分形图形及其在CAID中的应用研究
|
摘要
分形理论在计算机图形设计中的应用,目前也是局限于对一些常见的分形图形的绘制。而利用分形理论来生成的计算机图形,是用一般的平面图形设计软件很难生成的具有自相似的图形,且一般的平面图形设计的软件生成的图形都是按照经典的欧氏几何来进行图形的算法的建立,这样就很难逼真、形象地描述自然界的美,构造出绚丽多彩的分形图形。
本文对分形图形的计算机生成算法以及其在CAID中的应用进行了深入的研究,利用Visual C++ 6.0良好的用户界面和强大的图形编程技术,实现一些经典分形图的生成软件。在计算机上生成牛顿迭代分形图,以及Mandelbrot集、Julia集等经典分形图形。同时软件功能还包括分形图形的应用,使用纹理映射算法,将生成的图形映射到三维实体模型表面,使系统拥有比较好的三维立体显示效果,充分体现分形图形的欣赏价值和实际应用价值。通过计算机生成的分形图形,可以提供给广告、包装、家居设计等所需的精美图案。
本文详细研究了基于逃逸时间算法、牛顿迭代法生成的分形图形,通过研究,改进了逃逸时间函数并提出了一种改进的逃逸时间算法,在保持图形精度的情况下,大大提高了绘制图形的效率。在研究过程中,详细研究了分形图形的颜色渲染方法,采取颜色渐变算法实现颜色复杂渐变,使得生成的分形图形色彩丰富,绚烂美丽,具有很好的艺术效果,为艺术设计提供广阔的艺术空间。
The application of the fractal theory in computer graphic design can only draw some general fractal graphic. It can not draw the fractal graphic by using some graphic design software. And it is hard to describe the beauty of natural.
The study focused on the method of drawing fractal graphics by using computer and the application of fractal graphic in CAID(Computer Aided Industry Design).It took advantage of Visual C++ 6.0 in the better user interface and programming technology;the paper can realize the software of drawing fractal images. In virtue of the knowledge related to fractal theory,it has already been realized on computer to draw some fractal graphics,such as Newton iteration fractal graphics,Mandelbrot set,Julia set and so on. Meanwhile,the fractal image can be mapped on a surface of 3D model,by the color texture mapping algorithm. Using the fractal theory to the device of computer graphic, it can not only draw many beautiful fractal graphic but also can offer the width space of device graphic for the device of advertisement,the decoration of house.
Based on the analyses and research the arithmetic of escape-time and Newton iteration,this article redefined the escape time function and provides the accelerated escape time algorithm. Through a great lot data validation,keeping the aboriginal-precision,this algorithm makes the efficiency increase prominently. Then,this article gives several fractal patterns that are applied to product design by analyzing and researching the arithmetic of color rendering. And many beautiful and colorful fractal pictures are worked out to apply on product design by the new method of rendering. Also it offer the width space of art design.
本文对分形图形的计算机生成算法以及其在CAID中的应用进行了深入的研究,利用Visual C++ 6.0良好的用户界面和强大的图形编程技术,实现一些经典分形图的生成软件。在计算机上生成牛顿迭代分形图,以及Mandelbrot集、Julia集等经典分形图形。同时软件功能还包括分形图形的应用,使用纹理映射算法,将生成的图形映射到三维实体模型表面,使系统拥有比较好的三维立体显示效果,充分体现分形图形的欣赏价值和实际应用价值。通过计算机生成的分形图形,可以提供给广告、包装、家居设计等所需的精美图案。
本文详细研究了基于逃逸时间算法、牛顿迭代法生成的分形图形,通过研究,改进了逃逸时间函数并提出了一种改进的逃逸时间算法,在保持图形精度的情况下,大大提高了绘制图形的效率。在研究过程中,详细研究了分形图形的颜色渲染方法,采取颜色渐变算法实现颜色复杂渐变,使得生成的分形图形色彩丰富,绚烂美丽,具有很好的艺术效果,为艺术设计提供广阔的艺术空间。
The application of the fractal theory in computer graphic design can only draw some general fractal graphic. It can not draw the fractal graphic by using some graphic design software. And it is hard to describe the beauty of natural.
