平行断层轮廓线的RBF隐函数曲面造型

将基于径向基函数（Radial Basis Function,RBF)的隐函数插值技术应用于平行断层轮廓线的曲面造型，由于RBF造型方法以曲面能量最小化为目标，因此能够生成较为光滑的曲面，其缺点是计算量较大，文中提出以分段进行曲面重构的局部RBF技术来降低问题的规模和复杂度，并提出相应的快速隐函数多边形化的算法，实验结果表明，该算法是一个较实用的造型方法。     

利用隐式曲面创建实体的多分辨率表示

最近 ,对隐式曲面的研究取得了一些新进展 ,研究者可以通过对一个点集的插值来得到隐式曲面 ,插值过程只需要求解一个简单的线性系统即可 .采用基于包围球的层次结构对原始点集进行不同尺度的采样 ,使用采样后的点集来构造隐式曲面 ,从而得到实体的不同尺度的表示形式 .与基于多边形网格的表示形式相比 ,作者探讨了利用插值型隐式曲面来创建多尺度表示的一些优点     

一种基于遗传算法的数字曲线多边形逼近方法

提出了一种基于遗传算法的数字曲线多边形改进逼近方法。该方法针对规则形状数字曲线的多边形逼近问题,以二进制向量序列表示的染色体作为每一个对应的逼近多边形候选解,将简化前后多边形质心偏移误差以及各被替换线段欧氏距离的方差引入到适应函数中,用迭代次数的sigmoid函数作为变异概率来控制遗传算法优化求解过程中的全局和局部搜索特性。实验结果表明,该方法对于保持曲线多边形简化逼近后的形状特征具有较好的效果。     

基于sign(x)函数的点在多边形内外判别算法及应用

在对已有的点与多边形位置关系判断算法分析与研究的基础之上,提出一种新的判断点在多边形内外的算法。该算法用三维空间来解决二维平面问题,将二维平面内的点看作是三维空间在平面上的点,从而得出简单的待判断点与多边形顶点之间的坐标关系式。由于符号函数仅仅有三个值,巧妙地利用符号函数的特殊性来表示待判断点与多边形的顶点之间的坐标关系。最终,可以简单地由符号函数之和判断点是否位于多边形内部。程序验证表明,该算法简单、易于实现。同时,将该算法应用于基于RTK GPS定位技术的机动车驾驶证申领场地考试系统中,结果表明,判断准确率高,且实时性好。     

浅谈一元隐函数求导方法

在高等数学的教学过程中，隐函数求导是既是一个重点，又是一个难点。本文介绍了三种隐函数求导方法：（1）方程两边同时求导法；（2）方程两边同时微分法；（3）基于隐函数存在定理的求导法。     

基于任意骨架的隐式曲面造型技术

给出了一个新的基于任意多面体网格骨架的构造性自由曲面造型算法.算法首先由每个给定骨架构造出一个距离场,然后利用隐函数光滑过渡技术和CSG(constructive solid geometry)表示技术将所构造的隐式曲面自由地两两粘合成一张光滑曲面.隐式曲面的多边形化算法则用来生成最终曲面网格.以任意骨架作为基本体素,突破了传统隐式曲面以点为基本骨架的限制.而且,距离曲面很好地逼近了原骨架形状,使用户可直观地对复杂曲面进行交互设计.而形变函数的引入,则极大地丰富了此方法的造型能力.实验结果表明,基于该算法的原型系统能够方便、直观地构造复杂的自由曲面.     

隐式曲面快速多边形化

隐式曲面多边形化是隐式曲面绘制的常用算法。该文提出了一个隐式曲面快速多边形化算法。首先用Bloo-menthal的多边形化算法生成一个粗糙的初始网格,再进行网格优化提高网格规则性,最后用多边形细分策略细分优化后的网格。实验结果表明,该算法在网格生成速度和网格规则性上都胜于Bloomenthal的多边形化算法。     

结合失真函数的稀疏域图像隐写算法

稀疏域图像隐写利用稀疏表示在载体图像中嵌入秘密信息。提出设计稀疏域图像隐写的失真函数,通过选择使失真函数最小的修改方式进行秘密嵌入,从而减小秘密信息嵌入对载体的影响。实验结果表明,该算法可以在保持图像视觉效果的同时,更有效地抵抗现有的隐写分析算法。     

基于简化多边形类正切空间表示的图形渐变算法

采用多边形简化的方法提取出包含源图形主要特征点的多边形.在简化多边形的类正切空间表示下,利用图形对应边在渐变过程中所掠过面积总和最小这一特征构造相似度量函数,由动态规划算法求解实现初始和目标简化多边形之间的顶点对应,再进一步建立源图形顶点之间的整体对应,最后通过插值边和角的方法实现图形渐变.实验结果表明:该算法简单有效,对应效果自然、合理.     

基于基函数展开的双隐层过程神经元网络及其应用

提出一类基于基函数展开的双隐层过程神经元网络模型．过程神经元隐层完成对输入信息过程模式特征的提取和对时间的聚合运算，非时变一般神经元隐层用于提高网络对系统输入输出之间复杂关系的映射能力．在输入空问中引入一组函数正交基，将输入函数和网络权函数表示为该组正交基的展开形式，利用基函数的正交性简化过程神经元聚合运算．以旋转机械故障诊断和油藏开发过程采收率的模拟为例，验证了模型和算法的有效性。     

On the intersection of two planar polygons

Polygons have proved to be important elements for representing and manipulating visual data. A knowledge of the geometric and the combinatorial nature of the intersection of planar polygons may thus serve to tackle such problems as the removal of hidden surfaces. A complete classifying scheme for the intersection of stable pairs of polygons and an explicit enumeration for the case of two triangles is given.     

Optimal Polygonal Representation of Planar Graphs

In this paper, we consider the problem of representing planar graphs by polygons whose sides touch. We show that at least six sides per polygon are necessary by constructing a class of planar graphs that cannot be represented by pentagons. We also show that the lower bound of six sides is matched by an upper bound of six sides with a linear-time algorithm for representing any planar graph by touching hexagons. Moreover, our algorithm produces convex polygons with edges having at most three slopes and with all vertices lying on an O(n)×O(n) grid.     

Corner cutting algorithms associated with optimal shape preserving representations

Given a space of functions which admits shape preserving representations using control polygons, we construct a corner cutting algorithm which will be called B-algorithm. It is an evaluation algorithm satisfying important properties such as subdivision property and convergence to the curve of the resulting control polygons. Many examples are given.     

一种GIS缓冲区矢量生成算法及实现

缓冲区分析是地理信息系统重要的空间分析功能之一。缓冲区生成分为点、线、面三种,其中线状目标缓冲区生成是关键和基础,线状目标缓冲区生成分为单个线状目标缓冲区多边形独立生成过程和所有线状目标缓冲区多边形重叠合并两个阶段。在缓冲区圆弧矢量生成算法思想的基础上,提出了一种新的有效的缓冲区半径旋转矢量生成算法。另外,对缓冲区生成过程中出现的特殊情况进行了处理,并应用递归方法管理和存储缓冲区边界的自相交多边形。     

A polygon-based clustering and analysis framework for mining spatial datasets

Polygons provide natural representations for many types of geospatial objects, such as countries, buildings, and pollution hotspots. Thus, polygon-based data mining techniques are particularly useful for mining geospatial datasets. In this paper, we propose a polygon-based clustering and analysis framework for mining multiple geospatial datasets that have inherently hidden relations. In this framework, polygons are first generated from multiple geospatial point datasets by using a density-based contouring algorithm called DCONTOUR. Next, a density-based clustering algorithm called Poly-SNN with novel dissimilarity functions is employed to cluster polygons to create meta-clusters of polygons. Finally, post-processing analysis techniques are proposed to extract interesting patterns and user-guided summarized knowledge from meta-clusters. These techniques employ plug-in reward functions that capture a domain expert’s notion of interestingness to guide the extraction of knowledge from meta-clusters. The effectiveness of our framework is tested in a real-world case study involving ozone pollution events in Texas. The experimental results show that our framework can reveal interesting relationships between different ozone hotspots represented by polygons; it can also identify interesting hidden relations between ozone hotspots and several meteorological variables, such as outdoor temperature, solar radiation, and wind speed.     

基于三角剖分的平面沉积相快速编辑

编制平面沉积相图需要对沉积相多边形进行多次拾取和修改,工作量大,使得沉积相的快速编辑这一功能需求迫切。应用三角剖分技术,通过相边界线自动识别沉积相闭合多边形,实现了相的快速编辑。该功能的开发提升了平面沉积相成图的编制工作效率,同时对涉及区域识别和划分的相关功能开发提供了借鉴。     

基于圆形窗口的简单多边形填充算法

提出了一种新颖而实用的圆形窗口简单多边形填充算法，它具有快速裁剪与填充双重功能，也可完成单纯地裁剪功能，该算法将多边形的边视为有向线段，通过引入多边形顶点的入边和出边产我点的概念，深入研究了多这形被圆形窗口裁剪后区域的确定性填充问题，使截剪功能隐含于填充过程中，从而节省了填充之前的裁剪过程。     

Point-in-Polygon Analysis Under Certainty and Uncertainty

The point-in-polygon query in geographical information systems under certainty and uncertainty is formally analyzed in this paper. It is argued that points and polygons can be precise, fuzzy (imprecise), and random (with error) with different schemes of representations. Under certainty, points and polygons can generally be represented by their characteristic functions. Under imprecision induced uncertainty, they can be represented by fuzzy sets characterized by membership functions. If uncertainty is induced by randomness, points and polygons can be described by locational error models in which probability arguments are employed. Points and polygons under certainty turn out to be a special case of that under imprecision and randomness induced uncertainty.Since points and polygons may be precisely, imprecisely or randomly captured or recognized within a spatial information system, the point-in-polygon query is then rather complicated, and its entertainment is not straight forward. In general, the point-in-polygon query can be entertained under nine basic situations. It consists of the queries of whether a precise or fuzzy or random point is in a precise or fuzzy or random polygon. As a consequence, the answer to the query may take on various forms with certain types of uncertainty arguments attached. It involves the integrative utilization of fuzzy set and probability theories to derive the results.The present analysis clarifies some unresolved issues of the point-in-polygon query and provides a generalization to its entertainment. Furthermore, it sheds light on the way certainty and uncertainty can be addressed and implemented in spatial information systems.     

Search for the Intersection Polygon of any Two Polygons: Application to the Garment Industry

One of the biggest problems usually encountered by the clothes manufacturer consists of placing various pattern parts on a rectangular area in such a way that the waste of material between the pieces is minimized.
To bring some automated help in this field, computer programs need first to handle the complicated contours of the pieces. One needs not only to check the overlap of two contiguous patterns, but also to compute their precise area of intersection, allowing in this way the use of some kind of combinatorial optimization.
In a wider context, it is possible to design a general purpose algorithm, able to build the complete structure representing the intersection of two polygons. It is remarkable that the same algorithm can also be used, with only a few modifications, to compute the union and the difference of any two polygons.