参数化曲线树木枝干的可视化建模技术研究
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摘要
树木的模拟是计算机图形学在林学可视化领域应用的前沿课题之一,树木的形态结构在其生长过程中起着重要的作用,在树几何建模的过程中,真实地模拟树木枝条的自然弯曲状态是一个重要的因素。论文主要研究了树木可视化建模和树木可视化场景建模两个部分。树木建模采用分形理论的迭代函数系统来完成,建模时着重实现了以参数化曲线拟合的方法来模拟枝条的自然弯曲状态。通过引进Bezier:这种基于控制点的自由曲线来拟合枝条曲线,并将枝条定义为以Bezier曲线为轴、横截面直径变化的广义圆柱体。在可视化场景的建模中,对地形生成算法进行了研究,采用随机中点位移法中的"diamond-square"算法实现了分形地形的模拟,建立了一个三维虚拟场景。实验结果表明,相较于以往用圆柱或圆台绘制的树的枝干,本文所采用的基于控制点变化的Bezier曲线能较好地模拟枝条自然弯曲和光滑连续的状态,构建的树模型能更好地反映真实树木的形态特征。
The simulation of trees is one of the leading issues of computer graphics in the field of forestry visualization applications. The morphology of trees plays an important part in their growth. In the process of tree geometry modeling, the simulation of tree branches'bending state is very important. The paper includes the tree modeling and the virtual scene building. Tree modeling uses the iterated function system based on fractal theory. The parameterized curve is used to simulate the bending state of tree branches. Bezier curve, a free curve based on controlled points, is used to simulate dynamic of the branch axis curve. Generalized cylinder, a three-dimensional with Bezier curve as the axis, is used to define the branch. In the visualization of scene, the "diamond-square" algorithm based on random midpoint displacement is used to simulate the fractal terrain. As a result, a three-dimensional virtual scene is built. Experiments show that, compared to previous branches simulated by cylinder, Bezier curve can simulate the bending and smooth state of branches better. The tree model better reflects the true characteristics of real tree.
The simulation of trees is one of the leading issues of computer graphics in the field of forestry visualization applications. The morphology of trees plays an important part in their growth. In the process of tree geometry modeling, the simulation of tree branches'bending state is very important. The paper includes the tree modeling and the virtual scene building. Tree modeling uses the iterated function system based on fractal theory. The parameterized curve is used to simulate the bending state of tree branches. Bezier curve, a free curve based on controlled points, is used to simulate dynamic of the branch axis curve. Generalized cylinder, a three-dimensional with Bezier curve as the axis, is used to define the branch. In the visualization of scene, the "diamond-square" algorithm based on random midpoint displacement is used to simulate the fractal terrain. As a result, a three-dimensional virtual scene is built. Experiments show that, compared to previous branches simulated by cylinder, Bezier curve can simulate the bending and smooth state of branches better. The tree model better reflects the true characteristics of real tree.
引文
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8.刘文进.基于迭代函数系统的树木模拟[D].辽宁：辽宁工程技术大学硕士学位论文,2005(6).
9.石松,陈崇成等.形态结构特征约束下的树木参数化建模研究[J].计算机工程,2008,34(24)：250-252.
10.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.
11.孙静静,唐丽玉等.基于形态结构特征的马尾松几何建模研究[J].林业科学,2007,43(4)：71-76.
12.王莉莉,赵沁平.一种通用的植物逼真几何建模方法[J].中国图像图形学报,2003,8(8)：932-937.
13.王英杰,袁勘省,余卓渊.多维动态地学信息可视化[M].北京：科学出版社,2003.
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15.伍艳莲,汤亮,刘小军等.基于形态特征参数的稻穗几何建模及可视化研究[J].中国农业科学,2009,42(4)：1190-1196.
16.谢绍锋,肖化顺.虚拟森林资源信息三维可视化中树模型的生成方法[J].中南林业调查规划,2007,26(1)：43-47.
17.徐杨,朱林,常明.树木三维形态结构的计算机建模[J].计算机工程与应用,2001,21：141-143.
18.严涛,陈彦云,吴恩华.一种基于单幅图像的树木深度估计与造型方法[J].计算机学报,2000,23(4)：386-392.
19.严涛.基于图象的树木造型方法的研究[D].北京：中国科学院软件研究所,2000.
20.臧润国,蒋有绪.热带树木构筑学研究概述[J].林业科学,1998,34(5)：114-119.
21.曾文曲,王向阳.分形理论与分形的计算机模拟[M].沈阳：东北大学出版社,2001.