The study focused on the method of drawing fractal graphics by using computer and the application of fractal graphic in CAID(Computer Aided Industry Design).It took advantage of Visual C++ 6.0 in the better user interface and programming technology;the paper can realize the software of drawing fractal images. In virtue of the knowledge related to fractal theory,it has already been realized on computer to draw some fractal graphics,such as Newton iteration fractal graphics,Mandelbrot set,Julia set and so on. Meanwhile,the fractal image can be mapped on a surface of 3D model,by the color texture mapping algorithm. Using the fractal theory to the device of computer graphic, it can not only draw many beautiful fractal graphic but also can offer the width space of device graphic for the device of advertisement,the decoration of house.
Based on the analyses and research the arithmetic of escape-time and Newton iteration,this article redefined the escape time function and provides the accelerated escape time algorithm. Through a great lot data validation,keeping the aboriginal-precision,this algorithm makes the efficiency increase prominently. Then,this article gives several fractal patterns that are applied to product design by analyzing and researching the arithmetic of color rendering. And many beautiful and colorful fractal pictures are worked out to apply on product design by the new method of rendering. Also it offer the width space of art design.
引文
[1] Mandelbrot B B,Fractal:Form,Chance and Dimension,San Francisco:Freeman,1977:1～20
[2] Mandelbrot B B,The Fractal Geometry of Nature,San Francisco:Freeman,1982:1～23
[3]李后强,分形研究的若干问题及动向,合肥:中国科学技术大学出版社,1993:1～4
[4] Ljubisa,M.Kcic,AIFS-A Tool for Biomorphic Fractal Modeling,Nonlinear Dynamics,Psychology,and Life Scineces,2001,1
[5] ALF JONSSON,ANNA KAMONT,Piecewise linear bases and Besov spaces on fractal sets,Analysis Mathematica,27(2001)
[6] Michael Frame,Tatiana Cogevina,An infinite circle inversion limit set fractal,Computers &Graphics,24(2000)797～804
[7] K.W.Chung,H.S.Y.Chan,B.N.Wang,Efficient generation of hyperbolic symmetriesfrom dynamics,Chaos,Solitons and Fractals,13 (2002) 1175-1190
[8]李哲林,蔡秀云,刘就女,分形图案的球面投影的实现,计算机应用与软件,2004,4(21)
[9]王兴元,梁庆永,一类IFS吸引子界与动力学特征定量观测,大连理工大学学报第44卷第1期2004.1
