间的Ｖｏｒｏｎｏｉ边是二次曲线，给出了所有情形下两线段间的Ｖｏｒｏｎｏｉ边的具体形状和画法及线段加权的Ｖｏｒｏｎｏｉ图Ｖｎ的画法。     

基于Voronoi图理论的自由边界型腔加工路径规划

Ｖｏｒｏｎｏｉ图是计算几何研究中的一个有力工具。给出了基于Ｖｏｒｏｎｏｉ图和单调区划分的型腔数控加工环切轨迹规划算法,并首次将其应用于边界为自由曲线的型腔,提高了Ｖｏｒｏｎｏｉ图在该领域的应用价值。     

Voronoi图算法及其在混合电路的衬底耦合研究中？…

提出了对版图进行划分的Ｖｏｒｏｎｏｉ图的算法：将Ｖｏｒｏｎｏｉ图进行变换,通过扫描技术,从下到上对每个点与交点进行２,从而形成变换后的Ｖｏｒｏｎｏｉ图,最后将此图转换为Ｖｏｒｏｎｏｉ图。在 计算中,针对集成电路的物理特性,改进了阱区附近的Ｖ图的生成以及多个水平位置点和兼并问题。算法时间复杂度为Ｏ（ｎｌｏｇｎ）空间复杂度为Ｏ（ｎ）。     

Voronoi图算法及其在混合电路的衬底耦合研究中的应用

提出了对版图进行划分的Ｖｏｒｏｎｏｉ图的算法：将Ｖｏｒｏｎｏｉ图进行变换,通过扫描技术,从下到上对每个点与交点进行处理,从而形成变换后的Ｖｏｒｏｎｏｉ图,最后将此图转换为Ｖｏｒｏｎｏｉ图．在计算中,针对集成电路的物理特性,改进了阱区附近的Ｖ图的生成以及多个水平位置点和兼并问题．算法时间复杂度为Ｏ（ｎｌｏｇｎ）,空间复杂度为Ｏ（ｎ）．     

面条目标Voronoi图生成的动态距离变换策略

利用Ｖｅｃｔｏｒ－ｂａｓｅｄ方法生成的矢量Ｖｏｒｏｎｏｉ图用于ＧＩＳ有局限性,那么自然而然就会想到能否在栅格空间中生成栅格Ｖｏｒｏｎｏｉ图,与之对应的生成算法被称作Ｒａｓｔｉｒ－ｂａｓｉｄ方法。本文首先介绍了与Ｒａｓｔｅｒ－ｂａｓｅｄ方法有关的研究工作,在此基础上提出用传统的距离变换建立栅格Ｖｏｒｏｎｏｉ图,而后又指出这种方法建立Ｖｏｕｏｎｏｉ图引起的误差与距离成线性正比关系,为减小误差,作者提出     

基于改进的Voronoi图划分的边界元衬底耦合参数提取技术

提出了一种快速而准确的数模混合集成电路衬底耦合参数提取方法。采用边界元法求解衬底耦合电阻,与有限差分法相比,计算速度提高了一个数量级以上,且可以保持精度,结合改进的Ｖｏｒｏｎｏｉ图来划分版图,生成的衬底ＲＣ网络数目远小于同样采用Ｖｏｒｏｎｏｉ图的文献「４」,而且解决了文献「４」中由于解析公式计算衬底电阻导致精度不高的问题。     

一种基于图的平面点集Delaunay三角剖分算法

本文提出了一种基于图的平面点集Ｄｅｌａｕｎａｙ三角剖分算法。该算法首先求出平面点集的欧几里得最小生成树，然后逐次加入一边构造三角形网格，最后按最小内角最大的三角化准则，通过局部变换，得到平面点集的Ｄｅｌａｕｎａｙ三角剖分。本文同时阐述了它的对偶图；平面点集的Ｖｏｒｏｎｏｉ图的概念和性质。     

基于C~∞基函数的自然邻点插值(NNI)方法在科学计算可视化上的应用

插值方法及插值基函数的选择是可视化技术的一个关键问题。该文首先根据平面域上分布的数据点集,将平面域剖分为 Ｖｏｒｏｎｏｉ ｃｅｌｌｓ进而得到相应的 Ｄｅｌａｕｎａｒ三角化网格。然后基于 Ｖｏｒｏｎｏｉ ｃｅｌｌｓ的几何性质,应用自然邻点插值（ＮＮＩ）方法,介绍了一种具有无穷次连续可微的 Ｃ∞插值基函数及其数学性质。将基于 Ｃ”基函数的 ＮＮＩ方法用于把复杂数据场重构成一个具有规则网格的经验模型。最后再根据规则网格,生成三维立体图、等值线图、矢量分布图等。文章通过实例表明了基于Ｃ∞基函数的ＮＮＩ方法能够很好地应用于处理极不规则分布数据场的可视化。     

