CHS: Small: Real-Time Simulation of Elastic Solids

University Of Utah, Salt Lake City UT

Investigators

Abstract

Visual effects in modern films demonstrate that offline physics-based simulations achieve quality which often cannot be distinguished from real video footage. However, the opposite is true in real-time applications such as surgery simulators, where even non-expert users can quickly notice deficiencies in the simulation when compared to reference video recordings. The PI's goal in this project is to lay the algorithmic foundations for the next generation of surgery simulators, which would reduce the need for surgeons to practice on real patients or animals. In biomechanics applications, finite element software packages are often criticized for slow running times. The PI's new numerical methods will lead to more rapid iterations, allowing biomechanics researchers to test more hypotheses in less time. Fast physics would also be highly appreciated in the computer animation industry, because current methods are too slow for interactive character posing with physically accurate elasticity of skin and flesh. Virtual reality is a new but increasingly important application area. Real-time physics will be necessary to power virtual reality applications ranging from training simulators to creative applications (e.g., clothing design) and games, the latter being particularly useful for popularizing mathematics, physics, and computer science, thereby opening up new opportunities for education and outreach. Modern general-purpose methods for the numerical time integration of the equations of motion, typically used for offline simulation, feature advanced mechanisms for error control while striving to maximize computational efficiency. However, real-time physics-based simulation techniques must conform to a different set of requirements. In particular, the numerical integration algorithm must be able to advance the simulation while using only a small amount of computing resources. Interactive applications such as surgery simulators typically require at least 30 frames per second to create the illusion of smooth motion. This makes real-time physics computationally challenging, even with modern CPUs and GPUs. To cope with this challenge, specialized algorithms have been developed for entertainment applications (games), where accuracy is less critical. In this research the PI will study new numerical time integration algorithms which meet the difficult computational constraints of real-time physics but maximize accuracy, with a specific focus on the simulation of elastic solids such as biological soft tissues. Despite their complex nonlinear material properties, the PI's recent work suggests that accurate real-time simulations of detailed models are within reach. In particular, whereas implicit integration schemes, numerically solved using Newton's method, are the traditional computational workhorses of physics-based simulations, the PI's results demonstrate that Newton's method is not always the most effective approach, especially in the real-time setting. Implicit time stepping can be formulated as an optimization problem, which connects physics-based simulation with mathematical optimization, opening up many interesting research opportunities. The situation is complicated by the fact that even simple mechanical systems require non-convex objective functions. Real-time applications do not offer a second chance to fix incorrect results and, therefore, it is imperative to avoid simulation instability - without increasing computational complexity. All numerical integration schemes inevitably incur error due to time discretization and in difficult scenarios such error may be further exacerbated due to the real-time computing constraints. This project will seek to discover new numerical methods which simultaneously satisfy requirements of 1) real-time computing, 2) stability, and 3) accuracy, while supporting realistic material models.