[10]马石安,陈传波,基于迭代函数系统IFS的森林景物的动态模拟技术的研究,计算机工程与应用2002.11 [ 11 ] Saied , Effat A Anomalous , Diffusion on Fractal Objects : Additional Analytic Solutions.Chaos,Solitons & Fractals,2000, 11(9):1369-1376
[12]王瑞英,分形几何的特征及其维数,德州学院学报,2001,17(2):21～22
[13]曾文曲,等,分形理论与分形的计算机模拟,沈阳:东北大学出版社,1993:1～23
[14]张济忠,分形,北京:清华大学出版社,1995:7～110
[15]王东生,等,混沌、分形及其应用,合肥:中国科学技术大学出版社,1996:32～33,76～77
[16]胡瑞安,等,分形的计算机图像及其应用[M],北京:中国铁道出版社, 1995:113～137
[17]肯尼思,法尔科内,《分形几何-数学基础及其应用》[M],东北大学出版社,2001
[18] Kenneth.J.F,分形几何—数学基础及其应用(曾文曲,等译),东北大学出版社,1993
[19]胡纪阳,胡瑞安,Mandelbrot集及非线性过程的可视化,计算机辅助设计及图形学学报,1995:113～117
[20] Saber N.Elaydi,Discrete Chaos[M],The United States American:Trinity University Press,2000
[21] Barnsly MF,Fractal everywhere[M],Boston:Academic Press Professional,1993
[22] Bhavsar Virendra C,Gujar Uday G,Vangala Nagarjuna,Vectorization of generation of fractals from z=z 2 +c on IBM 3090/180VF,Computers&graphics,1993,17(2):P169～174
[23]胡纪阳,胡瑞安,Mandelbrot集及非线性过程的可视化,计算机辅助设计及图形学学报,No.6,2002
[24]冯玲,基于逃逸时间算法的M-集渲染方法的研究[J],计算机工程与应用,2003.12
[25]庞明勇,卢章平,一种基于逃逸时间算法的M-集渲染方法[J],计算机工程与应用,2003.12:121～123
[26]李宋,吴文权,等,颜色渐变的算法研究[J],上海理工大学学报,2004,26(3):224～228
[27]朱伟勇,付冲,陈良生,科学与艺术的结晶《Mandelbrot-Julia混沌分形图谱》[J],沈阳大学学报,2004,16(6)
[28]夏敏学,孙清华,居里叶分形在图案设计中的应用[J],空军雷达学报,2005,19(1)
[29]于红志,基于Julia集的花型图案绘制[J],大连大学学报,2003,24(4)
[30]李自胜,石宣化,秦小屿,一种于逃逸时间算法生成分形图像的加算法[J],四川工业学院学报,2003,22(3)
[31]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,1993:1163～1741
[32]曾文曲、刘世耀,等译,分形几何-数学基础及其应用[M],沈阳:东北大学出版社,1991:1266～2911
[33]叶瑞松,复动力系统生成的拟3D分形图像[J],计算机辅助设计与图形学学报,2001,(10):865～867.
[34]朱华锋,谭建荣,基于广义Mandelbrot集的复动力系统分形特性[J],小型微型计算机系统,2000,(11):1162～1165
[35]王兴元,顾树生,负实数阶J集的演化[J],中国图像图形学报(A版),2001,(5):491～494
[36] Sidharth.B.G,Issues in Quantized Fractal Space-time,Chaos,Solitions and Fractals, 2001, 12(8):P1149～1457
[37] Saber,N.Elaydi,Discrete Chaos[M],The United States of American:Trinity University Press,2000
[38] Barnsly MF,Fractal everywhere[M],Boston:Academic Press Professional,1993
[39]秦宣云,任波,逃逸时间法生成Julia集的算法分析和具体实现[J],计算机工程与应用,2007.5
[40]龙熙华,等,数值分析,陕西:陕西科学技术出版社,2000:20～22
[2] Mandelbrot B B,The Fractal Geometry of Nature,San Francisco:Freeman,1982:1～23
[3]李后强,分形研究的若干问题及动向,合肥:中国科学技术大学出版社,1993:1～4
[4] Ljubisa,M.Kcic,AIFS-A Tool for Biomorphic Fractal Modeling,Nonlinear Dynamics,Psychology,and Life Scineces,2001,1
[5] ALF JONSSON,ANNA KAMONT,Piecewise linear bases and Besov spaces on fractal sets,Analysis Mathematica,27(2001)