面条模型中空间关系动态推断方法研究

首先提出了面条模型概念的基础上指出基于面条模型的图形处理系统不具备动态生成空间关系的能力,将会退化为单纯的地理数据库。为此提出了面条模型中动态推断空间关系的基于Ｖｏｒｏｎｏｉ图的四邻近数字模型（简记为：４ａｄ）,并给出了唯一、完备的推断规则同时给出了其优点和需改进之处。     

基于区域骨架信息的目标识别方法

提出了一种基于棋盘距离的骨架定义方法，此骨架结构更接近了区域的实际形状，骨架的计算更为简单，传统的利用骨架信息识别目标的方法仅使用骨架的结构信息，而本文提出了骨架结构信息和骨架深度信息相结合的目标识别方法，在骨架的基础上提出了数种形态特征，以这些特征作为神经网络的输入进行目标识别得到较好的识别结果。     

A Pruning Algorithm for Stable Voronoi Skeletons

We present a skeleton computation algorithm for binary image shape which is stable and efficient. The algorithm follows these steps: first the shape boundary curves are subsampled, then the Voronoi Skeleton is computed from the resulting reduced boundary set of points, and finally, a?novel two stage pruning procedure is applied to obtain a?simplified skeleton. The first stage removes skeleton edges non fully included in the shape. The second stage applies an enhanced variation of the Discrete Curve Evolution (DCE) for Voronoi skeletons. We obtain improved skeleton stability, complexity reduction and noise robustness. Pruning computing time efficiency is improved thanks to some properties of Voronoi skeletons. Entire skeleton edges can be removed or retained on the basis of conditions tested on the edge endpoints. Pattern recognition experiments and skeleton stability experiments of the algorithm outperform previous approaches in the literature.     

A One-Step Crust and Skeleton Extraction Algorithm

We wish to extract the topology from scanned maps. In previous work [GNY] this was done by extracting a skeleton from the Voronoi diagram, but this required vertex labelling and was only useable for polygon maps. We wished to take the crust algorithm of Amenta et al. [ABE] and modify it to extract the skeleton from unlabelled vertices. We find that by reducing the algorithm to a local test on the original Voronoi diagram we may extract both a crust and a skeleton simultaneously, using a variant of the Quad-Edge structure of [GS]. We show that this crust has the properties of the original, and that the resulting skeleton has many practical uses. We illustrate the usefulness of the combined diagram with various applications. Received January 17, 1999; revised December 1, 1999.     

A Skeleton-based Approach for Detection of Perceptually Salient Features on Polygonal Surfaces

The paper presents a skeleton‐based approach for robust detection of perceptually salient shape features. Given ashape approximated by a polygonal surface, its skeleton is extracted using a three‐dimensional Voronoi diagramtechnique proposed recently by Amenta et al. [ 3 ]. Shape creases, ridges and ravines, are detected as curvescorresponding to skeletal edges. Salient shape regions are extracted via skeleton decomposition into patches.The approach explores the singularity theory for ridge and ravine detection, combines several filtering methodsfor skeleton denoising and for selecting perceptually important ridges and ravines, and uses a topological analysisof the skeleton for detection of salient shape regions. ACM CSS: I.3.5 Computational Geometry and Object Modeling     

Voronoi diagrams of polygons: A framework for shape representation

This paper describes an efficient shape representation framework for planar shapes using Voronoi skeletons.This paper makes the following significant contributions. First a new algorithm for the construction of the Voronoi diagram of a polygon with holes is described. The main features of this algorithm are its robustness in handling the standard degenerate cases (colinearity of more than two points; co-circularity of more than three points), and its ease of implementation. It also features a robust numerical scheme to compute non-linear parabolic edges that avoids having to solve equations of degree greater than two. The algorithm has been fully implemented and tested in a variety of test inputs.Second, the Voronoi diagram of a polygon is used to derive accurate and robust skeletons for planar shapes. The shape representation scheme using Voronoi skeletons possesses the important properties of connectivity as well as Euclidean metrics. Redundant skeletal edges are deleted in a pruning step which guarantees that connectivity of the skeleton will be preserved. The resultant representation is stable with respect to being invariant to perturbations along the boundary of the shape. A number of examples of shapes with and without holes are presented to demonstrate the features of this approach.     

