基于IFS的3D Fractal可视化技术研究

本文基于ＩＦＳ理论，将随机迭代算法进行拓广，使之可作用于３Ｄ对象的顶点集。在此基础上，分别给出基于Ｚ－缓存和基于测度理论的３ＤＦｒａｃｔａｌ绘制技术。进一步地，为使视觉深度信息能更好地得以再现，在此也给出一种在均匀颜色空间基于Ｂ样条的颜色计算模型，使得颜色选择、处理、插值皆具有很大的柔性。

Optimization of Fractal Iterated Function System(IFS) with Probability and Fractal Image Generation

There are several methods for rendering fractal images based on IFS (Iterated Function System) in computer graphic; but one concern of the computer graphic community has been the efficiency rendering algorithms. The invariant measures arising from IFSP (Iterate Function System with Probability) using the probabilistic algorithm are also known as chaos games. The role of these probabilities to generate the image of the attractor has been investigated using a multi-fractal analysis. The conventional choice of probability associated with each set /S/ to generate the attractor in least time possible is introduced, then a new method based on the self similarity and multi-fractal analysis is presented. The efficiency of the new method has been proved over the conventional method.

IFS ON BOUNDARIES OF HOMOGENEOUS TREES:WQB CONDITION AND MULTIFRACTAL ANALYSIS

We study, from the point of view of the multifractal analysis, iterated function systems on totally disconnected spaces, namely, the boundaries of homogeneous trees. In particular, we study in this setting the ＂weak quasi-Bernoulli property introduced by Testud [3, 4]. After projection on R or R2, we get new examples of self-similar measures which being WQB, obey the multifractal formalism for positive q,s.

The lift-off effect analysis of flexible differential pick-up koch fractal eddy current probe

This study utilized finite element simulation and experimental methods to investigate the evolution of crack detection performanceof a flexible differential fractal Koch eddy current probe at different excitation frequencies as the lift-off distance increases.As the lift-off distanceincreased,the distribution shape of induced eddy currents changed,leading to reduced similarity in the shape of the excitation coil and an expandeddistribution range of induced eddy currents,ultimately resulting in weakened output signal strength.The experimental results showed that forexcitation frequencies of 10 kHz,20 kHz,50 kHz,100 kHz,200 kHz,500 kHz,and1000 kHz,the maximum lift distances of the real partof the output signal when cracks were detected were 5.0 mm,7.0 mm,8.0 mm,8.0 mm,8.0 mm,6.5 mm,and 4.0 mm,respectively.Theimaginary parts were 6.5 mm,6.5 mm,7.5 mm,5.5 mm,8.0 mm,6.5 mm,and 6.5 mm,respectively.

Computational Quantification of Map Projection Distortion by Fractal Dimension of Coastlines

Maps, essential tools for portraying the Earth’s surface, inherently introduce distortions to geographical features. While various quantification methods exist for assessing these distortions, they often fall short when evaluating actual geographic features. In our study, we took a novel approach by analyzing map projection distortion from a geometric perspective. We computed the fractal dimensions of different stretches of coastline before and after projection using the divide-and-conquer algorithm and image processing. Our findings revealed that map projections, even when preserving basic shapes, inevitably stretch and compress coastlines in diverse directions. This analysis method provides a more realistic and practical way to measure map-induced distortions, with significant implications for cartography, geographic information systems (GIS), and geomorphology. By bridging the gap between theoretical analysis and real-world features, this method greatly enhances accuracy and practicality when evaluating map projections.

