基于L系统的植物三维建模方法的研究及实现
摘要
本文针对传统几何分形图形生成过程中的过多重复，提出了几何分形图形动态生成模式这一概念；从多个角度对L系统植物建模机制进行了理论分析，给出了植物属性算法及相关公式，构造出了七类典型植物的模型；将几何分形图形动态生成模式推广到非严格自相似的分形集生成，并改进了L系统植物建模算法；为了更真实模拟树枝弯曲的现象，将自由曲线曲面造型技术中的扫描造型法成功应用于树枝几何体构造中，通过编程实践，获得了较逼真的计算机植物模拟图形。
This paper advances a novel dynamic growth model of fractal collection, in contrast to the old static growth model , which is of a shortage of overly repeating the same process in create a fractal graphic. The new model of fractal collection can evidently reduce the number of recursion in the middle of generating graphic, make the course more
simply and more effectively. Later this new model has been used in the improvement L-system algorithms of plant modeling, receive good result, and it testify that this new model is of validity. After analyzing L-system theory, the paper give a new plant property arithmetic (including some formulas) which can enhance the reality of a computer tree figure .Seven typical three dimensions plant model are afforded on the basis of the above new conclusion, acquire seven high quality plant graphics. In order to better simulating the crook branch, the paper makes use of the sweeping surface in free-form curve and surface. The technique of sweeping surface is a useful 3D geometric construction method in the CAD, CAM field. A smooth curve cylinder geometry object trunk which has good geometric continuity is produced 6y trie way in trie later .So a beautiful 'curve structure ' tree appears .
This paper advances a novel dynamic growth model of fractal collection, in contrast to the old static growth model , which is of a shortage of overly repeating the same process in create a fractal graphic. The new model of fractal collection can evidently reduce the number of recursion in the middle of generating graphic, make the course more
simply and more effectively. Later this new model has been used in the improvement L-system algorithms of plant modeling, receive good result, and it testify that this new model is of validity. After analyzing L-system theory, the paper give a new plant property arithmetic (including some formulas) which can enhance the reality of a computer tree figure .Seven typical three dimensions plant model are afforded on the basis of the above new conclusion, acquire seven high quality plant graphics. In order to better simulating the crook branch, the paper makes use of the sweeping surface in free-form curve and surface. The technique of sweeping surface is a useful 3D geometric construction method in the CAD, CAM field. A smooth curve cylinder geometry object trunk which has good geometric continuity is produced 6y trie way in trie later .So a beautiful 'curve structure ' tree appears .
引文
[1] A.Lindenmayer,Mathematical models for cellular interaction in development,Parts Ⅰ and Ⅱ,Journal of Theoretical Biology,18,1968,280-315．
[2] Prusinkiewicz P,Lindenmayer A.The Algorithmic Beauty of Plants, New Springer-Verlag,1990,235-248．
[3] Oppenheimer PE,Real Time Design and Animation of Fractal Plants and Trees,SIGRRAPH' 86,1986,20(4) :55-64;
[4] Reeves W.T.Particle System-A Technique For Modeling of Fuzzy Object,Computer Graphics,1983．
[5] Weber,PennJ,Creation and Rendering of Realistic Trees,SIGRRAPH'95 1995,119-127．
[6] MF.Bamsley,S.Demko,Iterated function systems and the global construction of fractals,IProc.Royal Soc.London,A399,1985,243-275．
[7] A.D.Bell,D.Roberts,A.Smith,Branching patterns:the simulation of plant architecture,Journal of Theoretical Biology,81:351-375, 1979
[8] Smith A R,Plants,fractals and formal languages,Computer Graphics,1984,18 (3) ,1-10．
[9] B.B.Mandelbrot,The fractal geometry of nature.W.H.Freeman,San Francisco,1982
[10] Mercer,oit Mandelbrot,Les Objets Fractals,Beijing World Publishing Corporation,1995,17-24,In Chinese (中文版).
