基于空间曲线理论的植物叶片形态模拟  

Simulation of Plant Leaves Based on Space Curve Theory

作　　者：袁修久[1] 刘栋[1] 王胜勇[2] 杨荣[3] 赵学军[1] 

机构地区：[1]空军工程大学理学院 [2]93942部队 [3]空军工程大学导弹学院

出　　处：《空军工程大学学报（自然科学版）》2011年第3期78-83,共6页Journal of Air Force Engineering University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11071256);陕西电子信息系统综合集成重点实验室基金资助项目(201113Y12)

摘　　要：利用空间曲线理论建立了植物叶片的形态模型。通过调整参数可以得到不同种类的叶片形态,并且随着叶片轮廓线长度参数的增加,叶片可以生长。首先根据叶片的轮廓线的特征构造曲率函数族和挠率函数族,通过解空间曲线的基本方程,绘制出半边叶子的轮廓线。再利用对称性得到另半边叶子的轮廓线。综合利用投影和仿射变换方法确定叶中脉曲线。通过Loop细分得到光滑的叶面。在曲率函数是分段幂函数的情况下,证明了二维叶片的生长方向总是沿着初始叶片的对称轴方向。通过仿真试验验证了本文算法的可行性。本文的方法可以绘制出复杂的叶子。The paper has established the models of the plat leaf shapes by using space curve theory.Different types of leaf shapes can be obtained by adjusting the parameters,and with the increase of leaf outline length parameters,leaves can grow.First,according to the characteristics of leaves,the curvature and torsion functions of the edge line can be determined,then the outlines of half leaves are drawn by solving the basic equations of space curves,and the other half edge of line is drawn according to the symmetry of the leaves.The curves of the main venations can be determined by using projection method and affine transformation.Loop subdivisions have been used to obtain smooth leaves.In the situation that the curvature functions are piecewise power functions,the growths of two-dimensional leaf blades are always along the axils of initial directions have been demonstrated.Using the method mentioned in this paper can draw out complex leaves.The simulation experiment results verify the feasibility of the proposed method.

关 键 词：植物叶子模拟 空间曲线理论 仿射变换 掌形叶子 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]