基于L-系统的分形图案设计
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摘要
自然景物模拟一直是计算机图形学的研究热点。自然景物包罗万象,自相似性是其相当普遍的特征,而分形几何学正是表现这一特征的重要数学工具,分形法有多种形式,需要根据实际应用合理选择。
本文通过对分形理论的研究,将分形理论与包装CAD开发结合起来。通过将分形与计算机图形学结合起来,开发出参数化的包装CAD设计系统,在计算机上模拟生成各种变幻莫测、色彩绚烂而美丽的分形图案,将这些图案用于包装装潢设计,包装防伪以及包装商标设计中既具有很好的装饰效果又具有很好的防伪效果。
本文通过对L-系统的深入研究,在L-系统符号解释扩展的基础上,利用L-系统理论,采用标准图形软件接口OpenGL和支持可视化编程的集成开发环境VC++6.0,实现了植物模拟的演示系统。另一方面,运用光照、纹理映射等技术,实现了植物生长过程的计算机模拟,生成的植物具有三维立体效果,形态逼真,符合自然生长规律。
论文在结构上首先阐述了L-系统参数化设计这个课题的研究意义,然后简要的说明了当前自然景物模拟的一些研究成果和进展。论文的主体部分对用到的L-系统的理论进行了研究,然后着重对该参数化CAD系统的功能模块进行了设计并着重介绍了三维L-系统的真实感绘制;最后对系统的实现举例。
同时,本文的研究有助于揭示自然界的一个道理:看似复杂的自然现象背后其实蕴藏着简单的规律。
Simulation of natural scene has been a hotspot in the field of computer graphics. With so many scenes included, nature often shows its self-similarity in common. An important mathematical implement, fractal geometry, characterizes this kind of feature perfectly. Fractal method has versatile representations. Choices between these forms should be according as practical need.
This paper researched the Fractal theory and suggested to combine it with Package CAD System. Combining Fractal with computer graphics, we could develop Parameterizing CAD design system of packaging. The parameter design of fractal image was realized to scenes and a series of unpredictable amazing fractal patterns. The paper aimed to upholster publicize packing merchandises and to defend fake brands.
This paper makes a deep research on L-system and integrates other extension of symbol interpretation. Then it gives a computer program to demonstrate the simulation of plant. The program is developed by VC++6.0, using the stand graphic programming interface OpenGL. On the other hand, the drawing part of the program applies the technology of illumination and texture mapping. The plant, generated by the program, thus is three-dimensional, vivid, and accord with natural law.
First the paper introduces the research status of virtual plant growth, and illustrates the significance of the task. Second it studies the theories of L-system. Third it emphasizes on the function modules of this three-dimensional L-system and how to achieve third dimension designs. Last the dissertation gives examples using virtual plant system.
At the same time the research of this dissertation helps to discover a natural principle: a seemingly complicated natural phenomenon contains simple rules.
本文通过对分形理论的研究,将分形理论与包装CAD开发结合起来。通过将分形与计算机图形学结合起来,开发出参数化的包装CAD设计系统,在计算机上模拟生成各种变幻莫测、色彩绚烂而美丽的分形图案,将这些图案用于包装装潢设计,包装防伪以及包装商标设计中既具有很好的装饰效果又具有很好的防伪效果。
本文通过对L-系统的深入研究,在L-系统符号解释扩展的基础上,利用L-系统理论,采用标准图形软件接口OpenGL和支持可视化编程的集成开发环境VC++6.0,实现了植物模拟的演示系统。另一方面,运用光照、纹理映射等技术,实现了植物生长过程的计算机模拟,生成的植物具有三维立体效果,形态逼真,符合自然生长规律。
论文在结构上首先阐述了L-系统参数化设计这个课题的研究意义,然后简要的说明了当前自然景物模拟的一些研究成果和进展。论文的主体部分对用到的L-系统的理论进行了研究,然后着重对该参数化CAD系统的功能模块进行了设计并着重介绍了三维L-系统的真实感绘制;最后对系统的实现举例。
同时,本文的研究有助于揭示自然界的一个道理:看似复杂的自然现象背后其实蕴藏着简单的规律。
Simulation of natural scene has been a hotspot in the field of computer graphics. With so many scenes included, nature often shows its self-similarity in common. An important mathematical implement, fractal geometry, characterizes this kind of feature perfectly. Fractal method has versatile representations. Choices between these forms should be according as practical need.