基于Voronoi图的障碍不确定数据的聚类算法

数据采集过程中普遍存在不确定性,并且在现实地理空间中,不确定数据之间可能存在障碍物间隔。为解决障碍空间中不确定数据的聚类问题,提出APPGCUO算法,该算法包括三个过程:在障碍物约束下采用R树节点最小最大值方法提出的RPT-OUCure算法,用以生成局部最优解,提高生成局部最优解的效率;继而利用近似骨架的理论提出GIABO算法,以局部最优解生成有效初始解,避免划分聚类算法中任意初始解的不足;最后结合Voronoi图的特性提出VPT-KMediods算法,减少不确定数据的积分运算量。实验结果表明,APPGCUO算法具有较高的聚类效率和质量。     

Curve skeleton extraction by coupled graph contraction and surface clustering

In this paper, we present a practical algorithm to extract a curve skeleton of a 3D shape. The core of our algorithm comprises coupled processes of graph contraction and surface clustering. Given a 3D shape represented by a triangular mesh, we first construct an initial skeleton graph by directly copying the connectivity and geometry information from the input mesh. Graph contraction and surface clustering are then performed iteratively. The former merges certain graph nodes based on computation of an approximate centroidal Voronoi diagram, seeded by subsampling the graph nodes from the previous iteration. Meanwhile, a coupled surface clustering process serves to regularize the graph contraction. Constraints are used to ensure that extremities of the graph are not shortened undesirably, to ensure that skeleton has the correct topological structure, and that surface clustering leads to an approximately-centered skeleton of the input shape. These properties lead to a stable and reliable skeleton graph construction algorithm.Experiments demonstrate that our skeleton extraction algorithm satisfies various desirable criteria. Firstly, it produces a skeleton homotopic with the input (the genus of both shapes agree) which is both robust (results are stable with respect to noise and remeshing of the input shape) and reliable (every boundary point is visible from at least one curve-skeleton location). It can also handle point cloud data if we first build an initial skeleton graph based on k-nearest neighbors. In addition, a secondary output of our algorithm is a skeleton-to-surface mapping, which can e.g. be used directly for skinning animation.Highlights(1) An algorithm for curve skeleton extraction from 3D shapes based on coupled graph contraction and surface clustering. (2) The algorithm meets various desirable criteria and can be extended to work for incomplete point clouds.     

Finite element mesh deformation with the skeleton-section template

To develop fast finite element (FE) adaptation methods for simulation-driven design optimization, we propose a radial basis functions (RBF) method with a skeleton-section template to globally and locally deform FE meshes of thin-walled beam structures.The skeleton-section template is automatically formulated from the input mesh and serves as a hierarchical parameterization for the FE meshes. With this hierarchical parameterization, both the global and the local geometries of a thin-walled beam can be processed in the same framework, which is of importance for designing engineering components. The curve skeleton of the mesh is constructed with Voronoi decomposition, while the cross-sections are extracted from the mesh based on the curve skeleton.The RBF method is employed to locally and globally deform the mesh model with the cross-sections and the skeleton, respectively. The RBF method solves the spatial deformation field given prescribed deformations at the cross-sections. At the local scale, the user modifies the cross-sections to deform a region of the surface mesh. At the global level, the skeleton is manipulated and its deformation is transferred to all cross-sections to induce the mesh deformation.In order to handle curved mesh models and attain flexible local deformations, the input mesh is embedded into its skeleton frame field using an anisotropic distance metric. In this way, even strip-like features along arbitrary directions can be created on the mesh model using only a few cross-sections as the deformation handles. In addition, form features can be rigidly preserved at both deformation levels.Numerical examples demonstrate that intuitive and qualified FE mesh deformations can be obtained with manipulation of the skeleton-section template.     

一种基于点集自适应分组构建Voronoi 图的并行算法

论文提出一种基于点集自适应分组构建Voronoi 图的并行算法,其基本思 路是采用二叉树分裂的方法将平面点集进行自适应分组,将各分组内的点集独立生成 Voronoi 图,称为Voronoi 子图;提取所有分组内位于四边的边界点,对边界点集构建Voronoi 图,称为边界点Voronoi 图;最后,针对每个边界点,提取其位于Voronoi 子图和边界点Voronoi 图内所对应的两个多边形,进行Voronoi 多边形的合并,最终实现子网的合并。考虑到算法 耗时主要在分组点集的Voronoi 图生成,而各分组的算法实现不受其他分组影响,采用并行 计算技术加速分组点集的Voronoi 图生成。理论分析和测试表明,该算法是一个效率较高的 Voronoi 图生成并行算法。