分形软件及其应用

分形图案是使用计算机绘图工具做出的数学图案，它是运用计算机相关原理及分形理论设计得到的图案。文章介绍了分形软件的组成及其功能，展示了一些软件产生的分形图案，并且对不同参数设置所获得的分形图案和动画进行了比较。分形自身的特点决定了分形图案色彩及其形状，在开发设计过程中，分形算法的改善可获得更丰富的图案。最后简单描述了分形软件在各个领域中的应用。     

基于超复数系的分形准全息图象生成

提出了一种新型分形准全息图象，并采用基于超复数系分形图象的生成方法进行分形准全息图象序列的生成，生成的分形准全息图象在激光防伪等领域有着良好的应用前景。文中还给出了超复数系中分形三维图象生成的快速算法和生成结果。     

基于分形几何的真实场景物体表示及应用

介绍了分形维数的概念,对利用自拟似分形和自仿射分形实现分形物体的绘制算法进行了描述。实现了场景中不规则自然景物几何形状的真实感表达。     

基于参数的分形地形可控性研究

本文在深入研究分形布朗运动原理和中点位移算法的基础上，推导出分形地形参数之间的关系表达公式，分析了分形参数对地形形状的影响，提出了基于参数的可控分形地形生成方法，并进行了仿真。试验表明，该方法能快速有效地对分形地形进行控制，是自然景观仿真的一种有效手段。     

一类几何分形的表示模型

结合迭代函数系统和有限自动机,提出了几何分形的正则生成系统表示模型,并应用生成测试法和自动机归纳学习算法研究了一类几何分形的建模方法,实验结果表明,该模型是简单有效的。     

随机中点位移算法的改进

在研究用于分形图象生成的随机中点位移算法原理和实验结果的基础上，提出了改进的随机中点位移地，以例生成具有预定基本形状和轮廓的分形图象，并通过编程实验验证了改进算法的有效性。     

有理分形插值曲线的约束和单调保持EI北大核心CSCD

传统的多项式分形插值中,分形曲线曲面的局部形状约束和调整是一项困难的工作.为了使分形曲线能够在很好地逼近不规则数据的同时具有形状可调性,提出一种有理样条分形插值方法.首先基于经典的有理三次样条构造了1C连续的有理样条分形插值函数,这种有理分形插值函数的构造允许嵌入形状参数,以至于分形曲线的形状能够通过对尺度因子和形状参数的约束进行调整;然后研究了该插值函数的一些分析性质,包括一致收敛性和稳定性;最后基于构造的有理分形插值函数,通过对迭代函数系统参数的约束,分别给出了约束和单调曲线插值系统.实例结果表明,利用该方法可以将传统非递归形状可调插值分形一般化;形状参数的嵌入使得分形插值函数具有良好的拟局部性,为分形曲线的形状调整提供了有效的工具.     

有理复映射（m—1）z^m—c＼mz^m—1J集及其自相似外环分维估计

本文利用复系数多项式构造了牛顿变换有理映射ｆ（ｚ）＝（（ｍ－１）ｚ＾ｍ－ｃ）／（ｍｚ＾ｍ－１）。并构造了ｆ的充满的Ｊｕｌｉａ分形图。由充满的Ｊｕｌｉａ分形图的吸引域边界叠加构造Ｊｕｌｉａ集。用作者提出的同胚分形插值算法估计牛顿变换Ｊｕｌｉａ分形图的自相似花朵链外环分维。     

数字图像中作物病斑形状分形特征提取

应用分形理论的计盒维数法在数字图像中研究了棉花不同病害病斑的形状分形特征,结果表明,棉花病害病斑的形状具有明显的分形特性,其形状的复杂性可用分形维数量度。不同类病斑的形状分形维数存在明显的差异,炭疽病病斑的分形维数为1.804±0.0214,轮纹病斑的分形维数为1.8951±0.0224,叶枯病病斑的分形维数为1.8740±0.0345。其可作为识别诊断病害的特征,利用病斑形状分形特征进行棉花病害的识诊断别,识别准确率达到81%以上。实验研究表明在数字图像中应用分形理论研究作物病斑的形状特征及应用病斑形状分形特征识别作物病害是可行的。     

复映射Z←Z^W＋C（W=α＋iβ）构造J分形图

提出用复映射Ｚ←Ｚ＾ｗ＋ｃ，（ｗ＝α＋ｉβ，α，β∈Ｒ＾１），构造大量Ｊ分形图，当ｗ＝ａ〈０时，构造出琐于相关文献的Ｊｕｌｉａ分形图，根据大量实验，提出关于该映射参数平面上的Ｍ集与动力平面上的Ｊｕｌｉａ集之间的对应关系的Ｍ－Ｊ猜想及计算公式的ＰＮＯ，预报Ｍ集中参数ｃ的Ｊｕｌｉａ分形图图象特征。     

平面形状和布置的一种统一的定性表示方法

基于广义Ｖｏｒｏｎｏｉ图式，提出了Ｖｏｒｏｎｏｉ骨架边的跨度和势的概念，给出了保持连通性的层次骨架的建构算法。     

Fault diagnosis of a mixing process using deep qualitative knowledge representation of physical behaviour

