Physical Simulation of Deformable Models Based on Geometric Mapping

对数字化真实世界模型进行基于物理的交互式建模、仿真和分析是极具挑战性的任务。基于物理的仿真方法，如基于连续介质力学的有限元方法，是计算密集型的，这使得它们不适合实时仿真和可视化大规模复杂数据。本研究中几何映射的引入提供了复杂几何形状所固有的欧几里得参数域和规则结构，并提供了有效的工具（如基于GPU的计算）来加速模拟过程。本研究通过探索保角和调和几何映射与基于物理的仿真之间的关系，解决了物理仿真和可变形模型可视化的速度瓶颈，并开发了有效的算法，允许用户执行实时物理仿真，碰撞检测，材料建模和可视化的大规模，复杂的几何数据。特别是，高效和强大的算法进行了研究，使动态时空自适应物理变形的薄壳和体积的对象，通过利用新的数值方法来解决偏微分方程/常微分方程的图形硬件，表面和体积映射的基础上。PI研究了新的基于GPU的分层碰撞检测算法的可变形模型，使用多分辨率几何图像表示的边界变形树作为动态纹理的图形硬件，有效地检测对象间的碰撞和自碰撞的可变形模型在模拟过程中。该研究项目还开发了强大的基于GPU的多分辨率建模和并行可视化方法，以有效地表示和渲染模拟可变形模型的异质材料特性。这项调查对物理科学，机械工程，医学，K-12教育，培训和娱乐等一系列应用产生了广泛的影响。

Interactive physically based modeling, simulation, and analysis of digitized real-world models are extremely challenging tasks. Physically based simulation approaches, such as finite element methods based on continuum mechanics, are computationally intensive, which makes them impractical for simulating and visualizing large-scale complex data in real-time. The introduction of geometric mapping in this research provides Euclidean parametric domain and regular structure inherent to complex geometric shapes, and provides efficient tools (such as GPU-based computation) to speed up the simulation process. This research tackles the speed bottleneck of physical simulation and visualization of deformable models by exploring the relationship between conformal and harmonic geometric mapping with physically based simulation, and develops efficient algorithms that allow users to perform real-time physical simulation, collision detection, material modeling, and visualization of large-scale, complicated geometric data. In particular, efficient and robust algorithms are investigated to enable dynamic space & time adaptive physical deformation of thin-shells and volumetric objects, by exploiting novel numerical methods to solve PDEs/ ODEs on graphics hardware, based on surface and volumetric mappings. The PI investigates novel GPU-based hierarchical collision detection algorithms for deformable models, using multiresolution geometry images to represent the bounding deformation trees as dynamic textures in the graphics hardware, to efficiently detect both inter-objects collision and self-collision of deformable models during simulations. This research project also develops powerful GPU-based multiresolution modeling and parallel visualization methods to efficiently represent and render heterogeneous material properties of the simulated deformable models. This investigation has broad impacts on an array of applications spanning physical science, mechanical engineering, medicine, K-12 education, training, and entertainment.