22.张淮声,华炜,余莉,鲍虎军.基于层次多项式纹理的实时草地绘制[J].China-graph,2006:201-207.
23.张立强,童小华,杨崇俊,等.三维地形的动态生成及空间分析[J].同济大学学报,2005,6：38-42.
24.张树兵,王建中.基于L系统的植物建模方法改进[J].中国图像图形学报,2002,5：457-460.
25.赵星.忠于植物学的虚拟植物生长研究[D].安徽：中国科技大学,2001.
26.赵星.de Reffy,熊范仑,等.虚拟植物生长的双尺度自动机模型[J].计算机学报,2001,24(6)：608-615.
27.赵星,熊范纶,de Reffye.一种新的植物枝条弯曲生成算法[J].中国科学技术大学报,2001,31(6)：714-720.
28. Aono M, et al. Botanical tree image generation [J]. IEEE Computer Graphics and Application,1984, 4(5):10-34.
29.Barnsley M F, Demko S. Iterated Function Systems and the Global Construction of Fractals [J]. Proc. Roy. Soc. Lond. A.,1985,399:243-275.
30.Jirasek C, Prusinkiewicz P, Moulia B. Integrating Biomechanics into Developmental Plant Models Expressed Using L-systems [C]. In:Proceedings of the 3rd Plant Biomechanics Conference, Stuttgart,2000:615-624.
31. Dave Shreiner, Mason Woo. OpenGL Programming Guide [M]. Pearson Education, Inc.,2008.
32.Debevec P E, Taylor C J, Malik J. Modeling and Rendering Architecture from Photographs:A hybrid geometry-and image-based approach[C]. In:Computer Graphics Proceedings, Annual Conference Series, ACM SIGGRAPH, New Orleans, Louisiana,1996:11-20.
33.de Reffye P, Edelin C, Francon J, et al. Plants models faithful to botanical Structure and development [J]. Computer Graphics,1998,22(4):151-155.
34.Gilet G, Meyer A, Neyret F. Point-based rendering of trees [C]. In:Eurographics Workshop on Natural Phenomena, Dublin,2005,67-72.
35.Godin C, Sinoquet H, Costes E. A method for describing plant architecture which integrates topology and geometry [J]. Annals of Botany,1999,84(3):343-357.
36.Godin C, Carglio Y. A multiscale model of plant topological structures [J]. TheroBio,1998,84(3), 191:1-46.
37.Guennebaud G, Barthe L, Pauliny M. Deferred splatting. Computer Graphics Forum [J].2004,23(3): 653-660.
38.Haeseler, Peitgen H-O, Skordev G. Linear Cellular Automata, Substitutions, Hierarchocal Iterated Function Systems and Attractors [J]. In Fractal Geometry and Computer Graphics, J. L. Encarnacao, Peitgen H-O, Sakas G, Englert G, Eds, Springer-Verkag,1991:3-23.
39. Jules B. Modeling the mighty maple [J]. Computer Graphics,1985,19(3):305-311.
40.Karwowski R, Prusinkiewicz P. Design and implementiontation of the L+C modeling language [J]. Electionic Notes in Theoretical Compute Science 86,2(2003),134-152.
41.Kruszewski P. An algorithm for sculpting trees [J]. Computers and Graphics,1999,23:739-749.
42.Kurth W. Morphological models of Plant growth:Possibilities and ecological relevance [J]. Ecological Modeling,1994,75-76:299-308.
43.Levoy M, Whitted T. The use of points as a display primitive [R]. Technical report, CS Department, University of North Carolina at Chapel Hill,1985.
44.Linden J. Interactive view-dependent point clound rendering[C]. In:proceedings of Image and Vision Computing, Nov.2001, New Zealand,1-6.
45.Lindenmayer A. Mathematical models for cellular interactions in development [J]. TheorBiol,1968, 18:280-315.
46. Long Quan, Ping Tan, Gang Zeng, Lu Yuan, Jingdong Wang. Image-based plant modeling[C]. In: Computer Graphics Proceedings, Annual Conference Series, ACM SIGGRAPH, Boston,2006: 772-778.
47.Oppenheimer P. Real time design and animation of fractal Plants and trees [J]. Computer Graphics, 1986,20(4):55-64.
48.Paul Kruszewski, An algorithm for sculpting trees [J]. computer& graphics,1999,23(6):739-749.
