GPU加速的高质量物理仿真算法研究

High-quality physically-based simulation is a key problem for virtual reality, haptics, robotics, and mechanic/medical simulations. This project focuses on the research of GPU-accelerated high-quality physically-based simulation algorithms. Main contents include: 1. To design a parallel algorithm for dynamic assembling of sparse linear systems. It can accelerate parallel implicit time integration on simulation scenarios containing deformable objects with changing topologies. 2. To design a geometric exact continuous collision detection algorithm. It is capable of overcoming the rounding-errors of floating-point operations and guarantees to detect all the penetrations in complicated physically-based simulation scenarios. 3. To design a collision trajectory-based continuous penalty force formulation. It is capable of overcoming the intrinsic drawbacks for traditional discrete penalty forces, and improves the accuracy of collision handling in physically-based simulations. 4. To design a streaming mapping algorithm for all the key components of physically-based simulation. It enables the whole process of physically-based simulation be fully integrated and executed in parallel on GPUs. We expect to improve the robustness and accuracy of physically-based simulations, and achieve 10x speedups on the overall performance. Improving accuracy and efficiency are always the key problems in the field of physically-based simulation. This project will open a new avenue for improving the quality and efficiency of physically-based simulation algorithms, and will provide strong support for utilizing physically-based simulation algorithms in various applications.

高质量物理仿真是虚拟现实、触觉渲染、机器人、机械与医学仿真等领域的核心问题之一。本项目拟针对GPU加速的高质量物理仿真算法展开研究。核心内容包括：1、设计稀疏线性系统动态并行装配算法，使得包含拓扑变化的物理仿真场景中的隐式积分过程得以在GPU上获得并行加速。2、设计几何精确的连续碰撞检测算法，克服浮点计算的舍入误差，确保检测出复杂物理仿真中的所有穿透情况。3、设计基于碰撞轨迹信息的连续接触力计算公式，克服传统离散惩罚法的内在缺陷，提高物理仿真中碰撞响应过程的准确性。4、基于以上核心算法，设计物理仿真流式映射算法，将整个物理仿真过程完全集成在GPU上并行加速。预期在提高物理仿真系统鲁棒性与精确性的同时，将总体执行效率提升1个数量级。提升物理仿真算法的质量与效率一直是物理仿真领域的热点问题，本项目的研发将为提升物理仿真质量与效率开辟新的道路，为物理仿真在各领域的深入应用提供有力的技术支撑。

高质量物理仿真是虚拟现实、触觉渲染、机器人、机械与医学仿真等领域的核心问题之一。本项目针对GPU加速的高质量物理仿真算法展开了研究。核心内容包括：1、设计了稀疏线性系统动态并行装配算法，使得包含拓扑变化的物理仿真场景中的隐式积分过程得以在GPU上获得并行加速。2、设计了几何精确的连续碰撞检测算法，克服了浮点计算的舍入误差，确保检测出复杂物理仿真中的所有穿透情况。3、设计了基于碰撞轨迹信息的连续接触力计算公式，克服了传统离散惩罚法的内在缺陷，提高了物理仿真中碰撞响应过程的准确性。4、基于以上核心算法，设计了物理仿真流式映射算法，将整个物理仿真过程完全集成在GPU上并行加速。在提高物理仿真系统鲁棒性与精确性的同时，将总体执行效率提升了1个数量级。提升物理仿真算法的质量与效率一直是物理仿真领域的热点问题，本项目的研发为提升物理仿真质量与效率开辟了新的道路，为物理仿真在各领域的深入应用提供了有力的技术支撑。

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