[11] A.R.Smith.Plants,Fractals and Formal Languages,Computer Graphics (SIGGRAPH 84 Proceedings),18(3) :1-10,1984．
[12] H.Abelson,A.A.diSessa,Turtle geometry,M.I.T.Press,Cambridge, 1982．
[13] P.Prusinkiewicz,M.Hammel,J.Hanan,R.Mech:L-systems,From The Theory to Visual Model of Plants,Proceeding of the 2 nd CSIRO
Symposium on Computational Challenges in Life Sciences,1996． Document is available at the internet address http://www.cpsc.ucalgary.ca/Redirect/bmv/papers/1-sys.csiro96． ht ml
[14] Glassner ,A.S.Prusinkiewicz P,Hanan J (1990) Visualization of botanical structures and processes,In D.Thalmann editor,Scientific Visualization and Graphics Simulation,pages 183-201． J.Wiley & Sons,Chich-ester,"Geometric Substitution :A Tutorial" ,IEEE Computer Graphics and Application,1992,12(1) ,22-36．
[15] R.Mech,P.Prusinkiewicz,and J.Hanan,Extensions to the graphical interpretation of L-systems based on turtle geometry,Department of Computer Science University of Calgary,Calgary,Alberta,Canada T2N 1N4 e-mail: mech jpwp@cpsc.ucalgary.ca,or e-mail :jim@ctpm.uq.oz.au
[16] L.Piegl,W.Tiller,The NURBS Book,Springer,Heidelberg,1995．
[17] G.Farin,Curves and Surfaces for Compter Aided Geometric Design: A Practical Guide,4 th Edition,Academic Press,Boston 1996．
[18] Eck,M.Hoppe,Automatic Reconstruction of B-Spline Surfaces of Arbitrary Topological Type.Computer Graphics (Proc. SIGGRAPH'1996) : 325-334
[19] Farin,G,Curves and Surfaces for Computer Aided Geometric Design,A Practical Guide,4． ed,Academic Press,1996
[20] Welch,Witkin ,Free-Form Shape Design,Using Triangulated Surfaces. Computer Graphics (Proc.SIG-GRAPH'94) : 247-256
[21] do Carmo,M.P,Differential Geometry of Curves and Surfaces, Prentice Hall,1976
[22] G.Farin,Nurbs: From Projective Geometry to Practical Use,A K Peters Ltd,2nd edition,1999．
[23] J.W.Peterson,Tessellation of NURBS Surfaces,Graphic,Gems Ⅳ,Academic Press,1994 ,286-320．
[24]Rogers DF, Fog NG Constrained B-Spline Curve and Surface Fitting, Computer Aided Design ,1989,21: 641-648.
[25]R. Barrels, J. Beatty, and B. Barsky, editors, An introduction to splines for use in computer graphics and geometric modeling, Morgan Kaufman, Los Altos, California.
[26]E. Catmull and J. Clark, Recursively Generated B-spline Surfaces,Computer Aided Design, 10(6):350-355, 1978.
[27]孙家广，计算机图形学，清华大学出版社，1998，308-318，347-353，463-466。
[28]唐泽圣，周嘉玉等，计算机图形基础，清华大学出版社，1995，187-196。
[29]王义豹，计算机图形原理与编程，天津科学技术出版社，1993，321-331。
[30]彭群生 鲍虎军等，计算机真实感图形的算法基础，科学出版社，1999，14-420。
[31]陈元琰 张晓竟等，计算机图形学实用技术，科学出版社，2000，226-235。
[32]余祥宣 崔国华等，计算机算法基础，华中理工大学出版社，2000，13-14，29-33。
[33]白建军，OPENGL三维图形设计与制作，1999，137-229。
[34]罗杰斯，石教英等译，计算机图形学的算法基础，科学出版社，1987，125-131。
[35]齐东旭，分形及其计算机生成．科学出版社，1994，35-47．
[36]Kenneth Falconer,曾文曲译，分形几何---数学基础及其应用，东北大学出版社，1991，154-186。
[37]方逵，曲线曲面设计技术与显示原理，国防科技大学出版社，1997，188-204。
[38]朱心雄等，自由曲线曲面造型技术，科学出版社，2000，113-132。
[39]施法中，计算机辅助几何设计与非均匀有理B样条，北京航空航天大学出版社，1994，237-253，264-270。
[40]张谦等，几何分形图形的动态方向准则，计算机工程与科学，Vol18，No2，1996，4，73-78。
[41]朱田 刘文于等，计算机图形学中分形方法的研究，计算机工程，1994，2，34-38。
[42]陈昭炯，基于L系统的植物结构形态模拟方法，计算机辅助设计与图形学学报，2000，12(8)，571-574。
[43]张金秋 范总琳，L系统统生成树的计算机模拟，华侨大学学报，No1993，4，501—517。
[44]毛卫强 耿卫东 潘云鹤，基于特征综和的植物建模方法，计算机辅助设计与图形学学报，Vol 12，No 8，2000，8，595-600。
[45]李钢 刘华明，基于NURBS的扫描曲面造型方法的研究，机械研究与应用，Vol 13，NO 3，2000，9，5-6。
