基于迭代函数系统的分形图的研究与实现
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摘要
自然界中广泛存在着大量、复杂无规则的几何对象,它们都是传统欧氏几何学所不能描述的,而分形理论为解决大自然中千姿百态的自然景象的生成问题提供了一个新的方法。迭代函数系统(1FS)是生成分形图形的重要方法,它借助于计算机强大的迭代能力,将分形理论的精髓应用于计算机图形处理,可以产生许多具有无穷细节的分形图。
本论文是工程项目“分形图形生成算法与仿真系统的研究与实现”的一部分,主要研究使用迭代函数系统生成不同分形图的方法,以及迭代函数系统IFS参数对控制分形图不同形态的影响。首先提出了课题研究的意义和目的,阐述了分形的相关理论,研究了迭代函数系统生成分形图的基本原理和方法、以及用迭代函数系统生成分形图的应用领域。在此前提下,分析了已有的随机迭代算法存在的不足之处,并针对不同应用的要求,对算法作了相应的改进,实现了地板格、树木、蕨类植物、山脉等地模拟,同时实现了简单的分形动画——分形树的摇曳；另外针对已生成的分形树、蕨类植物,分析了IFS在生成分形图时,影响分形图的不同结构形态的特征参数,通过控制不同特征参数,实现了同一对象不同形态的分形图。最后,结合OpenGL图形接口,通过对山脉的模拟,探讨了OpenGL和IFS相结合生成分形图的方法,提出了山脉模拟的改进算法,并通过OpenGL提供的光照模型与色彩渲染等技术,实现了真实感山脉的绘制输出,克服了传统随机迭代算法绘制山脉的色彩单一、层次感不强的不足。算法的改进之处在于在IFS构图原则和色彩构成的理论指导下,如何在山脉产生的同时,确定图中各点的颜色以及颜色的层次,使其更真实地逼近自然景物。
所有分形图都是在VC++6.0的编译环境下生成,同时从实践方面证明了本论文对工程项目中所作的研究工作是可行的,取得了预期的效果。因此,可以得出使用迭代函数系统生成分形图,可以达到用少量数据描述复杂图像的目的。
A large amount of, complicated, irregular geometric target exists extensively in the nature, they can't be described using traditional Euklidische geometry, but fractal theory provides a new approach for resolving irregular natural landscape generating.Iterated Function System (IFS) is an important means of fractal graphics generating. By means of computers powerful iterative capabilities, it makes the essence of fractal theory apply to computer graphics processing, that can generate the fractal graphics having endless number of details.
The article involves the part of project item about research and realizing of fractal figures generating algorithm and simulation system. The main task is that how to generating fractal figures based on IFS algorithm, and how to control different shape of fractal figures by IFS parameter. First of all, this thesis puts forward the meaning and purpose of the study, elaborates relevant fractal theory, studies the fundamental principle and method of generating fractal figures based on IFS, as well as fractal figures applications. On the basis of this premise, analysis inadequacy of the existence about the random iteration algorithm, and makes corresponding algorithms optimization according to requirements for different applications, and achieves a floor grid, trees, ferns, mountain simulation. At the same time, simple fractal animation-fractal tree swaying is realized; In addition, in connection with the generated fractal trees, ferns, analysis the process of the generation of IFS fractal figures to effect different characteristics parameters of different structure shape. By controlling the parameters of characteristics, the same target different forms are generated. Finally, combining OpenGL graphical interface, An improved IFS fractal algorithm for building mountain is presented,the method of building fractal figures by applying OpenGL and IFS algorithm is discussed, which can realize the output of mountain by OpenGL illumination model and color rending. This algorithm can prevent the monotonous coloring and insufficient layering in mountain simulation by conventional random iterative algorithms. Improved Algorithm is how to define color of points and the level of color to make it more realistic in building mountain by the principle of the IFS and color theory constitutes.
All fractal figures are generated in VC++ 6.0 environment. The anticipated results are obtained by experimental verification, and can justify our work as viable to project item. Therefore, using IFS method can reach the purpose that using a small amount of data to describe the complex image.
