一种基于叶脉形状函数的叶片形态模拟改进方法
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摘要
植物叶片的薄片状结构使得叶片的二维形态更加引人注意,但叶片的弯曲、凹凸等三维形态特征同样是叶片形态的重要组成部分。文章对Runions等提出的二维平面内植物叶片形态的模拟方法做出了改进,提出了一种基于叶脉形状函数的叶片形态模拟方法,将叶片形态的模拟扩展至三维空间。首先,用B样条曲线为不同等级的叶脉指定其在第三维方向的形状函数,得到具有三维形态的叶脉;之后,根据叶脉结构移动叶片边缘,得到边缘的三维形态。再用约束Delaunay三角化算法和Loop细分算法分别对叶面进行三角化、网格平滑细分处理,生成叶面网格模型。最终得到具有三维形态的植物叶片模型。实验表明,该方法能够有效地生成多种形态的三维植物叶片模型,可用于真实植物叶片的形态模拟。
The shape of plant leaves is mostly flaky,which makes the two-dimensional shap of the leaves more attractive.However,the three-dimensional shapes of the leaves,such as bending and concave and convex,are also an important part of the blade morphology.Based on the simulation method proposed by Runions et al.for plant leaf morphology in a two-dimensional plane,a three-dimensional blade shape simulation method based on vein shape function was proposed.Firstly,the B-spline curve is used to specify the shape function in the third dimension for different grades of veins,and the veins with three-dimensional shape are obtained.The blade edge is then moved according to the vein structure to obtain the three-dimensional shape of the edge.Then the edge and the vein are sampled.The constellation Delaunay triangulation algorithm is used to construct the foliar triangle mesh,and the Loop subdivision algorithm is used to perform the mesh smooth subdivision processing to generate a smooth foliar mesh model.A plant leaf model with a three-dimensional morphology can then be obtained.Experiments show that this method can effectively generate three-dimensional plant leaf models of various forms,which can be used for morphological simulation of real plant lea-ves.
The shape of plant leaves is mostly flaky,which makes the two-dimensional shap of the leaves more attractive.However,the three-dimensional shapes of the leaves,such as bending and concave and convex,are also an important part of the blade morphology.Based on the simulation method proposed by Runions et al.for plant leaf morphology in a two-dimensional plane,a three-dimensional blade shape simulation method based on vein shape function was proposed.Firstly,the B-spline curve is used to specify the shape function in the third dimension for different grades of veins,and the veins with three-dimensional shape are obtained.The blade edge is then moved according to the vein structure to obtain the three-dimensional shape of the edge.Then the edge and the vein are sampled.The constellation Delaunay triangulation algorithm is used to construct the foliar triangle mesh,and the Loop subdivision algorithm is used to perform the mesh smooth subdivision processing to generate a smooth foliar mesh model.A plant leaf model with a three-dimensional morphology can then be obtained.Experiments show that this method can effectively generate three-dimensional plant leaf models of various forms,which can be used for morphological simulation of real plant lea-ves.
引文
[1] 赵春江,陆声链,郭新宇,等.西瓜三维形态几何建模和真实感绘制技术研究[J].中国农业科学,2008(12):4155-4163.
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[12] 曾兰玲,张巍,杨洋,等.基于有限细节的植物叶片多密度点云重建算法[J].计算机科学,2016,43(8):292-296.
[13] RUNIONS A,TSIANTIS M,PRUSINKIEWICZ P.A common developmental program can produce diverse leaf shapes[J].New Phytologist,2017,216(2):401-418.
[14] RICHARDS O W,KAVANAGH A J.The analysis of the relative growth gradients and changing form of growing organisms:illustrated by the tobacco leaf[J].The American Naturalist,1943,77(772):385-399.
[15] HEJNOWICZ Z,ROMBERGER J A.Growth tensor of plant organs[J].Journal of Theoretical Biology,1984,110(1):93-114.
[16] BILSBOROUGH G D,RUNIONS A,BARKOULAS M,et al.Model for the regulation of Arabidopsis thaliana leaf margin development[J].Proceedings of the National Academy of Sciences,2011,108(8):3424-3429.
[17] BAYER E M,SMITH R S,MANDEL T,et al.Integration of transport-based models for phyllotaxis and midvein formation[J].Genes & development,2009,23(3):373-384.
[18] SACK L,SCOFFONI C.Leaf venation:structure,function,development,evolution,ecology and applications in the past,present and future[J].New Phytologist,2013,198(4):983-1000.
[19] RUNIONS A,FUHRER M,LANE B,et al.Modeling and visua- lization of leaf venation patterns[J].ACM Transactions on Graphics (TOG),2005,24(3):702-711.
[20] SHINOZAKI K,YODA K,HOZUMI K,et al.A quantitative analysis of plant form-the pipe model theory:I.Basic analyses[J].Japanese Journal of ecology,1964,14(3):97-105.
[21] CIGNONI P,MONTANI C,SCOPIGNO R.DeWall:A fast divide and conquer Delaunay triangulation algorithm in Ed[J].Computer-Aided Design,1998,30(5):333-341.