49. Ping Tan, Gang Zeng, Jingdong Wang, Sing Bing Kang, Long Quan. Image-based tree modeling. In: Proceedings of SIGGRAPH 2007, ACM SIGGRAPH and ACM Trans, on Graphics, San Diego, CA, Aug.2007, Article 87:7.
50. Prusinkiewicz P, Muendermann L, Karwowski R, et al. The Use of Positional in Formation in the Modeling of Plants[C]. Computer Graphics Proceeding, Annual Conference Series, ACM SIGGRAPH, Los Angeles,2001:289-300.
51. Prusinkiewicz P, Hammel M, Language-restricted iterated function systems, Koch Constructions and L-systems [C]. In:Fractal Modeling in 3D Computer Graphics and Imagery, J C Hart (eds.). ACM SIGGRAPH, Course Note 13,1994, (4):1-14.
52. Prusinkiewicz P, Lindenmayer A. The algorithmic beauty of plants [M]. New York:Springer-Verlag, 1990.
53.Prusinkiewicz P. Modeling of spatial structure and development of plant:A review [J]. Scientia Horticulturae,1998,74:113-149.
54.Prusinkiewiez P. Modeling Plant growth and development [J]. Current Opinion in Plant Biology, 2004,7(1):79-83.
55.Qunsheng Peng, Wei H, Xuehui Y. A new approach for point-based rendering [C]. In:proceedings of Computer Graphics International 2001, Hong Kong,275-282.
56.Reeves W T. Particle systems-A technique for modeling a class of fuzzy objects [J]. Computer Graphics,1983,17(3):59-376.
57. Room P M, Hanan J S, Prusinkiewicz P. Virtual Plants:new Perspectives for ecologists, Pathologists and agricultural scientists [J]. Trends in Plant Science,1996,1(1):33-38.
58.Rusinkiewics S, Levoy M. Qsplat:A multi-resolution point rendering system for large meshes [C]. In:proceedings of Siggraph 2000, New Orleans, LA USA,343-352.
59. Smith AR. Plants, fractals, and formal languages [C]. In:Proceedings of SIGGRAPH 1984, Computer Graphics,1984,18(3):1-10.
60. Stamminger M, Drettakis G. Interactive sampling and rendering for complex and procedural geometry [C]. In:proceedings of Eurographics Workshop on Rendering,2001,231-242.
61.Julia T. Incorporating Biomechanics into Architectural Tree Models [C]. In:proceedings of SIBGRAPHI'05. Washington D. C., USA:IEEE Computer Society,2005:299-306.
62. Viennot X G, Eyrolles G. Combinatorial analysis of ramified patterns and computer imagery of trees [J]. Computer graphics,1989,23(3):31-39.
63. Wand M, Fischer M, Peter I, Meyer F, Straer W. The randomized z-buffer algorithm:interactive rendering of highly complex scenes[C]. In:proceeding of siggraph 2001,2001,363-370.
64. Weber J, Penn J. Creation and rendering of realistic trees [C]. In:Proceedings of SIGGRAPH'95, ACM SIGGRAPH, Los Angeles, California,1995:119-128.
65.Zwicker M, Pfister H, Baar J, Gross M. EWA splatting [J]. IEEE Transactions on Visualization and Graphics,2002,8(3):223-238.
2.陈敏智,丁维龙,张维统.基于参数化L系统的植物结构模型可视化模[J].浙江工业大学学报,2007,35(4)：427-430.
3.胡包钢,赵星,严红平,等.植物生长建模与可视化——回顾与展望[J].自动化学报,2001,21(6)：816-835.
4.康孟珍,de Reffye,胡包钢,等.快速构造植物几何结构的子结构算法[J].中国图象图形学报,2004,9(1)：79-86.
5.雷相东,常敏,等.虚拟树木生长建模及可视化研究综述[J].林业科学,2006,42(11)：124-131.
6.雷相东,常敏,陆元昌,等.长白落叶松单木生长可视化系统设计与实现[J].计算机工程与应用,2006,42(17)：180-183.
7.林艳梅.三维树木形态结构及风吹效果虚拟技术研究[D].陕西：西北农林科技大学,2007.
8.刘文进.基于迭代函数系统的树木模拟[D].辽宁：辽宁工程技术大学硕士学位论文,2005(6).
9.石松,陈崇成等.形态结构特征约束下的树木参数化建模研究[J].计算机工程,2008,34(24)：250-252.
10.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.
11.孙静静,唐丽玉等.基于形态结构特征的马尾松几何建模研究[J].林业科学,2007,43(4)：71-76.