This paper describes an on-line fault diagnosis system which diagnoses faults in a pilot scale mixing process using on-line measurements. Fault detection and fault diagnosis is performed based on a qualitative model of the mixing process. The qualitative model provides a set of constraints for the system being diagnosed. Once it is violated, a particular fault is detected. Since most of the information used by the diagnosis system comes from on-line measurements, it is important to determine whether sensors are working normally or not before considering failures of other components. Sensor failure is mainly diagnosed from heuristic considerations, while the failures of other components are diagnosed from a procedure of hypothesis generation, qualitative simulation, and comparison. Based on a hypothesis, the behaviour of the system being diagnosed is simulated from its qualitative model and is compared with the actual measurements. Depending upon whether they conflict or not, the hypothesis is denied or retained. A new approach for reducing the ambiguity in qualitative simulation is described. Ambiguity is reduced by taking account of the information on the order of magnitude relations between different physical variables.     

Using point cloud data to identify,trace, and regularize the outlines of buildings

Rectilinear building outline generation from the point set of a building usually works in three steps. Boundary edges that constitute the building outline are first identified. A sequence of points is then traced from the edges to define the building boundary. Finally, lines are generated from the sequence of points and adjusted to form a regular building outline. Existing solutions have shortcomings in one or more of the following cases: identifying details along a concave shape, separate identification of a ‘hole’ inside the shape, proper boundary tracing, and preservation of detailed information along a regularized building outline. This article proposes new solutions to all three steps. By using the maximum point-to-point distance in the input data, the solution to the identification step properly detects the boundary edges for any type of shape and separately recognizes holes, if any, inside the shape. The proposed tracing algorithm divides boundary edges into segments, accurately obtains the sequence of points for each segment and then merges them, if necessary, to produce a single boundary for each shape. The regularization step proposes an improved corner and line extraction algorithm and adjusts the extracted lines with respect to the automatically determined principal directions of buildings. In order to evaluate the performance, an evaluation system that makes corner correspondences between an extracted building outline and its reference outline is also proposed. Experimental results show that the proposed solutions can preserve detail along the building boundary and offer high pixel-based completeness and geometric accuracy, even in low-density input data.     

用局部阻尼波形法的自连贯网格生成法

介绍将生成或已有的有限元规则六面体单元改变成形状复杂且光滑的六面体单元的一种新技术——波形法．简单建立了波形法的数学模型并编程进行了网格生成．实验结果表明，只要把复杂外部形状按波的形式传输给指定的规则六面体单元模型，就可以得到具有复杂外部形状的六面体单元网格模型，且网格生成速度快、不出现单元或节点漏洞、欠缺等问题，同时不受单元类型的限制。     

Polygonal representation of digital planar curves through dominant point detection—a nonparametric algorithm

We describe a new algorithm that detects a set of feature points on the boundary of an 8-connected shape that constitute the vertices of a polygonal approximation of the shape itself. The set of feature points (nodes) is a ranked subset of the original shape points whose connected left and right arm extents cover the entire shape. Nodes are ranked based on their strength (in terms of their importance to other boundary points), length of support region, and distance from the centroid. The polygon obtained by linking the detected nodes approximates the contour in an intuitive way. The proposed algorithm does not require an input parameter and works well for shapes with features of multiple sizes.     

On the Recognition and Location of Partially Occluded Objects

The recognition and location of partially occluded objects is important for image-guided robot automation. A computational object recognition system consists of three main parts: shape representation, matching strategies and verification. The shape representation scheme, which is always application-oriented, should keep extracted features as invariant as possible. This paper presents a new model-based object recognition scheme for general two dimensional objects in a cluttered scene. The scheme considers objects subjected to similarity transformations (i.e., a combination of rotation, scaling and translation). It employs a new feature detection algorithm, combining curvature measures and polygonal approximation. An approximate, but efficient matching strategy is proposed for hypothesis generation and synthetic verification procedures are introduced to improve the robustness of the system. Experiment results are presented to show that the system works effectively and efficiently.     

快速成型中STL数据模型的B-Rep实体精确重建

针对快速成型机广泛使用的STL数据模型，建立了STL文件拓扑重建的数据结构，给出了边界提取和面片分割的具体实施方法，实现了基于边界表示的实体建模．利用回转面的内在几何性质，提出了球面、柱面等规则曲面的识别方法，从而还原机械型面的原貌并实现规则型面的精确表示．对于自由曲面，采用调和映射参数化技术，实现了该类网格曲面的精确NURBS建模，给出了曲面片间保持G^1连续的优化拼接方法．实际的验证结果表明，重构的实体模型精度较高且便于系统间的数据交换，非常适于数控加工领域．     

基于边界表示的体抽壳算法

形体的抽壳是构造具有薄壁外壳形状物体的一种有效方法.文章基于边界表示的正则形体,给出体抽壳运算的数学定义,并提出实现体抽壳运算的算法.该算法把形体的三维运算转化到曲面的参数域上,进行二维环之间的合并运算,从而降低了问题的复杂度.