复杂条件下真实感树动画模拟方法研究

It is a challenging problem to animate trees under complex conditions by taking Lissajous curves, aerodynamics, the deformation of leaves and the fracturing of branches into account in the field of natural phenomena simulation. Our project is going to solve the problem mainly by a hybrid method that combining a simplified modal analysis method and a video based method. The project mainly consists of three parts: (1) The first part is the creation of a video driven theoretical basis for realistic tree animation. To achieve this goal, we approximate the forced vibration of three dimensional curved beams by using simplified modal analysis method, and then we consider three dominant modes with slightly different natural frequencies and damping ratios to generate Lissajous curves. For each leaf, we employ a physically-based method to animate its deformation. The dynamics of a tree is created by using the dynamics of branches after carrying out matrix transformation. Aerodynamics model is used to improve the realism of tree animation. The video based method is employed to extract the natural frequencies and damping ratios of branches and leaves; (2) The second part is the animation of the fracture of branches and the falling of leaves in a strong wind field. We first generate a three dimensional wind field based on a spectral method and an extracted coarse wind field from video; second, we use a procedural method to predict the broken positions of branches and leaves; third, we assmue that the branches consist of many thin fibre tubes to simplify the generation of geometrical structure of branch cross sections; after that, we propose an axis-aligned hierachical bounding ellipsoid structure to accelerate tree collision detection for fallen leaves and broken branches; (3) The third part is the animation of the change of tree apperance in wind and rain. We intend to use metaballs to represent rain drops, and employ Free Form Deformation and Constructive Solid Geometry techniques to deform and clip the rain drops on a surface. In order to interact with trees, we will employ precomputation, data-driven, LOD and GPU acceleration method to optimize the animation system. Finally, we will create the realistc animation of a tree in a strong wind field or in a wind and rain. The main advatage of this project is the construction of a new theoretical basis for tree animation under complex conditions with wide application in film industry, video games and virtual reality environments.

复杂条件（如强风和暴风雨等）下树枝的折断、树叶的变形与落叶等现象的真实感模拟是自然现象模拟中的关键问题。本项目从利萨茹曲线、树的植物学特性以及空气动力学等影响树真实感运动的关键性因素出发，结合简化模态分析法和基于视频的方法研究树的运动机制。通过简化模态分析法分析三维空间弯曲悬臂梁的振动模型，结合空气动力学建立阔叶的动力学方程，并采用基于视频的方法提取特定树枝和树叶的自然频率、阻尼系数，首次建立一种视频驱动的树动力学理论模型；针对强风条件下枝叶的折断与落叶现象，提出一种用于判断枝叶折断位置、并能处理折断后树枝几何形状变化及碰撞检测的新方法；运用频谱分析法和基于视频的方法构建风场并模拟落叶现象；结合粒子模型、自由变形等技术，建立风雨条件下雨水与枝叶的交互式模拟新方法；综合运用优化技术加速树的真实感动画模拟，在影视特效、三维动画及虚拟现实等领域具有重要的研究意义和应用价值。

解决强风等复杂条件下树枝及树叶的真实感动画模拟这一关键科学问题首先需要解决四个关联性问题：其一，需构建真实感静态三维树模型，为后续动态模拟做数据准备；其二，需建立强风或大变形拉放试验条件下依然能保持稳定的动力学模型，构成树动画模拟的理论基础；其三，需解决树多目标跟踪中的遮挡和重影问题；其四，需解决跟踪后枝叶自然频率、阻尼系数的提取方法，为树动画模型提供输入参数。围绕上述问题，（1）研究了一种基于图像和极线约束的交互式静态树模型构建方法，该方法能生成有效保持树枝干结构的树模型；研究了一种基于稀疏航空激光点云的高效树三维建模方法，该方法实现了树点云的有效分割和快速三维重建；（2）构建了一种基于简化模态分析法的树动力学模型，该模型解决了强风条件下树枝的大变形问题；（3）研究了一种结合L-K光流法自动跟踪和交互式手动选择跟踪目标的半自动跟踪方法，有效解决了自动跟踪过程中难以解决的遮挡和重影问题；（4）基于跟踪获取的枝叶轨迹，分别采用了快速傅里叶变换和半功率带宽法计算枝叶的自然频率和阻尼系数。最后，将提取的树枝和树叶动力学参数输入已构建的树静态模型和动力学模型，模拟结果表明，基于视频驱动的树动力学模型能够模拟强风条件下树的大变形，通过与实际拍摄树的拉放试验视频对比，模拟结果与视频图像在动态特征上保持一致。