12.王莉莉,赵沁平.一种通用的植物逼真几何建模方法[J].中国图像图形学报,2003,8(8)：932-937.
13.王英杰,袁勘省,余卓渊.多维动态地学信息可视化[M].北京：科学出版社,2003.
14.王永皎,莫国良,张引,张三元.植物的三维建模研究进展[J].计算机应用研究,2005,21(11)：34-37.
15.伍艳莲,汤亮,刘小军等.基于形态特征参数的稻穗几何建模及可视化研究[J].中国农业科学,2009,42(4)：1190-1196.
16.谢绍锋,肖化顺.虚拟森林资源信息三维可视化中树模型的生成方法[J].中南林业调查规划,2007,26(1)：43-47.
17.徐杨,朱林,常明.树木三维形态结构的计算机建模[J].计算机工程与应用,2001,21：141-143.
18.严涛,陈彦云,吴恩华.一种基于单幅图像的树木深度估计与造型方法[J].计算机学报,2000,23(4)：386-392.
19.严涛.基于图象的树木造型方法的研究[D].北京：中国科学院软件研究所,2000.
20.臧润国,蒋有绪.热带树木构筑学研究概述[J].林业科学,1998,34(5)：114-119.
21.曾文曲,王向阳.分形理论与分形的计算机模拟[M].沈阳：东北大学出版社,2001.
22.张淮声,华炜,余莉,鲍虎军.基于层次多项式纹理的实时草地绘制[J].China-graph,2006:201-207.
23.张立强,童小华,杨崇俊,等.三维地形的动态生成及空间分析[J].同济大学学报,2005,6：38-42.
24.张树兵,王建中.基于L系统的植物建模方法改进[J].中国图像图形学报,2002,5：457-460.
25.赵星.忠于植物学的虚拟植物生长研究[D].安徽：中国科技大学,2001.
26.赵星.de Reffy,熊范仑,等.虚拟植物生长的双尺度自动机模型[J].计算机学报,2001,24(6)：608-615.
27.赵星,熊范纶,de Reffye.一种新的植物枝条弯曲生成算法[J].中国科学技术大学报,2001,31(6)：714-720.
28. Aono M, et al. Botanical tree image generation [J]. IEEE Computer Graphics and Application,1984, 4(5):10-34.
29.Barnsley M F, Demko S. Iterated Function Systems and the Global Construction of Fractals [J]. Proc. Roy. Soc. Lond. A.,1985,399:243-275.
30.Jirasek C, Prusinkiewicz P, Moulia B. Integrating Biomechanics into Developmental Plant Models Expressed Using L-systems [C]. In:Proceedings of the 3rd Plant Biomechanics Conference, Stuttgart,2000:615-624.
31. Dave Shreiner, Mason Woo. OpenGL Programming Guide [M]. Pearson Education, Inc.,2008.
32.Debevec P E, Taylor C J, Malik J. Modeling and Rendering Architecture from Photographs:A hybrid geometry-and image-based approach[C]. In:Computer Graphics Proceedings, Annual Conference Series, ACM SIGGRAPH, New Orleans, Louisiana,1996:11-20.
33.de Reffye P, Edelin C, Francon J, et al. Plants models faithful to botanical Structure and development [J]. Computer Graphics,1998,22(4):151-155.
34.Gilet G, Meyer A, Neyret F. Point-based rendering of trees [C]. In:Eurographics Workshop on Natural Phenomena, Dublin,2005,67-72.
35.Godin C, Sinoquet H, Costes E. A method for describing plant architecture which integrates topology and geometry [J]. Annals of Botany,1999,84(3):343-357.
36.Godin C, Carglio Y. A multiscale model of plant topological structures [J]. TheroBio,1998,84(3), 191:1-46.
37.Guennebaud G, Barthe L, Pauliny M. Deferred splatting. Computer Graphics Forum [J].2004,23(3): 653-660.
38.Haeseler, Peitgen H-O, Skordev G. Linear Cellular Automata, Substitutions, Hierarchocal Iterated Function Systems and Attractors [J]. In Fractal Geometry and Computer Graphics, J. L. Encarnacao, Peitgen H-O, Sakas G, Englert G, Eds, Springer-Verkag,1991:3-23.
39. Jules B. Modeling the mighty maple [J]. Computer Graphics,1985,19(3):305-311.
40.Karwowski R, Prusinkiewicz P. Design and implementiontation of the L+C modeling language [J]. Electionic Notes in Theoretical Compute Science 86,2(2003),134-152.