本论文是工程项目“分形图形生成算法与仿真系统的研究与实现”的一部分,主要研究使用迭代函数系统生成不同分形图的方法,以及迭代函数系统IFS参数对控制分形图不同形态的影响。首先提出了课题研究的意义和目的,阐述了分形的相关理论,研究了迭代函数系统生成分形图的基本原理和方法、以及用迭代函数系统生成分形图的应用领域。在此前提下,分析了已有的随机迭代算法存在的不足之处,并针对不同应用的要求,对算法作了相应的改进,实现了地板格、树木、蕨类植物、山脉等地模拟,同时实现了简单的分形动画——分形树的摇曳；另外针对已生成的分形树、蕨类植物,分析了IFS在生成分形图时,影响分形图的不同结构形态的特征参数,通过控制不同特征参数,实现了同一对象不同形态的分形图。最后,结合OpenGL图形接口,通过对山脉的模拟,探讨了OpenGL和IFS相结合生成分形图的方法,提出了山脉模拟的改进算法,并通过OpenGL提供的光照模型与色彩渲染等技术,实现了真实感山脉的绘制输出,克服了传统随机迭代算法绘制山脉的色彩单一、层次感不强的不足。算法的改进之处在于在IFS构图原则和色彩构成的理论指导下,如何在山脉产生的同时,确定图中各点的颜色以及颜色的层次,使其更真实地逼近自然景物。
所有分形图都是在VC++6.0的编译环境下生成,同时从实践方面证明了本论文对工程项目中所作的研究工作是可行的,取得了预期的效果。因此,可以得出使用迭代函数系统生成分形图,可以达到用少量数据描述复杂图像的目的。
A large amount of, complicated, irregular geometric target exists extensively in the nature, they can't be described using traditional Euklidische geometry, but fractal theory provides a new approach for resolving irregular natural landscape generating.Iterated Function System (IFS) is an important means of fractal graphics generating. By means of computers powerful iterative capabilities, it makes the essence of fractal theory apply to computer graphics processing, that can generate the fractal graphics having endless number of details.
The article involves the part of project item about research and realizing of fractal figures generating algorithm and simulation system. The main task is that how to generating fractal figures based on IFS algorithm, and how to control different shape of fractal figures by IFS parameter. First of all, this thesis puts forward the meaning and purpose of the study, elaborates relevant fractal theory, studies the fundamental principle and method of generating fractal figures based on IFS, as well as fractal figures applications. On the basis of this premise, analysis inadequacy of the existence about the random iteration algorithm, and makes corresponding algorithms optimization according to requirements for different applications, and achieves a floor grid, trees, ferns, mountain simulation. At the same time, simple fractal animation-fractal tree swaying is realized; In addition, in connection with the generated fractal trees, ferns, analysis the process of the generation of IFS fractal figures to effect different characteristics parameters of different structure shape. By controlling the parameters of characteristics, the same target different forms are generated. Finally, combining OpenGL graphical interface, An improved IFS fractal algorithm for building mountain is presented,the method of building fractal figures by applying OpenGL and IFS algorithm is discussed, which can realize the output of mountain by OpenGL illumination model and color rending. This algorithm can prevent the monotonous coloring and insufficient layering in mountain simulation by conventional random iterative algorithms. Improved Algorithm is how to define color of points and the level of color to make it more realistic in building mountain by the principle of the IFS and color theory constitutes.
All fractal figures are generated in VC++ 6.0 environment. The anticipated results are obtained by experimental verification, and can justify our work as viable to project item. Therefore, using IFS method can reach the purpose that using a small amount of data to describe the complex image.
引文
[1]孙博文.分形算法与程序设计——vc++实现[M].北京：科学出版社,2004.11
[2]曾文曲,王向阳等.分形理论与分形的计算机模拟[M].沈阳：东北大学出版社,2001.7
[3]沙震.分形与拟合[M].杭州：浙江大学出版社,2005.3
[4]李水根.分形[M].北京：高等教育出版社,2004.
[5]孙家广.计算机图形学[M].北京：清华大学出版社,1998.
[6]覃凤清,何小海.IFS在分形图形构造中的应用研究[J].郑州轻工业学院学报,2007,22(4)：126-128.
[7]孙霞,吴自勤.分形原理及应用[M].合肥：中国科学技术大学出版社,2003.11
[8]翟俊海,刘振鹏.基于IFS的图形模拟方法[J].河北大学学报(自然科学版),2004,24(1)：87-90.
[9]段俊生,葛素桥.用MATLAB模拟分形[J].天津商学院学报,2005.25(6)：60-64.
[10]文志英.分形几何的数学基础[M].上海：上海科技教育出版社,2000.
[11]张越川,张国旗.分形理论的科学和哲学底蕴[J].社会科学研究,2005(5)：81-86.