This paper researched the Fractal theory and suggested to combine it with Package CAD System. Combining Fractal with computer graphics, we could develop Parameterizing CAD design system of packaging. The parameter design of fractal image was realized to scenes and a series of unpredictable amazing fractal patterns. The paper aimed to upholster publicize packing merchandises and to defend fake brands.
This paper makes a deep research on L-system and integrates other extension of symbol interpretation. Then it gives a computer program to demonstrate the simulation of plant. The program is developed by VC++6.0, using the stand graphic programming interface OpenGL. On the other hand, the drawing part of the program applies the technology of illumination and texture mapping. The plant, generated by the program, thus is three-dimensional, vivid, and accord with natural law.
First the paper introduces the research status of virtual plant growth, and illustrates the significance of the task. Second it studies the theories of L-system. Third it emphasizes on the function modules of this three-dimensional L-system and how to achieve third dimension designs. Last the dissertation gives examples using virtual plant system.
At the same time the research of this dissertation helps to discover a natural principle: a seemingly complicated natural phenomenon contains simple rules.
引文
[1]李水银,吴纪桃.分形与小波[M].北京:科学出版社,2002
[2]孙博文.分形算法与程序设计——Visual C++实现[M].北京:科学出版社,2004
[3]齐尔旭.分形及其计算机生成[M].第二版.北京:科学出版社,1996.196-207
[4]P.Prusinkiewicz and A.Lindenmayer.The Algorithmic Beauty of Plants.Springer Verlag,1990.
[5]张莉,刘弘.分形艺术在产品信息防伪中的研究与应用.信息技术与信息化[J],2007,No.1:111-113,123
[6]Pascal Ferraro,Chdstophe Godin,and Przemyslaw Prusinkiewicz:Toward a quantification of self-similarity in plants.Fractals 13(2),pp.91-109.
[7]黄艳峰,薛占熬,陈涛.基于L-系统的植物模拟研究.计算机工程与应用[J],2005,No.19:53-55,165
[8]Prusinkiewicz P.Modeling of spatial structure and development of plants:a review[J].Scientia Horticulturae,1998,74:113-149
[9]韩向峰。刘希玉.基于分形理论的创新设计及其应用[D].山东:山东师范大学,2005
[10]刘华杰,分形艺术,湖南电子音像出版社,1997.
[11]Mandelbrot B.B.The Fractal Geometry of Nature[J].Freeman,San Franciso,1982:6-9.
[12]Briggs,J.Fractals.The Patterns of Chaos,Discovering aNew Aesthetic of Art,science and Nature.Simon and Schuster,New York,1992.Mandelbrot,B.B.The Fractal Geometry of Nature.Freeman,San Franciso,1982:16.
[13]Barnsley M.F.Fraetals Everywhere[M].Aeademie Press Professional,Boston,1993:6.
[14]Peitgen,H.O,Richter,P.H.The Beauty of fractals[J].Springer-Verlag,Berlin Heidelberg,1986:96-98.