41.Kruszewski P. An algorithm for sculpting trees [J]. Computers and Graphics,1999,23:739-749.
42.Kurth W. Morphological models of Plant growth:Possibilities and ecological relevance [J]. Ecological Modeling,1994,75-76:299-308.
43.Levoy M, Whitted T. The use of points as a display primitive [R]. Technical report, CS Department, University of North Carolina at Chapel Hill,1985.
44.Linden J. Interactive view-dependent point clound rendering[C]. In:proceedings of Image and Vision Computing, Nov.2001, New Zealand,1-6.
45.Lindenmayer A. Mathematical models for cellular interactions in development [J]. TheorBiol,1968, 18:280-315.
46. Long Quan, Ping Tan, Gang Zeng, Lu Yuan, Jingdong Wang. Image-based plant modeling[C]. In: Computer Graphics Proceedings, Annual Conference Series, ACM SIGGRAPH, Boston,2006: 772-778.
47.Oppenheimer P. Real time design and animation of fractal Plants and trees [J]. Computer Graphics, 1986,20(4):55-64.
48.Paul Kruszewski, An algorithm for sculpting trees [J]. computer& graphics,1999,23(6):739-749.
49. Ping Tan, Gang Zeng, Jingdong Wang, Sing Bing Kang, Long Quan. Image-based tree modeling. In: Proceedings of SIGGRAPH 2007, ACM SIGGRAPH and ACM Trans, on Graphics, San Diego, CA, Aug.2007, Article 87:7.
50. Prusinkiewicz P, Muendermann L, Karwowski R, et al. The Use of Positional in Formation in the Modeling of Plants[C]. Computer Graphics Proceeding, Annual Conference Series, ACM SIGGRAPH, Los Angeles,2001:289-300.
51. Prusinkiewicz P, Hammel M, Language-restricted iterated function systems, Koch Constructions and L-systems [C]. In:Fractal Modeling in 3D Computer Graphics and Imagery, J C Hart (eds.). ACM SIGGRAPH, Course Note 13,1994, (4):1-14.
52. Prusinkiewicz P, Lindenmayer A. The algorithmic beauty of plants [M]. New York:Springer-Verlag, 1990.
53.Prusinkiewicz P. Modeling of spatial structure and development of plant:A review [J]. Scientia Horticulturae,1998,74:113-149.
54.Prusinkiewiez P. Modeling Plant growth and development [J]. Current Opinion in Plant Biology, 2004,7(1):79-83.
55.Qunsheng Peng, Wei H, Xuehui Y. A new approach for point-based rendering [C]. In:proceedings of Computer Graphics International 2001, Hong Kong,275-282.
56.Reeves W T. Particle systems-A technique for modeling a class of fuzzy objects [J]. Computer Graphics,1983,17(3):59-376.
57. Room P M, Hanan J S, Prusinkiewicz P. Virtual Plants:new Perspectives for ecologists, Pathologists and agricultural scientists [J]. Trends in Plant Science,1996,1(1):33-38.
58.Rusinkiewics S, Levoy M. Qsplat:A multi-resolution point rendering system for large meshes [C]. In:proceedings of Siggraph 2000, New Orleans, LA USA,343-352.
59. Smith AR. Plants, fractals, and formal languages [C]. In:Proceedings of SIGGRAPH 1984, Computer Graphics,1984,18(3):1-10.
60. Stamminger M, Drettakis G. Interactive sampling and rendering for complex and procedural geometry [C]. In:proceedings of Eurographics Workshop on Rendering,2001,231-242.
61.Julia T. Incorporating Biomechanics into Architectural Tree Models [C]. In:proceedings of SIBGRAPHI'05. Washington D. C., USA:IEEE Computer Society,2005:299-306.
62. Viennot X G, Eyrolles G. Combinatorial analysis of ramified patterns and computer imagery of trees [J]. Computer graphics,1989,23(3):31-39.
63. Wand M, Fischer M, Peter I, Meyer F, Straer W. The randomized z-buffer algorithm:interactive rendering of highly complex scenes[C]. In:proceeding of siggraph 2001,2001,363-370.
64. Weber J, Penn J. Creation and rendering of realistic trees [C]. In:Proceedings of SIGGRAPH'95, ACM SIGGRAPH, Los Angeles, California,1995:119-128.
65.Zwicker M, Pfister H, Baar J, Gross M. EWA splatting [J]. IEEE Transactions on Visualization and Graphics,2002,8(3):223-238.