[6] Michael Frame,Tatiana Cogevina,An infinite circle inversion limit set fractal,Computers &Graphics,24(2000)797～804
[7] K.W.Chung,H.S.Y.Chan,B.N.Wang,Efficient generation of hyperbolic symmetriesfrom dynamics,Chaos,Solitons and Fractals,13 (2002) 1175-1190
[8]李哲林,蔡秀云,刘就女,分形图案的球面投影的实现,计算机应用与软件,2004,4(21)
[9]王兴元,梁庆永,一类IFS吸引子界与动力学特征定量观测,大连理工大学学报第44卷第1期2004.1
[10]马石安,陈传波,基于迭代函数系统IFS的森林景物的动态模拟技术的研究,计算机工程与应用2002.11 [ 11 ] Saied , Effat A Anomalous , Diffusion on Fractal Objects : Additional Analytic Solutions.Chaos,Solitons & Fractals,2000, 11(9):1369-1376
[12]王瑞英,分形几何的特征及其维数,德州学院学报,2001,17(2):21～22
[13]曾文曲,等,分形理论与分形的计算机模拟,沈阳:东北大学出版社,1993:1～23
[14]张济忠,分形,北京:清华大学出版社,1995:7～110
[15]王东生,等,混沌、分形及其应用,合肥:中国科学技术大学出版社,1996:32～33,76～77
[16]胡瑞安,等,分形的计算机图像及其应用[M],北京:中国铁道出版社, 1995:113～137
[17]肯尼思,法尔科内,《分形几何-数学基础及其应用》[M],东北大学出版社,2001
[18] Kenneth.J.F,分形几何—数学基础及其应用(曾文曲,等译),东北大学出版社,1993
[19]胡纪阳,胡瑞安,Mandelbrot集及非线性过程的可视化,计算机辅助设计及图形学学报,1995:113～117
[20] Saber N.Elaydi,Discrete Chaos[M],The United States American:Trinity University Press,2000
[21] Barnsly MF,Fractal everywhere[M],Boston:Academic Press Professional,1993
[22] Bhavsar Virendra C,Gujar Uday G,Vangala Nagarjuna,Vectorization of generation of fractals from z=z 2 +c on IBM 3090/180VF,Computers&graphics,1993,17(2):P169～174
[23]胡纪阳,胡瑞安,Mandelbrot集及非线性过程的可视化,计算机辅助设计及图形学学报,No.6,2002
[24]冯玲,基于逃逸时间算法的M-集渲染方法的研究[J],计算机工程与应用,2003.12
[25]庞明勇,卢章平,一种基于逃逸时间算法的M-集渲染方法[J],计算机工程与应用,2003.12:121～123
[26]李宋,吴文权,等,颜色渐变的算法研究[J],上海理工大学学报,2004,26(3):224～228
[27]朱伟勇,付冲,陈良生,科学与艺术的结晶《Mandelbrot-Julia混沌分形图谱》[J],沈阳大学学报,2004,16(6)
[28]夏敏学,孙清华,居里叶分形在图案设计中的应用[J],空军雷达学报,2005,19(1)
[29]于红志,基于Julia集的花型图案绘制[J],大连大学学报,2003,24(4)
[30]李自胜,石宣化,秦小屿,一种于逃逸时间算法生成分形图像的加算法[J],四川工业学院学报,2003,22(3)
[31]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,1993:1163～1741
[32]曾文曲、刘世耀,等译,分形几何-数学基础及其应用[M],沈阳:东北大学出版社,1991:1266～2911
[33]叶瑞松,复动力系统生成的拟3D分形图像[J],计算机辅助设计与图形学学报,2001,(10):865～867.
[34]朱华锋,谭建荣,基于广义Mandelbrot集的复动力系统分形特性[J],小型微型计算机系统,2000,(11):1162～1165
[35]王兴元,顾树生,负实数阶J集的演化[J],中国图像图形学报(A版),2001,(5):491～494
[36] Sidharth.B.G,Issues in Quantized Fractal Space-time,Chaos,Solitions and Fractals, 2001, 12(8):P1149～1457
[37] Saber,N.Elaydi,Discrete Chaos[M],The United States of American:Trinity University Press,2000
[38] Barnsly MF,Fractal everywhere[M],Boston:Academic Press Professional,1993
[39]秦宣云,任波,逃逸时间法生成Julia集的算法分析和具体实现[J],计算机工程与应用,2007.5
[40]龙熙华,等,数值分析,陕西:陕西科学技术出版社,2000:20～22