[12]施吉林,刘淑珍.计算机数值方法(第二版)[M].北京：高等教育出版社.2005.
[13]任哲MFC Windows应用程序设计[M].北京：清华大学出版社.2004.
[14]周长发.精通vc++图像处理编程[M].北京：电子工业出版社.2006.
[15]朱晴婷.VC++程序设计基础与实例分析[M].北京：清华大学出版社.2004.
[16]和平鸽工作室OPENGL高级编程与可视化系统开发——系统开发篇[M].北京：中国水利水电出版社.2006.
[17]郭兆荣.VC++和OPENGL应用程序开发[M].北京：人民邮电出版社.2006.6
[18]刘静华,王永生.最新VC++绘图程序设计技巧与实例教程[M].北京：科学出版社.2001.
[19]仲兰芬,王琰,程磊.三维分形树木IFS生成算法[J].沈阳理工大学学报,2005,24(1)：28-31.
[20]魏小鹏,周运红,张建明.自然景物的IFS建模技术研究[J].工程图学学报,2003.4：103-109.
[21]刘孝贤,张凤山.对分形参数施加随机性影响的研究[J].山东大学学报(工学版),2002,3(8)：358-363.
[22]陈倩,陈乃立.几种基于分形思想的图像生成技术[J].浙江大学学报(工学版),2001,4(11)：695-700.
[23]阮火军.递归IFS维数公式的推广[J].浙江大学学报(理学版),2000,27(3)：243-246.
[24]闫玉宝.分形图的IFS码设计[J].江苏工业学院学报,2003,15(4)：47-50.
[25]李庆忠,韩金姝.基于IFS的树木形态模拟真实感的研究[J].计算机辅助工程,2005,15(7)：86-88.
[26]张有会,李秀丽.自然树木形状的分形模拟[J].计算机工程,2000,26(9)：112-114.
[27]祁燕,王琰,申铁成.分形几何在三维树木建模中的应用[J].沈阳理工大学学报,2005,24(2)：33-36.
[28]潘陆益.IFS分形图拟仿射变换模型及其实现[J].计算机系统应用,2008.1：83-86.
[29]王瑞英,季桂林用迭代函数系统构造分形图形[J].德州学院学报,2003,19(4)：24-26.
『30]袁杰,李霞丽.迭代函数系统及其应用[J].中央民族大学学报(自然科学版),2004,13(4)：3]7-321.
[31]过润秋.基于分形法在计算机上仿真自然景观方法研究[J].计算机仿真,2005,22(12)：155-157.
[32]Dietrich A,Wald I.VRML scene graphs on an interactive ray tracing engine[J].Virtual REALITY,2004,21 (4):109-282.
[33]Donghui Xie,Menxin Wu,etal.Quantitative remote sensing research on the vegetation 3-D visual simulation based on object oriented technique[J].Geoscience and Remote Sensing Symposium,2003.7(3):3922-3924.
[34]Guan Ke, Kong Fanrang.The Generation and research of Quaternion Fractal[J].Jurnal of engineering Graphicsm,2005,(3):133-136.
[35]Jermy T.Barron,Brian p.sorge,Thmothy A.Real-Time Procedural animition of Trees[J]. eurgraghics.2001,4:35-43.
[36]Hui Fang,John C.Randomly accessible procedural Animation of Physically Approximate Turbulent Motion[J].Computer Aimntimm 2002,geneva,Switzerland,2002.
[37]Mario Polver,Michele Nappi.Speed-up In Fractal Image coding;Comparison of Methods[J]. IEEE Transactions on image Processing,2000,9(6).
[38]Bruce M A,Kevin C J.Iterated function systems with symmetry in the hyperbolic plane[J].Computer & Graphics,2000,24(20):791-796.
[39]Teewoon Tan,Hong Yan.Object recognition based on fractal neighbor distance[J].Signal Processing.2001,81:2105-2129.
[40]http://www.csc.pku.edu.cn
[2]曾文曲,王向阳等.分形理论与分形的计算机模拟[M].沈阳：东北大学出版社,2001.7
[3]沙震.分形与拟合[M].杭州：浙江大学出版社,2005.3
[4]李水根.分形[M].北京：高等教育出版社,2004.
[5]孙家广.计算机图形学[M].北京：清华大学出版社,1998.
[6]覃凤清,何小海.IFS在分形图形构造中的应用研究[J].郑州轻工业学院学报,2007,22(4)：126-128.