[15]黄艳峰.何华灿.植物形态的分形模拟[D],陕西:西北工业大学,2004
[16]Reeves W T,Blau R.Approximate and probabilistic algorithms for shading and rendering
[17]胡包钢,赵星,严红平,植物生长建模与可视化.回顾与展望[J].自动化学报2001,27(6):816-835
[18]Lindenmayer A.Mathematical models for cellular interaction in development.Journal of Theoretical Biology,1968,18(1):280-315
[19]韩向峰,刘希玉.基于L系统的三维分形图的生成算法.计算机应用[J],2004,Vol.24 No.10:86-87,91
[20]朱岳,邹北骥.基于三维分枝模型的树木模拟算法研究及其实现[D],湖南:湖南大学,2005
[21]谷廷华,胥芳.基于L-系统的植物生长模拟研究[D].浙江:浙江工业大学,2005
[22]Prusinkiewicz P,Lindenmayer A,Hanan J.Developmental Models of Herbaceous Plants for Computer Imagery Purpose.Computer Graphics,1988,22(4):141-150
[23]Smith A R.Plant,Fractals and Formal Languages.Computer Graphics,1984,18(3):1-10
[24]Prusinkiewicz P,Hanan J,Lindenmayer.Systems,Fractals,and Plants.New York:Springer-Verlag,1989,11-89
[25]Mech R,Prusinkiewicz P.Visual Models of Plants Interacting With Their Environment.Computer Graphics,1996,30(3):397-410
[26]周春江,朱庆生.基于L系统的虚拟植物生长的模拟研究[D].重庆:重庆大学,2005
[27]张树兵,王建中.基于L-系统的植物三维建模方法的研究和实现[D]。太原:华北工学院,2002
[28]陈洁,段会川.树的三维建模[D].山东:山东师范大学,2004
[29]Przemyslaw Prusinkiewicz and Anne-Gaelle Rolland-Lagan.Modeling plant morphogenesis.Current Opinion in Plant Biology,volume 9,pp.83-88.
[30]Pascal Ferraro,Christophe Godin,and Przemyslaw Prusinkiewicz:Toward a quantification of self-similarity in plants.Fractals 13(2),pp.91-109.
[31]Kenneth J F.分形几何-数学基础及其应用[M].曾文曲,刘世耀译.沈阳:东北大学出版社,1991.173-185
[32]崔劲,徐凯声.自然景物的分形模拟[D].湖北:武汉理工大学,2005
[33]Mitch Allen,Przemyslaw Prusinkiewicz,and Theodore DeJong.Using L-systems for modeling source-sink interactions,architecture and physiology of growing trees:the L-PEACH model.New Phytologist 166,pp.869-880.
[34](美)Richard S.Wright,JL.,Benjamin Lipchak.OpenGL超级宝典[M],北京:人民邮电出版社,2005
[35]Dave Shreimer,Mason Woo,Jackie Neider,Tom Davis著.OpenGL编程指南[M],北京:人民邮电出版社,2005
[36]和平鸽工作室.OpenGL高级编程与可视化系统开发.(系统开发篇),北京:中国水利水电出版社,2006
[37]邓炜等.OpenGL视类及其在三维图形开发中的应用.现代计算机,2000
[38]刘彦宏,王洪斌.基于图像的树类物体的三维重建.计算机学报[J],2002,25(5):930-935
[2]孙博文.分形算法与程序设计——Visual C++实现[M].北京:科学出版社,2004
[3]齐尔旭.分形及其计算机生成[M].第二版.北京:科学出版社,1996.196-207
[4]P.Prusinkiewicz and A.Lindenmayer.The Algorithmic Beauty of Plants.Springer Verlag,1990.
[5]张莉,刘弘.分形艺术在产品信息防伪中的研究与应用.信息技术与信息化[J],2007,No.1:111-113,123
[6]Pascal Ferraro,Chdstophe Godin,and Przemyslaw Prusinkiewicz:Toward a quantification of self-similarity in plants.Fractals 13(2),pp.91-109.
[7]黄艳峰,薛占熬,陈涛.基于L-系统的植物模拟研究.计算机工程与应用[J],2005,No.19:53-55,165
[8]Prusinkiewicz P.Modeling of spatial structure and development of plants:a review[J].Scientia Horticulturae,1998,74:113-149
[9]韩向峰。刘希玉.基于分形理论的创新设计及其应用[D].山东:山东师范大学,2005
[10]刘华杰,分形艺术,湖南电子音像出版社,1997.
