在计算机图形学中，不同自然场景间的交互作用模拟成为近年来研究的热点问题之一。树木作为自然界最常见也是最重要的组成元素之一，其与周围环境之间的交互作用模拟在电影、游戏等行业中发挥着举足轻重的作用。为了满足人们对视觉效果的追求，基于物理的动画算法被引入到图形学中来，这使得树木与周围场景间交互作用仿真效果更加真实；然而，由于当前计算机硬件发展水平以及软件并行算法的限制，计算机求解大量的物理方程组是一个非常耗时的过程。本文对此领域进行了深入而有针对性的研究与探讨，解决了树木与周围环境（如风、雨等）交互作用模拟问题以及基于物理方法的CUDA并行加速技术问题。本文的贡献与创新主要体现在以下几个方面：

l         提出一种由层次树枝结构与小细枝结构组成的树木结构模型，以及树木骨架提取算法。本文树木模型由树枝与树叶组成，树枝结构采用具有父子关系的层次结构，树叶来源于用户定义的具有多种树木种类的小细枝集。树枝骨架结构是驱动树木动画的基础，本文实现两种树枝骨架结构生成算法：一为基于规则的骨架生成算法，二为基于三维美工树木模型的骨架提取算法。最后，结合树木的表皮几何结构与树皮、树叶纹理对场景进行真实感绘制。

l         提出一种树木在风场中多尺度运动的算法。本文将树木风中动态分解为低频树枝动态与高频树叶动态。本文提出两种实现树枝低频动态模拟的算法：一为基于物理的转化矩阵计算（physically-based transformation matrix calculations，简称PTMC）动态模型，二为改进的Euler-Bernoulli动态模型；同时，本文提出一种称之为angular-shell的树叶动态模拟算法，该算法能够将树叶限制于预先定义好的angular-shell空间内做高频运动。实验结果表明该算法可以真实、有效地模拟树木在风力作用下的摇摆运动。

l         提出一种模拟树木与雨滴交互作用算法。本文提出一种扩展三棱柱弹簧模型（extended three-prism spring model，简称ETPSM）用于控制树枝与叶柄在外力作用下的振动、扭转、反弹等运动；同时，应用简单几何模型结构与Shallow Water Equations（SWE）两种不同方法模拟雨滴在具有亲水性的树叶表面上的多种运动现象，包括液滴的飞溅、流动、合并、下落、拖长尾巴以及叶片表面变湿等现象。树叶与液滴之间的相互作用是通过彼此间的压力进行传递的。

l         提出一种基于CUDA的实时树木风中动画并行算法。本文采用当前NVIDIA公司设计的GPGPU模型的CUDA框架，重新设计适合树木运动并行计算的数据结构，改进并行算法，真实地模拟树木在风力下摇曳等实时动画效果，提高了树木动画仿真效率。此外，本文将上述算法应用于基于物理的树叶形变算法的并行加速过程，亦取得了近七倍的加速效果。

In computer graphics (CG), the simulations of interactive coupling among different natural scenes become one of the hottest research problems in recent years. As one of most popular and important elements in nature, trees interactively coupled with surrounding environment take an active part in the industrial applications, such as movies, games and so on. To the pursuit of visual effects for us, the physically-based methods in computer animation (CA) have been introduced into CG to enhance the simulation reality of interactive coupling among different scenes; however, due to the limitations of computer hardwares and parallel algorithms, it is rather time-consuming to solve lots of physical equations. In this case, this thesis achieves a deep and specialized research and discussion in this field, solving the problems in  simulation of trees interactively coupled with surrounding environment (such as wind, rain etc) and the problem of CUDA-based parallel acceleration approach derived from physically-based methods. The main contributions and innovations of our work include the following aspects:

l         We propose a tree structural model composed of branches and twigs and an algorithm for tree skeleton capture. As the structure of tree is composed of branches and leaves, the branch model adopts a hierarchical structure of parent-child relationship and the leaf model is selected from a twig set of various species of trees pre-defined by user. Tree's skeleton is the structural basics of tree animation, therefore in this thesis, we present two approaches to generate tree's skeleton: one is rule-based growth algorithm, the other is skeleton-capture algorithm for artist-made tree model. The geometries of tree branches and leaves together with their textures are used to render the final whole tree.

l         We propose a multi-resolution approach to simulate tree motion in the wind field. In this thesis, we separate the motion of tree into low-frequency branch dynamic and high-frequency leaf dynamic. To achieve the branch dynamic simulation, we present two algorithms: one is the approach called physically-based transformation matrix calculations (PTMC), the other is derived from improved Euler-Bernoulli beam model. In addition, a novel angular-shell dynamic model of leaf simulation is proposed as well. This method can control leaf's motion among the angular-shell space in a higher frequency. Experimental results of tree motion in the wind show us that our algorithms can achieve the tree's swaying under the influence of wind.

l         We propose a novel approach to simulate the interactive coupling between tree and raindrops. In this thesis, we use a new elastic model call extended three-prism spring model (ETPSM) to control branch/petiole's motions, such as vibration, rotation, rebound etc. In addition, both of different methods based simple geometry mesh and Shallow Water Equations(SWE) are taken into account to simulate various phenomena incurred from the interactive coupling, respectively. These include, among from others for instance, part of raindrops splash into the air, flow with a tail, merge or hang on the leaf surface and the leaf surfaces become wet, etc. The interactive coupling between tree and raindrops can be realized through the transfer of pressure between both of themselves.

l         We propose a CUDA-based parallel algorithm of real-time tree animation in the wind field. In this thesis, we use CUDA platform of recent GPGPU designed by NVidia company to simulate tree swaying in wind field by re-arranging parallel tree data and improving parallel algorithm. Experimental results show us this algorithm can accelerate tree animation greatly. In addition, this parallel algorithm can also speedup physically-based leaf deformation up to seven times.