[7]孙霞,吴自勤.分形原理及应用[M].合肥：中国科学技术大学出版社,2003.11
[8]翟俊海,刘振鹏.基于IFS的图形模拟方法[J].河北大学学报(自然科学版),2004,24(1)：87-90.
[9]段俊生,葛素桥.用MATLAB模拟分形[J].天津商学院学报,2005.25(6)：60-64.
[10]文志英.分形几何的数学基础[M].上海：上海科技教育出版社,2000.
[11]张越川,张国旗.分形理论的科学和哲学底蕴[J].社会科学研究,2005(5)：81-86.
[12]施吉林,刘淑珍.计算机数值方法(第二版)[M].北京：高等教育出版社.2005.
[13]任哲MFC Windows应用程序设计[M].北京：清华大学出版社.2004.
[14]周长发.精通vc++图像处理编程[M].北京：电子工业出版社.2006.
[15]朱晴婷.VC++程序设计基础与实例分析[M].北京：清华大学出版社.2004.
[16]和平鸽工作室OPENGL高级编程与可视化系统开发——系统开发篇[M].北京：中国水利水电出版社.2006.
[17]郭兆荣.VC++和OPENGL应用程序开发[M].北京：人民邮电出版社.2006.6
[18]刘静华,王永生.最新VC++绘图程序设计技巧与实例教程[M].北京：科学出版社.2001.
[19]仲兰芬,王琰,程磊.三维分形树木IFS生成算法[J].沈阳理工大学学报,2005,24(1)：28-31.
[20]魏小鹏,周运红,张建明.自然景物的IFS建模技术研究[J].工程图学学报,2003.4：103-109.
[21]刘孝贤,张凤山.对分形参数施加随机性影响的研究[J].山东大学学报(工学版),2002,3(8)：358-363.
[22]陈倩,陈乃立.几种基于分形思想的图像生成技术[J].浙江大学学报(工学版),2001,4(11)：695-700.
[23]阮火军.递归IFS维数公式的推广[J].浙江大学学报(理学版),2000,27(3)：243-246.
[24]闫玉宝.分形图的IFS码设计[J].江苏工业学院学报,2003,15(4)：47-50.
[25]李庆忠,韩金姝.基于IFS的树木形态模拟真实感的研究[J].计算机辅助工程,2005,15(7)：86-88.
[26]张有会,李秀丽.自然树木形状的分形模拟[J].计算机工程,2000,26(9)：112-114.
[27]祁燕,王琰,申铁成.分形几何在三维树木建模中的应用[J].沈阳理工大学学报,2005,24(2)：33-36.
[28]潘陆益.IFS分形图拟仿射变换模型及其实现[J].计算机系统应用,2008.1：83-86.
[29]王瑞英,季桂林用迭代函数系统构造分形图形[J].德州学院学报,2003,19(4)：24-26.
『30]袁杰,李霞丽.迭代函数系统及其应用[J].中央民族大学学报(自然科学版),2004,13(4)：3]7-321.
[31]过润秋.基于分形法在计算机上仿真自然景观方法研究[J].计算机仿真,2005,22(12)：155-157.
[32]Dietrich A,Wald I.VRML scene graphs on an interactive ray tracing engine[J].Virtual REALITY,2004,21 (4):109-282.
[33]Donghui Xie,Menxin Wu,etal.Quantitative remote sensing research on the vegetation 3-D visual simulation based on object oriented technique[J].Geoscience and Remote Sensing Symposium,2003.7(3):3922-3924.
[34]Guan Ke, Kong Fanrang.The Generation and research of Quaternion Fractal[J].Jurnal of engineering Graphicsm,2005,(3):133-136.
[35]Jermy T.Barron,Brian p.sorge,Thmothy A.Real-Time Procedural animition of Trees[J]. eurgraghics.2001,4:35-43.
[36]Hui Fang,John C.Randomly accessible procedural Animation of Physically Approximate Turbulent Motion[J].Computer Aimntimm 2002,geneva,Switzerland,2002.
[37]Mario Polver,Michele Nappi.Speed-up In Fractal Image coding;Comparison of Methods[J]. IEEE Transactions on image Processing,2000,9(6).
[38]Bruce M A,Kevin C J.Iterated function systems with symmetry in the hyperbolic plane[J].Computer & Graphics,2000,24(20):791-796.
[39]Teewoon Tan,Hong Yan.Object recognition based on fractal neighbor distance[J].Signal Processing.2001,81:2105-2129.
[40]http://www.csc.pku.edu.cn