[11]Mandelbrot B.B.The Fractal Geometry of Nature[J].Freeman,San Franciso,1982:6-9.
[12]Briggs,J.Fractals.The Patterns of Chaos,Discovering aNew Aesthetic of Art,science and Nature.Simon and Schuster,New York,1992.Mandelbrot,B.B.The Fractal Geometry of Nature.Freeman,San Franciso,1982:16.
[13]Barnsley M.F.Fraetals Everywhere[M].Aeademie Press Professional,Boston,1993:6.
[14]Peitgen,H.O,Richter,P.H.The Beauty of fractals[J].Springer-Verlag,Berlin Heidelberg,1986:96-98.
[15]黄艳峰.何华灿.植物形态的分形模拟[D],陕西:西北工业大学,2004
[16]Reeves W T,Blau R.Approximate and probabilistic algorithms for shading and rendering
[17]胡包钢,赵星,严红平,植物生长建模与可视化.回顾与展望[J].自动化学报2001,27(6):816-835
[18]Lindenmayer A.Mathematical models for cellular interaction in development.Journal of Theoretical Biology,1968,18(1):280-315
[19]韩向峰,刘希玉.基于L系统的三维分形图的生成算法.计算机应用[J],2004,Vol.24 No.10:86-87,91
[20]朱岳,邹北骥.基于三维分枝模型的树木模拟算法研究及其实现[D],湖南:湖南大学,2005
[21]谷廷华,胥芳.基于L-系统的植物生长模拟研究[D].浙江:浙江工业大学,2005
[22]Prusinkiewicz P,Lindenmayer A,Hanan J.Developmental Models of Herbaceous Plants for Computer Imagery Purpose.Computer Graphics,1988,22(4):141-150
[23]Smith A R.Plant,Fractals and Formal Languages.Computer Graphics,1984,18(3):1-10
[24]Prusinkiewicz P,Hanan J,Lindenmayer.Systems,Fractals,and Plants.New York:Springer-Verlag,1989,11-89
[25]Mech R,Prusinkiewicz P.Visual Models of Plants Interacting With Their Environment.Computer Graphics,1996,30(3):397-410
[26]周春江,朱庆生.基于L系统的虚拟植物生长的模拟研究[D].重庆:重庆大学,2005
[27]张树兵,王建中.基于L-系统的植物三维建模方法的研究和实现[D]。太原:华北工学院,2002
[28]陈洁,段会川.树的三维建模[D].山东:山东师范大学,2004
[29]Przemyslaw Prusinkiewicz and Anne-Gaelle Rolland-Lagan.Modeling plant morphogenesis.Current Opinion in Plant Biology,volume 9,pp.83-88.
[30]Pascal Ferraro,Christophe Godin,and Przemyslaw Prusinkiewicz:Toward a quantification of self-similarity in plants.Fractals 13(2),pp.91-109.
[31]Kenneth J F.分形几何-数学基础及其应用[M].曾文曲,刘世耀译.沈阳:东北大学出版社,1991.173-185
[32]崔劲,徐凯声.自然景物的分形模拟[D].湖北:武汉理工大学,2005
[33]Mitch Allen,Przemyslaw Prusinkiewicz,and Theodore DeJong.Using L-systems for modeling source-sink interactions,architecture and physiology of growing trees:the L-PEACH model.New Phytologist 166,pp.869-880.
[34](美)Richard S.Wright,JL.,Benjamin Lipchak.OpenGL超级宝典[M],北京:人民邮电出版社,2005
[35]Dave Shreimer,Mason Woo,Jackie Neider,Tom Davis著.OpenGL编程指南[M],北京:人民邮电出版社,2005
[36]和平鸽工作室.OpenGL高级编程与可视化系统开发.(系统开发篇),北京:中国水利水电出版社,2006
[37]邓炜等.OpenGL视类及其在三维图形开发中的应用.现代计算机,2000
[38]刘彦宏,王洪斌.基于图像的树类物体的三维重建.计算机学报[J],2002,25(5):930-935