[22] CHEW L P.Constrained delaunay triangulations[J].Algorithmica,1989,4(1-4):97-108.
[23] YVINEC M.2D Triangulation [EB/OL].https://www.cgal.org.
[24] SHUUE L J A.3D Surface Subdivision Methods [EB/OL].https://www.cgal.org.
[25] LOOP C.Smooth subdivision surfaces based on triangles[D].University of Utah,1987.
[26] HEMMER M,PION S.Modular Arithmetic [EB/OL].https://www.cgal.org.
[27] 江焯林,黎绍发,贾西平,等.典型三角网格细分算法[J].计算机工程,2009,35(6):7-10.
[2] 刘晓东,蒋立华.基于Bezier曲线的植物形态建模和显示[J].计算机工程与应用,2002,38(13):97-98.
[3] 刘晓东,曹云飞,刘国荣,等.基于NURBS曲面的水稻叶形态建模[J].微电子学与计算机,2004,21(9):117-119.
[4] 王芸芸,温维亮,郭新宇,等.基于球 B 样条函数的烟草叶片虚拟实现[J].农业工程学报,2011,27(1):230-235.
[5] QUAN L,TAN P,ZENG G,et al.Image-based plant modeling[C]//ACM SIGGRAPH.ACM,2006:599-604.
[6] MUNDERMANN L,MACMURCHY P,PIVOVAROV J,et al.Modeling lobed leaves[C]//Computer Graphics International,2003.IEEE,2003:60-65.
[7] 杨亮,郭新宇,陆声链,等.基于多幅图像的黄瓜叶片形态三维重建[J].农业工程学报,2009,25(2):141-144.
[8] LOCH B.Surface fitting for the modeling of plant leaves[D].Brisbance:University of Queensland,2004:26-38.
[9] LOCH B I,BELWARD J A,HANAN J S.Application of Surface Fitting Techniques for the Representation of Leaf Surfaces[C]//MODSIM05.2005:1272-1278.
[10] OQIELAT M,BELWARD J A,TURNER I W,et al.A Hybrid Clough-Tocher Radial Basis Function Method for Modelling Leaf Surfaces[C]//Proceedings of the International Congress on Modelling & Simulation.2007.
[11] 孙智慧,陆声链,郭新宇,等.基于点云数据的植物叶片曲面重构方法[J].农业工程学报,2012,28(3):184-190.
[12] 曾兰玲,张巍,杨洋,等.基于有限细节的植物叶片多密度点云重建算法[J].计算机科学,2016,43(8):292-296.
[13] RUNIONS A,TSIANTIS M,PRUSINKIEWICZ P.A common developmental program can produce diverse leaf shapes[J].New Phytologist,2017,216(2):401-418.
[14] RICHARDS O W,KAVANAGH A J.The analysis of the relative growth gradients and changing form of growing organisms:illustrated by the tobacco leaf[J].The American Naturalist,1943,77(772):385-399.
[15] HEJNOWICZ Z,ROMBERGER J A.Growth tensor of plant organs[J].Journal of Theoretical Biology,1984,110(1):93-114.
[16] BILSBOROUGH G D,RUNIONS A,BARKOULAS M,et al.Model for the regulation of Arabidopsis thaliana leaf margin development[J].Proceedings of the National Academy of Sciences,2011,108(8):3424-3429.
[17] BAYER E M,SMITH R S,MANDEL T,et al.Integration of transport-based models for phyllotaxis and midvein formation[J].Genes & development,2009,23(3):373-384.
[18] SACK L,SCOFFONI C.Leaf venation:structure,function,development,evolution,ecology and applications in the past,present and future[J].New Phytologist,2013,198(4):983-1000.
[19] RUNIONS A,FUHRER M,LANE B,et al.Modeling and visua- lization of leaf venation patterns[J].ACM Transactions on Graphics (TOG),2005,24(3):702-711.
[20] SHINOZAKI K,YODA K,HOZUMI K,et al.A quantitative analysis of plant form-the pipe model theory:I.Basic analyses[J].Japanese Journal of ecology,1964,14(3):97-105.
[21] CIGNONI P,MONTANI C,SCOPIGNO R.DeWall:A fast divide and conquer Delaunay triangulation algorithm in Ed[J].Computer-Aided Design,1998,30(5):333-341.
[22] CHEW L P.Constrained delaunay triangulations[J].Algorithmica,1989,4(1-4):97-108.
[23] YVINEC M.2D Triangulation [EB/OL].https://www.cgal.org.
[24] SHUUE L J A.3D Surface Subdivision Methods [EB/OL].https://www.cgal.org.
[25] LOOP C.Smooth subdivision surfaces based on triangles[D].University of Utah,1987.
[26] HEMMER M,PION S.Modular Arithmetic [EB/OL].https://www.cgal.org.
[27] 江焯林,黎绍发,贾西平,等.典型三角网格细分算法[J].计算机工程,2009,35(6):7-10.