基于分形的自然景物图形的生成

论文编号:TX065        论文字数:23592,页数:58

 摘  要
分形学是近二、三十年才发展起来的一门新的学科，主要描述自然界和非线形系统中不光滑和不规则的几何形体。自然界中种类繁多的植物虽然形态千差万别，却大都具有自我相似、自我繁殖的分形特征。近年来，随着分形学的发展，分形植物模拟成为计算机仿真领域的重要课题，其原因在于分形几何学可以很好的描述用传统的几何工具进行描述时会遇到极大的困难复杂的自然景物的模拟，能很逼真的描述自然景物,获得令人惊奇的自然景物模拟图像。
本论文主要研究基于分形的自然景物图形的生成。研究模拟自然景物的两种方法L-系统和迭代函数系统,在此基础上利用可视化编程，对三维景物进行了分形生成。针对L-系统生成规则简洁，但实现过程烦琐的特点，本论文深入研究了景物的结构形态、动态生成过程等，提出一种层次遍历的算法，大大简化了实现过程。针对IFS系统，通过对典型图例的分析，得出IFS系统模拟出的自然景物较接近事物本身。
迭代函数系统（IFS）的吸引子能够很好的模拟传统几何难以描述的各种自然景物。采用IFS进行景物模拟时，需要已知构成该IFS的各个压缩映射的参数，但对那些无已知参数的景物就无法模拟了。本文研究了分形理论在计算机图形学中的应用，基于分形的自然景物模拟技术研究中关于松柏科树叶模拟生成技术。利用迭代函数系统模拟自然景物，在OpenGL环境下结合分形理论，绘制出松柏科植物的三维立体叶片，并可以从不同角度进行浏览。通过学习自然景物模拟的基本方法，在计算机上实现松柏科树叶的模拟生成。

关键词  分形  L-系统  迭代函数系统   OpenGL   松柏科树叶

Abstract
Fractal theory is a science newly developed in the past 20 to 30 years, it can describe roughness and irregular geometric shapes in the nature or in non-linear system. Although the shapes of plants various species is difference, they have the common character of self-similarity and self-reproduce. With the development of fractal theory, simulate plants using fractal became an important problem on computer simulate field. The reason is that the fractal geometry can be well described using traditional tools for geometric description will encounter great difficulties complex the natural landscape simulation can be very vivid description of the beauty of nature, was amazing natural features simulated images.
There are two methods for natural scenery simulation, L-system method and IFS system method, making a comparison between the two methods, and implementing 3D scenery fractal generation by means of the visualizing. This paper discusses deeply the scenery structure shape, dynamic generated process in accordance with the characteristics of simple generated law and complicated practice process of L-system. Since the hierarchical traverse calculation is used, the practice process will greatly be simplified, the information transmission speed will be increased, and the information storage will be reduced. For IFS system., by analyzing the typical graphic examples, the natural scenery simulated is more similar to the real object by the triangle method.
Iterated function system (IFS) is one of the main formation ways to generate fractal graphics, and its attractor is good enough to simulate natural objects and scenery, but it is difficult to find the IFS parameters for simulation. In this paper, the fractal theory in computer graphics applications, Fractal - based simulation of natural phenomena technical studies on coniferous tree leaves generation simulation technology. Using Iterated Function System Simulation natural landscape, in OpenGL environment with fractal theory, coniferous map out the three-dimensional plant leaves, and can be from a different perspective here. Through studying simulation of natural phenomena, the basic methodology implemented in the computer simulation of coniferous leaves generation.

Key words：  fractal theory；L-system； iteration function system；OpenGL； Coniferous tree leaves

目录
1 绪论  1
1.1 序言  1
1.2 课题的内容及研究方法  1
1.3 分形的定义及发展简介  2
2 L-系统的景物模拟及生成规则  7
2.1 L-系统简介及原理  7
2.2 L-系统对植物结构的模拟  9
2.3 L-系统算法  10
3迭代函数系统景物模拟及分形生成  12
3.1迭代函数系统的主要思想  12
3.2迭代函数系统的基本理论  13
4分形景物的生成  16
4.1分形植物的生成  16
4.2分形树叶的生成  16
5分形理论中有待解决的问题及分形的应用前景  22
5.1分形理论中有待解决的问题  22
5.2分形的应用前景  22
5.3目前国内外分形研究现状和展望  23
6结论与展望  27
6.1结论  27
6.2进一步研究方向  27
7实验结果  23
7.1几种分形图生成方法的比较  29
7.2一组确定性L-系统模拟植物图片  29
7.3一组IFS模拟植物图片  30
参考文献  32
致 谢 辞  33
附录1 外文原文  35
附录2 中文译文  46

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