GIPC: Fast and stable Gauss-Newton optimization of IPC barrier energy

IF 7.8 1区 计算机科学 Q1 COMPUTER SCIENCE, SOFTWARE ENGINEERING ACM Transactions on Graphics Pub Date : 2024-01-27 DOI:10.1145/3643028
Kemeng Huang, Floyd M. Chitalu, Huancheng Lin, Taku Komura
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Abstract

Barrier functions are crucial for maintaining an intersection and inversion free simulation trajectory but existing methods which directly use distance can restrict implementation design and performance. We present an approach to rewriting the barrier function for arriving at an efficient and robust approximation of its Hessian. The key idea is to formulate a simplicial geometric measure of contact using mesh boundary elements, from which analytic eigensystems are derived and enhanced with filtering and stiffening terms that ensure robustness with respect to the convergence of a Project-Newton solver. A further advantage of our rewriting of the barrier function is that it naturally caters to the notorious case of nearly-parallel edge-edge contacts for which we also present a novel analytic eigensystem. Our approach is thus well suited for standard second order unconstrained optimization strategies for resolving contacts, minimizing nonlinear nonconvex functions where the Hessian may be indefinite. The efficiency of our eigensystems alone yields a 3 × speedup over the standard IPC barrier formulation. We further apply our analytic proxy eigensystems to produce an entirely GPU-based implementation of IPC with significant further acceleration.

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GIPC:快速稳定的工频阻挡能高斯-牛顿优化算法
障碍函数对于保持无交叉和无反转的模拟轨迹至关重要,但直接使用距离的现有方法会限制实现设计和性能。我们提出了一种重写障碍函数的方法,以获得其 Hessian 的高效、稳健近似值。其关键思路是利用网格边界元素制定一个简单的接触几何度量,并由此推导出解析特征系统,再通过过滤和加强项进行增强,从而确保 Project-Newton 求解器收敛的稳健性。我们对障碍函数进行重写的另一个优势是,它自然而然地适用于近乎平行的边-边接触这种众所周知的情况,我们还针对这种情况提出了一个新颖的解析特征系统。因此,我们的方法非常适合用于解决接触的标准二阶无约束优化策略,最小化非线性非凸函数,其中的 Hessian 可能是不确定的。与标准的 IPC 障碍公式相比,仅我们的特征系统的效率就提高了 3 倍。我们进一步应用我们的分析代理特征系统,生成了完全基于 GPU 的 IPC 实现,进一步显著加快了速度。
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来源期刊
ACM Transactions on Graphics
ACM Transactions on Graphics 工程技术-计算机:软件工程
CiteScore
14.30
自引率
25.80%
发文量
193
审稿时长
12 months
期刊介绍: ACM Transactions on Graphics (TOG) is a peer-reviewed scientific journal that aims to disseminate the latest findings of note in the field of computer graphics. It has been published since 1982 by the Association for Computing Machinery. Starting in 2003, all papers accepted for presentation at the annual SIGGRAPH conference are printed in a special summer issue of the journal.
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