Research status and prospects of the fractal analysis of metal material surfaces and interfaces

As a mathematical analysis method,fractal analysis can be used to quantitatively describe irregular shapes with self-similar or self-affine properties.Fractal analysis has been used to characterize the shapes of metal materials at various scales and dimensions.Conventional methods make it difficult to quantitatively describe the relationship between the regular characteristics and properties of metal material surfaces and interfaces.However,fractal analysis can be used to quantitatively describe the shape characteristics of metal materials and to establish the quantitative relationships between the shape characteristics and various properties of metal materials.From the perspective of two-dimensional planes and three-dimensional curved surfaces,this paper reviews the current research status of the fractal analysis of metal precipitate interfaces,metal grain boundary interfaces,metal-deposited film surfaces,metal fracture surfaces,metal machined surfaces,and metal wear surfaces.The relationship between the fractal dimensions and properties of metal material surfaces and interfaces is summarized.Starting from three perspectives of fractal analysis,namely,research scope,image acquisition methods,and calculation methods,this paper identifies the direction of research on fractal analysis of metal material surfaces and interfaces that need to be developed.It is believed that revealing the deep influence mechanism between the fractal dimensions and properties of metal material surfaces and interfaces will be the key research direction of the fractal analysis of metal materials in the future.

FRACTAL DIMENSION OF SHAPE CHANGE OF CAVITIFS DURING SUPERPLASTIC DEFORMATION IN HIGH STRENGTH Al ALLOY

The fractal dimension changes of cavities have been determined during superplastic deformation of the high strength aluminiurn alloy 7475 with different strain,temperature, strain rate and grain size.The fractal dimension of cavities may increase with the increase of strain.It becomes higher as the alloy deformed under lower temperatures,greater strain rate and coarser grain size.The alloy would be approaching to rupture if the fractal dimension of cavities raised to a certain extent.

Real-Time Tool for Affine Transformations of Two Dimensional IFS Fractal

This work introduces a novel tool for interactive, real-time affine transformations of two dimensional IFS fractals. The tool uses some of the nice properties of the barycentric coordinates that are assigned to the points that constitute the image ofa fractal, and thus enables any affine transformation of the affine basis, done by click-and-drag, to be immediately followed by the same affine transformation of the fractal. The barycentric coordinates can be relative to an arbitrary affine basis of ~2, but in order to have a better control over the fractal, a kind of minimal simplex that contains the fractal attractor is used.

分区IFS图像压缩编码

本文提出了一种基于“区”的ＩＦＳ图像压缩编码算法，简述了其原理及实现过程。实验结果表明，其性能优于ＪＰＥＧ算法及Ｊａｃｑｕｉｎ的基于“块”

一种基于IFS的图像边缘检测方法

首次提出了一种基于IFS的图像边缘检测方法，该方法以IFS理论为基础、以MSE为失真测度，对图像进行边缘检测，改进的局部快速算法可以有效减少检测搜索时间。实验结果表明，本文所采用的边缘检测方法是一种有效的图像边缘检测方法。

基于IFS的非规则分形组织设计方法

针对L系统在绘制织物分形组织图方面存在的局限,基于IFS的生成规则,研究不受任何基本组织形式限制的非规则分形组织设计方法。该方法以非规则、大循环的基本组织为应用对象,运用VC++编程,利用Kronecker叉积进行组织矩阵的迭代运算,快捷地生成此类基本组织的分形组织图。在此基础上,利用分形组织自相似结构所具有的多级层次关系,通过选择不同的填充组织,设计形成结构复杂、风格多变的分形织物。通过织造实验证明,此分形组织设计方法形成的织物纹理效果具有复杂性强,不易模仿等特点。

局部放电超声信号的自仿射IFS模型

通过仿射变换建立了变压器局部放电超声信号的分段自仿射 IFS模型。该模型用于在线监测中可实现局部放电信号数据的压缩 ,并通过计算 IFS分形维数为局部放电模式识别提供新的特征参数。

迭代函数系IFS吸引子的参数控制与树木的模拟

文章讨论了迭代函数系ＩＦＳ吸引子的参数控制，讨论了ＩＦＳ参数控制实现模拟树木的方法。

一种基于IFS分形算法和分解和弦的耳鸣康复音合成新方法

耳鸣是在无外界声源刺激下的一种主观感知,在临床上十分常见.习服治疗是目前公认的一种有效的耳鸣治疗方法.研究表明,具有相似却又不重复的分形音乐可以作为耳鸣习服治疗的治疗声源.本文提出了一种基于IFS(Iterated Function System)分形算法和分解和弦的耳鸣康复音合成新方法,该方法将分形图形处理技术运用到耳鸣康复音的合成中,使得生成的音符整体在可控范围内随机出现,并且相邻音符在可调节的范围内波动,可有效的避免音调突变现象.此方法保留了图像信号中的分形特征,实现了可控范围内的确定性与可预测性的统一;在加入了分解和弦后,音乐更加连贯.试听结果表明,该耳鸣康复音具有相似不重复、流畅且突变少的特点,对耳鸣治疗有一定的参考价值.

基于迭代函数系统IFS的动态树木模拟

植物作为自然景物中最常见的现象之一,模拟的方法是应用数学和图形学领域的一个重要课题。迭代函数系统IFS是分形理论的重要分支,由于植物结构的自相似性,利用IFS(Iterated Function System)可以逼真地模拟各植物形态,简述几种模拟植物的方法,主要研究迭代函数系统IFS模型,并在VC++6.0环境下基于IFS模型构造出静态蕨叶和树木,详细讨论利用带参量的IFS随机系统实现动画的过程,并利用双缓冲技术,形象逼真地模拟随风摇摆的蕨叶和生长树木的动画效果。实验结果表明,带参数的IFS可使图像发生预期的变化,如果让参数在适当的范围保持连续变化,则动画效果良好。

基于IFS随机迭代算法的印花图案设计

根据纺织面料印花图案的特点,利用IFS随机迭代算法的便捷性,运用可视化方法,在基于随机迭代算法讨论IFS图形生成原理的同时,研究了通过参数变化使IFS图形发生变化的基本方法;在此基础上,运用计算机图形技术,对应用IFS图形设计纺织面料印花图案的方法作了初步的尝试,并借助电子(喷)印花手段进行印花试验,对纺织面料运用IFS图形资源开发印花产品的途径进行了初步的探讨。

基于IFS块的快速图象编码算法

文中首先叙述了目前分形块编码研究领域的大致情况，然后，提出了一种新的快速编码算法．用Ｌ１距离替换了以往算法所用的Ｌ２距离，把匹配过程转换成类似于矢量量化的搜索过程，因而采纳了许多矢量量化的加速算法．还讨论了对平坦区的处理并提出了新的剖分方法，取得了较好的效果．同其它的分形块编码方法相比，该算法大大缩短了编码时间，改善了压缩图象的质量，特别是它能较大程度地消除块效应，压缩比也有了进一步的提高．

一种基于IFS的二维真彩分形变形方法

提出了一种由迭代函数系统(IFS)所描述的二维真彩分形变形的新方法。首先建立二维真彩IFS分形模型,然后通过仿射变换的对应、规范化、匹配及插值实现了变形过程。实验结果表明:分形吸引子形状颜色过渡自然,这为分形的生成与动画提供了新的有效途径。

基于IFS和IPSO算法的干扰资源分配方法

针对多干扰系统同时干扰多部雷达的干扰资源分配问题,提出一种基于直觉模糊集(IFS)和改进粒子群优化(IPSO)算法相结合的干扰资源分配方法。利用己方无源探测系统获得的敌方雷达参数,根据IFS理论得到敌方雷达的威胁系数;整合数据库中战场的己方干扰系统与敌方雷达系统信息,从空域、频域、极化方式和干扰样式4个方面定义了匹配度,表示己方干扰系统对敌方雷达系统的干扰效率,得到匹配度矩阵,结合敌方雷达威胁系数建立干扰目标函数;提出一种自适应调整权重、异步变化学习因子、针对离散问题的IPSO算法,并引入补偿粒子进行盲区搜索,求解出最佳干扰决策。仿真表明,本文提出的干扰资源分配方法相较于传统算法最优解正确率更高,且实时性更好。

一种双二次插值与IFS相结合的图象压缩新方法

本文提出了一种基于Ｗａｌｓｈ四子带分解的，将二次插值与改进的分形编码相结合的图象压缩方法。实验结果表明，与基本的自动分形图象编码方法相比，在基本保持重建图象质量的前提下，运算时间下降而压缩比提高。