Abstract: The shape of a tree is mostly determined by the reality to the nature layout of branches. In order to simulate a 3D tree branch to mimic the natural tree shape, using the theory of fractal algorithm and mechanics of material, a simulating method for the 3D's bending branch and fractal root based on the gravity field was proposed. The stress state of the branch was reflected by its bending degree. Bending degree could be controlled by changing the value of Young's modulus. Also, with X3D and Java, fractal algorithm combined with Extrusion node of X3D was used to simulate the geotropism of the bending root. A realistic 3D tree can be easily created with some input data using our simulation. By using the close relationship of the tree's underground part and upper part, a simulation method of gravity's effect on the tree shape was established. The experimental results show that the method can easily generate realistic three-dimensional form of fractal trees.

Key words: gravity field, mechanics of materials, 3D, bending branch, fractal root

摘要： 枝条的逼真度在很大程度上影响着整棵树的形态效果，为了模拟出更符合自然规律的三维树，结合了分形算法和材料力学原理，提出了基于重力场的三维弯曲枝条和分形树根的模拟方法。枝条的弯曲程度体现了它的受力情况，同时也可以用杨氏弹性模量来控制其弯曲度；另一方面，采用X3D及Java，运用分形算法结合X3D的Extrusion节点模拟了分形弯曲树根的向地性。用户只需要输入相关参数就可以得到形态较为逼真的三维树。同时将树的地下部分与地上部分有机地结合在一起，模拟了基于重力场的三维树形态。实验结果表明，该方法可以比较方便地生成形态逼真的三维分形树。

关键词: 重力场, 材料力学, 三维, 弯曲树枝, 分形树根