[46]秦开怀 孙家广，三次NURBS曲线的插值方法，计算机辅助设计与图形学学报，Vol 5，No 3，1993，7，179-183。
[47]范劲松 郭钢，利用NURBS进行复杂形体的设计，重庆大学学报(自然科学版)，Vol 19，No 1，1996，1，18-25。
[48]张翔立 王明礼，NURBS插值曲面的构造方法，华中理工大学学报，Vol 21，No 4，1993，8，13-19。
[49]张乐年 周来水，基于复杂曲线的NURBS蒙皮曲面，工程图学报，1996，2，58-63。
[50]王哲，王知行，NURBS曲线、曲面造型过程的可视化设计，机械设计，1999 5，13-15。
[51]张树兵 王建中，基于L系统植物建模方法的改进，中国图象图形学报，2002，5
[2] Prusinkiewicz P,Lindenmayer A.The Algorithmic Beauty of Plants, New Springer-Verlag,1990,235-248．
[3] Oppenheimer PE,Real Time Design and Animation of Fractal Plants and Trees,SIGRRAPH' 86,1986,20(4) :55-64;
[4] Reeves W.T.Particle System-A Technique For Modeling of Fuzzy Object,Computer Graphics,1983．
[5] Weber,PennJ,Creation and Rendering of Realistic Trees,SIGRRAPH'95 1995,119-127．
[6] MF.Bamsley,S.Demko,Iterated function systems and the global construction of fractals,IProc.Royal Soc.London,A399,1985,243-275．
[7] A.D.Bell,D.Roberts,A.Smith,Branching patterns:the simulation of plant architecture,Journal of Theoretical Biology,81:351-375, 1979
[8] Smith A R,Plants,fractals and formal languages,Computer Graphics,1984,18 (3) ,1-10．
[9] B.B.Mandelbrot,The fractal geometry of nature.W.H.Freeman,San Francisco,1982
[10] Mercer,oit Mandelbrot,Les Objets Fractals,Beijing World Publishing Corporation,1995,17-24,In Chinese (中文版).
[11] A.R.Smith.Plants,Fractals and Formal Languages,Computer Graphics (SIGGRAPH 84 Proceedings),18(3) :1-10,1984．
[12] H.Abelson,A.A.diSessa,Turtle geometry,M.I.T.Press,Cambridge, 1982．
[13] P.Prusinkiewicz,M.Hammel,J.Hanan,R.Mech:L-systems,From The Theory to Visual Model of Plants,Proceeding of the 2 nd CSIRO
Symposium on Computational Challenges in Life Sciences,1996． Document is available at the internet address http://www.cpsc.ucalgary.ca/Redirect/bmv/papers/1-sys.csiro96． ht ml
[14] Glassner ,A.S.Prusinkiewicz P,Hanan J (1990) Visualization of botanical structures and processes,In D.Thalmann editor,Scientific Visualization and Graphics Simulation,pages 183-201． J.Wiley & Sons,Chich-ester,"Geometric Substitution :A Tutorial" ,IEEE Computer Graphics and Application,1992,12(1) ,22-36．
[15] R.Mech,P.Prusinkiewicz,and J.Hanan,Extensions to the graphical interpretation of L-systems based on turtle geometry,Department of Computer Science University of Calgary,Calgary,Alberta,Canada T2N 1N4 e-mail: mech jpwp@cpsc.ucalgary.ca,or e-mail :jim@ctpm.uq.oz.au
[16] L.Piegl,W.Tiller,The NURBS Book,Springer,Heidelberg,1995．
[17] G.Farin,Curves and Surfaces for Compter Aided Geometric Design: A Practical Guide,4 th Edition,Academic Press,Boston 1996．
[18] Eck,M.Hoppe,Automatic Reconstruction of B-Spline Surfaces of Arbitrary Topological Type.Computer Graphics (Proc. SIGGRAPH'1996) : 325-334
[19] Farin,G,Curves and Surfaces for Computer Aided Geometric Design,A Practical Guide,4． ed,Academic Press,1996
[20] Welch,Witkin ,Free-Form Shape Design,Using Triangulated Surfaces. Computer Graphics (Proc.SIG-GRAPH'94) : 247-256
[21] do Carmo,M.P,Differential Geometry of Curves and Surfaces, Prentice Hall,1976
[22] G.Farin,Nurbs: From Projective Geometry to Practical Use,A K Peters Ltd,2nd edition,1999．
[23] J.W.Peterson,Tessellation of NURBS Surfaces,Graphic,Gems Ⅳ,Academic Press,1994 ,286-320．
[24]Rogers DF, Fog NG Constrained B-Spline Curve and Surface Fitting, Computer Aided Design ,1989,21: 641-648.
