Penetration-free projective dynamics on the GPU
Penetration-free projective dynamics on the GPU
复制标题
DOI：
10.1145/3528223.3530069
复制
发表时间：
2022-07
期刊：
影响因子：
--
通讯作者：
L. Lan;Guanqun Ma;Yin Yang;Changxi Zheng;Minchen Li;Chenfanfu Jiang
中科院分区：
文献类型：
--
作者：
L. Lan;Guanqun Ma;Yin Yang;Changxi Zheng;Minchen Li;Chenfanfu Jiang
提出了一种可变形仿真的GPU算法。该方法具有较好的计算效率和无穿透性保证，这是现有技术所不具备的。主要思想是投影动力学（PD）和增量潜在接触（IPC）的算法集成。PD是一种基于位置的仿真框架，具有鲁棒收敛性和实现方便等优点。我们证明了PD可以用来处理变分优化与内点法，如IPC。虽然概念上很简单，但这需要在碰撞分辨率和迭代模式上进行专门的返工，以避免不正确的碰撞投影和改进的数值收敛。IPC利用了一个基于障碍的公式，当约束即将被违反时，它会产生无限大的惩罚。该机构保证了在仿真过程中变形体的无相交轨迹，只要它们在静止构型上是分开的。缺点是，IPC给系统带来了大量的非线性，使PD收敛速度变慢。为了解决这一问题，我们提出了一种新的GPU算法a - jacobi，用于在PD的全局步骤上更快地线性求解。a -Jacobi基于Jacobi迭代，但通过将几个Jacobi步骤集中到单个迭代中，它可以更好地利用现代gpu的计算能力。此外，我们还利用一种新的最小梯度牛顿算法重新设计了CCD寻根程序。这些节省的时间预算允许更多的迭代来适应严格的IPC障碍，从而使结果既真实又无冲突。总之，我们的算法在GPU上以交互速率甚至实时模拟固体和外壳的复杂模型。
We present a GPU algorithm for deformable simulation. Our method offers good computational efficiency and penetration-free guarantee at the same time, which are not common with existing techniques. The main idea is an algorithmic integration of projective dynamics (PD) and incremental potential contact (IPC). PD is a position-based simulation framework, favored for its robust convergence and convenient implementation. We show that PD can be employed to handle the variational optimization with the interior point method e.g., IPC. While conceptually straightforward, this requires a dedicated rework over the collision resolution and the iteration modality to avoid incorrect collision projection with improved numerical convergence. IPC exploits a barrier-based formulation, which yields an infinitely large penalty when the constraint is on the verge of being violated. This mechanism guarantees intersection-free trajectories of deformable bodies during the simulation, as long as they are apart at the rest configuration. On the downside, IPC brings a large amount of nonlinearity to the system, making PD slower to converge. To mitigate this issue, we propose a novel GPU algorithm named A-Jacobi for faster linear solve at the global step of PD. A-Jacobi is based on Jacobi iteration, but it better harvests the computation capacity on modern GPUs by lumping several Jacobi steps into a single iteration. In addition, we also re-design the CCD root finding procedure by using a new minimum-gradient Newton algorithm. Those saved time budgets allow more iterations to accommodate stiff IPC barriers so that the result is both realistic and collision-free. Putting together, our algorithm simulates complicated models of both solids and shells on the GPU at an interactive rate or even in real time.