基于分形的自然景物圖形的生成

電子通信論文編號(hào):TX065        論文字?jǐn)?shù):23592,頁(yè)數(shù):58

目錄
1 緒論  1
1.1 序言  1
1.2 課題的內(nèi)容及研究方法  1
1.3 分形的定義及發(fā)展簡(jiǎn)介  2
2 L-系統(tǒng)的景物模擬及生成規(guī)則  7
2.1 L-系統(tǒng)簡(jiǎn)介及原理  7
2.2 L-系統(tǒng)對(duì)植物結(jié)構(gòu)的模擬  9
2.3 L-系統(tǒng)算法  10
3迭代函數(shù)系統(tǒng)景物模擬及分形生成  12
3.1迭代函數(shù)系統(tǒng)的主要思想  12
3.2迭代函數(shù)系統(tǒng)的基本理論  13
4分形景物的生成  16
4.1分形植物的生成  16
4.2分形樹(shù)葉的生成  16
5分形理論中有待解決的問(wèn)題及分形的應(yīng)用前景  22
5.1分形理論中有待解決的問(wèn)題  22
5.2分形的應(yīng)用前景  22
5.3目前國(guó)內(nèi)外分形研究現(xiàn)狀和展望  23
6結(jié)論與展望  27
6.1結(jié)論  27
6.2進(jìn)一步研究方向  27
7實(shí)驗(yàn)結(jié)果  23
7.1幾種分形圖生成方法的比較  29
7.2一組確定性L(fǎng)-系統(tǒng)模擬植物圖片  29
7.3一組IFS模擬植物圖片  30
參考文獻(xiàn)  32
致 謝 辭  33
附錄1 外文原文  35
附錄2 中文譯文  46

 摘  要
分形學(xué)是近二、三十年才發(fā)展起來(lái)的一門(mén)新的學(xué)科，主要描述自然界和非線(xiàn)形系統(tǒng)中不光滑和不規(guī)則的幾何形體。自然界中種類(lèi)繁多的植物雖然形態(tài)千差萬(wàn)別，卻大都具有自我相似、自我繁殖的分形特征。近年來(lái)，隨著分形學(xué)的發(fā)展，分形植物模擬成為計(jì)算機(jī)仿真領(lǐng)域的重要課題，其原因在于分形幾何學(xué)可以很好的描述用傳統(tǒng)的幾何工具進(jìn)行描述時(shí)會(huì)遇到極大的困難復(fù)雜的自然景物的模擬，能很逼真的描述自然景物,獲得令人驚奇的自然景物模擬圖像。
本論文主要研究基于分形的自然景物圖形的生成。研究模擬自然景物的兩種方法L-系統(tǒng)和迭代函數(shù)系統(tǒng),在此基礎(chǔ)上利用可視化編程，對(duì)三維景物進(jìn)行了分形生成。針對(duì)L-系統(tǒng)生成規(guī)則簡(jiǎn)潔，但實(shí)現(xiàn)過(guò)程煩瑣的特點(diǎn)，本論文深入研究了景物的結(jié)構(gòu)形態(tài)、動(dòng)態(tài)生成過(guò)程等，提出一種層次遍歷的算法，大大簡(jiǎn)化了實(shí)現(xiàn)過(guò)程。針對(duì)IFS系統(tǒng)，通過(guò)對(duì)典型圖例的分析，得出IFS系統(tǒng)模擬出的自然景物較接近事物本身。
迭代函數(shù)系統(tǒng)（IFS）的吸引子能夠很好的模擬傳統(tǒng)幾何難以描述的各種自然景物。采用IFS進(jìn)行景物模擬時(shí)，需要已知構(gòu)成該IFS的各個(gè)壓縮映射的參數(shù)，但對(duì)那些無(wú)已知參數(shù)的景物就無(wú)法模擬了。本文研究了分形理論在計(jì)算機(jī)圖形學(xué)中的應(yīng)用，基于分形的自然景物模擬技術(shù)研究中關(guān)于松柏科樹(shù)葉模擬生成技術(shù)。利用迭代函數(shù)系統(tǒng)模擬自然景物，在OpenGL環(huán)境下結(jié)合分形理論，繪制出松柏科植物的三維立體葉片，并可以從不同角度進(jìn)行瀏覽。通過(guò)學(xué)習(xí)自然景物模擬的基本方法，在計(jì)算機(jī)上實(shí)現(xiàn)松柏科樹(shù)葉的模擬生成。

關(guān)鍵詞  分形  L-系統(tǒng)  迭代函數(shù)系統(tǒng)   OpenGL   松柏科樹(shù)葉

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