[25]R. Barrels, J. Beatty, and B. Barsky, editors, An introduction to splines for use in computer graphics and geometric modeling, Morgan Kaufman, Los Altos, California.
[26]E. Catmull and J. Clark, Recursively Generated B-spline Surfaces,Computer Aided Design, 10(6):350-355, 1978.
[27]孙家广，计算机图形学，清华大学出版社，1998，308-318，347-353，463-466。
[28]唐泽圣，周嘉玉等，计算机图形基础，清华大学出版社，1995，187-196。
[29]王义豹，计算机图形原理与编程，天津科学技术出版社，1993，321-331。
[30]彭群生 鲍虎军等，计算机真实感图形的算法基础，科学出版社，1999，14-420。
[31]陈元琰 张晓竟等，计算机图形学实用技术，科学出版社，2000，226-235。
[32]余祥宣 崔国华等，计算机算法基础，华中理工大学出版社，2000，13-14，29-33。
[33]白建军，OPENGL三维图形设计与制作，1999，137-229。
[34]罗杰斯，石教英等译，计算机图形学的算法基础，科学出版社，1987，125-131。
[35]齐东旭，分形及其计算机生成．科学出版社，1994，35-47．
[36]Kenneth Falconer,曾文曲译，分形几何---数学基础及其应用，东北大学出版社，1991，154-186。
[37]方逵，曲线曲面设计技术与显示原理，国防科技大学出版社，1997，188-204。
[38]朱心雄等，自由曲线曲面造型技术，科学出版社，2000，113-132。
[39]施法中，计算机辅助几何设计与非均匀有理B样条，北京航空航天大学出版社，1994，237-253，264-270。
[40]张谦等，几何分形图形的动态方向准则，计算机工程与科学，Vol18，No2，1996，4，73-78。
[41]朱田 刘文于等，计算机图形学中分形方法的研究，计算机工程，1994，2，34-38。
[42]陈昭炯，基于L系统的植物结构形态模拟方法，计算机辅助设计与图形学学报，2000，12(8)，571-574。
[43]张金秋 范总琳，L系统统生成树的计算机模拟，华侨大学学报，No1993，4，501—517。
[44]毛卫强 耿卫东 潘云鹤，基于特征综和的植物建模方法，计算机辅助设计与图形学学报，Vol 12，No 8，2000，8，595-600。
[45]李钢 刘华明，基于NURBS的扫描曲面造型方法的研究，机械研究与应用，Vol 13，NO 3，2000，9，5-6。
[46]秦开怀 孙家广，三次NURBS曲线的插值方法，计算机辅助设计与图形学学报，Vol 5，No 3，1993，7，179-183。
[47]范劲松 郭钢，利用NURBS进行复杂形体的设计，重庆大学学报(自然科学版)，Vol 19，No 1，1996，1，18-25。
[48]张翔立 王明礼，NURBS插值曲面的构造方法，华中理工大学学报，Vol 21，No 4，1993，8，13-19。
[49]张乐年 周来水，基于复杂曲线的NURBS蒙皮曲面，工程图学报，1996，2，58-63。
[50]王哲，王知行，NURBS曲线、曲面造型过程的可视化设计，机械设计，1999 5，13-15。
[51]张树兵 王建中，基于L系统植物建模方法的改进，中国图象图形学报，2002，5
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |