一个适合于特征计算的多边形逼近算法

逼近是加快图形特征计算的一个重要方法．本文提出了一个具有确定性的高效的多边形逼近算法，算法设置了一容错系数以满足用户对逼近的不同要求．算法稍加修改后可以处理开端曲线．作者在人体三围特征识别和语音频谱分析时应用了该算法，速度快、效果好．     

一个改进的简单多边形凸包算法

凸包问题是计算几何的基本问题之一，在许多领域均有应用。该文通过给出反例，证明文献[4]提出的简单多边形凸包的双动线检测算法不能正确求出任意多边形的凸包，并分析了其缺点，提出了一个改进的算法。改进的算法解决了线性算法所不能解决的自交问题，且实现简单。     

基于有序简单多边形的平面点集凸包快速求取算法

凸包问题是计算几何的基本问题之一，在许多领域均有应用。传统平面点集凸包算法和简单多边形凸包算法平行发展，互不相干。本文将改进的简单多边形凸包算法应用于平面点集凸包问题中，提出了新的点集凸包算法。该算法首先淘汰掉明显不位于凸包上的点，然后对剩余点集排序，再将点集按照一定顺序串联成有序简单多边形，最后利用前瞻回溯方法搜索多边形凸包，从而得到点集的凸包。本文算法不仅达到了Ｏ的理论时间复杂度下限，而且算法     

基于凸包求解的简单多边形方向判断新算法

Graham ScanA求解简单多边形凸包算法简洁高效,但是对于未确定方向的简单多边形,该算法需设定一个方向求解其凸包。提出一种新的算法,该算法通过利用凸包求解的Graham ScanA算法来判断简单多边形的方向。算法取得了较好的实用效果。     

一个快速的多边形凸包求取算法

多边形凸包算法是计算机图形学中的基础算法。本文提出一个时间复杂性为O(nlog_2n)的凸包算法:先通过极角坐标转化一般多边形为一种特殊多边形——点可见多边形,然后利用比较斜率和回溯来完成点可见多边形的凸包解。该算法将在三维立体造形系统中采用。     

简单多边形凸包的双动线检测算法

计算凸包问题不仅是计算几何的基本工具之一，而且在实际应用中也是很重要的，本文运用Ｇｒａｈａｍ扫描技术及双动线检测的方法，构造了测定简单多边形凸包的Ｏ（ｎ）快速算法。     

基于链码和特征形的多边形内外点判断算法

通过对多边形各个顶点与待测点相对位置进行判别，给出了多边形的垂直（水平）链码序列生成方法．该方法根据多边形的链码将原多边形中对判别无关的冗余边或冗余点删除，形成多边形的特征形；待测点在特征形与原多边形内外位置关系上具有一致性，从而大大简化了运算．同时给出了一种点在多边形内外点判断算法，把点在原多边形内外的判断转化为点与其特征形的位置判断，特征形的提取过程是一个线性扫描及条件判断过程，可以避免大量的又积运算，从而有效地提高了多边形内外点判断算法的效率．程序验证表明：文中算法易于实现，具有运行速度快、稳定性高等优点．     

对平面简单多边形求凸包的线性时间算法

本文提出一种求平面简单多边形凸包的线性时间算法,这种算法是在一般局部凸算法上加了陷阱,这样就可克服局部凸算法产生的自交现象,文中还证明了这种算法的正确性。     

保持特征的平面形状近似骨架的抽取算法

针对多边形骨架抽取中轮廓噪声严重影响骨架的问题,提出一种保持特征的多边形近似骨架的抽取算法.通过分水岭算法检测平面多边形的特征突起点,在分支末端点引导骨架的抽取,从而避免多边形轮廓噪声对骨架的影响,得到有效的形状简洁的近似骨架.另外,该方法还适用于半自动的骨架抽取,即允许用户手动指定骨架末端点,使计算所得的骨架具有更高的实用性.实验结果表明,文中方法简单易行,能应用于计算机动画和形状检索等领域.     

简单多边形分解成凸多边形差组合的算法

本文说明一种把简单多边形分斛成凸多边形的差形式的组合的算法。该算法在求一简单多边形凸包的同时求出凸包和原多边形的差(把差称为内多边形),再对内多边形递归地作同样计算便可得到最终结果。最后证明了运算法的时间复杂性为O(N~2),其中N为原多边形的边数。     

一个改进的简单多边形凸包算法

本文改进了一个有名的简单多边形凸包算法－陈氏算法，使得改进后的算法不但具有线性效率、可避免自交等优点，而且实现简单。     

Interactive real-time motion blur

Motion blurring of fast-moving objects is highly desirable for virtual environments and 3D user interfaces. However, all currently known algorithms for generating motion blur are too slow for inclusion in interactive 3D applications. We introduce a new motion-blur algorithm that works in three dimensions on a per object basis. The algorithm operates in real time even for complex objects consisting of several thousand polygons. While it only approximates true motion blur, the generated results are smooth and visually consistent. We achieve this performance break-through by taking advantage of hardware-assisted rendering of semitransparent polygons, a feature commonly available in today's workstations.     

On the conditions for success of sklansky''s convex hull algorithm

The convex hull algorithm for simple polygons, due to Sklansky, fails in some cases, but its extreme simplicity, compared to the later algorithms, revived an interest in this algorithm. A sufficient condition for its success was given recently by Toussaint and Avis. They have proved that the algorithm works for polygons known as weakly externally visible polygons.

In this paper a new notion called external left visibility is introduced and it is shown that this is a necessary and sufficient condition for the success of Sklansky's algorithm. Moreover, algorithms testing simple polygons for external left visibility and weak external visibility are given.     

简单要素模型多边形拓扑检查并行算法

将并行计算应用到大数据量简单要素模型多边形拓扑检查中,设计实现了简单要素模型多边形拓扑检查并行算法。算法针对拓扑检查的计算特点,改进了主从式并行策略,在主进程中进一步划分线程以实现任务并行,从而隐藏拓扑错误提取和结果写入时间。采用MPI和PThread实现进程与线程的结合。利用苏南五市土地现状调查地类图斑数据对算法进行测试。经测试,该算法能够对大数据量简单要素模型多边形进行准确、快速的拓扑检查。算法提出的进程与线程结合的任务并行策略相对于传统主从式策略加速比提高约20%。     

一种加权剖分简单多边形为三角形和凸四边形子域的算法

针对计算几何与有限元网格自动剖分中多边形子域剖分问题，给出了一种适用于有限元网格子域单元（即大单元）剖分的标准，并提出了一种通过在可视点对之间引进适当的多边形剖分和根据子域单元的形状质量判定因子来引导剖分的算法。由于建立的权函数和凹角（凸角）本身有关，因此对同属于凹角（凸角）的权函数也可以加以权值上的区分。该算法通过分步进行剖分，即先将简单多边形剖分为凸多边形，然后再将凸多边形剖分为凸六边形和凸五边形，最后将凸六边形和凸五边形剖分为三角形和凸四边形，以得到满足要求的剖分结果。在以上的每个剖分过程中，都引进了权重来引导剖分，使得剖分结果更加优化、合理。     

允许自由旋转的2个简单多边形匹配算法

为了解决二维不规则排料问题中的匹配问题,提出了一种允许自由旋转条件下,2个无孔洞的简单多边形之间的匹配算法.该算法基于2个多边形可以自由旋转的假设,对它们之间NFP为凹或凸的情况,选择适当的匹配方法,找出一种使得其匹配后空隙尽可能小,同时保证其整体的矩形的规整度也较高的匹配方案;并用匹配空隙的利用率、匹配后整体面积的利用率,以及匹配后整体的矩形规整度等多个指标来衡量匹配的效果.实验选择于ESICUP中的部分代表性的多边形样例与多个算法进行对比实验,结果表明,该算法在任意旋转精度的要求下,均具有运行速度快的特点,可以很好地应用于服装排料等实际问题.     

基于中介面加快光线跟踪计算

提出一种新的光线跟踪方法,以提高光线找到相交面片的效率.它在场景中生成一些面积较大的规整中介面片,然后为中介面上的每个点建立一个场,以记录到达该点的不同方向的光线将相交的面片.由此,光线跟踪时,一条光线可方便地找到相交的中介面,并通过查找中介面上所记录的内容,就能得到它所相交的面片.与已有方法相比,新方法不仅能很好加速主光线与阴影光线的计算,而且能很好地加速反射、折射等二次光线的计算.它能在GPU上方便地实现,并能有效地处理动态场景.     

An intuitive polygon morphing

We present a new algorithm for morphing simple polygons that is inspired by growing forms in nature. While previous algorithms require user-assisted definition of complicated correspondences between the morphing objects, our algorithm defines the correspondence by overlapping the input polygons. Once the morphing of one object into another is defined, very little or no user interaction is necessary to achieve intuitive results. Our algorithm is suitable namely for growth-like morphing. We present the basic algorithm and its three variations. One of them is suitable mainly for convex polygons, the other two are for more complex polygons, such as curved or spiral polygonal forms.     

Translational polygon containment and minimal enclosure using mathematical programming

A new algorithm is given for the two-dimensional translational containment problem: find translations for k polygons which place them inside a polygonal container without overlapping. Both the polygons and the container can be non-convex. The algorithm is based on mathematical programming principles. The containment algorithm is generalized to solve minimal enclosure problems: find the minimal area enclosing square or minimal area enclosing rectangle for k translating polygons. The containment algorithm consists of new algorithms for restriction , evaluation , and subdivision of two-dimensional configuration spaces. Restriction establishes lower bounds through relaxation and the solution of linear programs. Evaluation establishes upper bounds by finding potential solutions. Subdivision branches, when necessary, by introducing a cutting plane. The algorithm shows that either the upper bound of the objective (overlap) is exactly zero or the lower bound is greater than zero. Hence, it gives an exact solution to the containment problem. Experiments show that new containment algorithm clearly outperforms purely geometric containment algorithms. For data sets from the apparel industry, it can solve containment for up to ten non-convex polygons in practice. An implementation of the algorithm given in this paper has been licensed by Gerber Garment Technologies, the largest provider of textile CAD/CAM software in the US, and they are incorporating it into an existing CAD/CAM software product.     

Drawing complete binary trees inside rectilinear polygons

Most of graph drawing algorithms draw graphs on unbounded planes. However, there are applications that require graphs to be drawn on the plane inside a given polygon. In this paper, a new algorithm for planar orthogonal drawing of complete binary trees inside rectilinear polygons is presented. Uniform distribution of nodes of graphs on drawing regions is one of the aesthetics criteria in graph drawing. The goal of this paper is to produce planar orthogonal drawings with a relatively uniform node distribution and few edge bends. The proposed algorithm can be considered as a generalization of the H-tree layout method for rectilinear polygons. A new linear time algorithm is also given for bisecting rectilinear polygons into two equi-area rectilinear sub-polygons.