Physics-Based Animation

Recent advances in physically-based simulations have made it possible to generate realistic animations. However, in the case of solid-fluid coupling, wetting effects have rarely been noticed despite their visual importance especially in interactions between fluids and granular materials. This paper presents a simple particle-based method to model the physical mechanism of wetness propagating through granular materials; Fluid particles are absorbed in the spaces between the granular particles and these wetted granular particles then stick together due to liquid bridges that are caused by surface tension and which will subsequently disappear when over-wetting occurs. Our method can handle these phenomena by introducing a wetness value for each granular particle and by integrating those aspects of behavior that are dependent on wetness into the simulation framework. Using this method, a GPU-based simulator can achieve highly dynamic animations that include wetting effects in real time.

Real-time Animation of Sand-Water Interaction

We propose an efficient scheme for evaluating nonlinear subspace forces (and Jacobians) associated with subspace deformations. The core problem we address is efficient integration of the subspace force density over the 3D spatial domain. Similar to Gaussian quadrature schemes that efficiently integrate functions that lie in particular polynomial subspaces, we propose cubature schemes (multi-dimensional quadrature) optimized for efficient integration of force densities associated with particular subspace deformations, particular materials, and particular geometric domains. We support generic subspace deformation kinematics, and nonlinear hyperelastic materials. For an r-dimensional deformation subspace with O(r) cubature points, our method is able to evaluate subspace forces at O(r^2) cost. We also describe composite cubature rules for runtime error estimation. Results are provided for various subspace deformation models, several hyperelastic materials (St.Venant-Kirchhoff, Mooney-Rivlin, Arruda-Boyce), and multimodal (graphics, haptics, sound) applications. We show dramatically better efficiency than traditional Monte Carlo integration.

Optimizing Cubature for Efficient Integration of Subspace Deformations

We introduce magnetic interaction for rigid body simulation. Our approach is based on an equivalent dipole method and as such it is discrete from the ground up. Our approach is symmetric as we base both field and force computations on dipole interactions.

Enriching rigid body simulation with magnetism allows for many new and interesting possibilities in computer animation and special effects. Our method also allows the accurate computation of magnetic fields for arbitrarily shaped objects, which is especially interesting for pedagogy as it allows the user to visually discover properties of magnetism which would otherwise be difficult to grasp.

We demonstrate our method on a variety of problems and our results reflect intuitive as well as surprising effects. Our method is fast and can be coupled with any rigid body solver to simulate dozens of magnetic objects at interactive rates.

Magnets in Motion

There seem to be quite a few companies in the business of physics simulation these days.

Graham Fyffe pointed out this one to me: Algoryx focuses on 3D multi-physics simulations. They are also responsible for the Phun demo I posted a while ago, that has also been floating around YouTube.  

Another company that does rigid-body physics simulations is CMLabs.

Christopher Twigg’s thesis from CMU:

“Animation techniques for controlling passive simulation are commonly based on an optimization paradigm: the user provides goals a priori, and sophisticated numerical methods minimize a cost function that represents these goals. Unfortunately, for multibody systems with discontinuous contact events these optimization problems can be highly nontrivial to solve, and many-hour offline optimizations, unintuitive parameters, and convergence failures can frustrate end-users and limit usage. On the other hand, users are quite adaptable, and systems which provide interactive feedback via an intuitive interface can leverage the user’s own abilities to quickly produce interesting animations. However, the online computation necessary for interactivity limits scene complexity in practice. This thesis presents two methods for controlling the rigid body simulations.

The first is Many-Worlds Browsing, a method which exploits the speed of multibody simulators to compute numerous simulations in parallel (offline and online), and allow the user to browse and modify them interactively. By bolting responsive, powerful, intuitive interfaces onto relatively simple sampling techniques we get a method that enables animators to produce compelling results with a minimum of effort. The second method is time-reversed simulation: we provide only the final resting configuration of the system and run the simulator backwards in time. During the development of this method we encountered a number of surprisingly counter-intuitive results, which can be elucidated using a combination of numerical simulation and thought experiments.”

Controlling Multibody Dynamics via Browsing and Time Reversal

Cosserat nets are networks of elastic rods that are linked by elastic joints. They allow to represent a large variety of objects such as elastic rings, coarse nets, or truss structures. In this paper, we propose a novel approach to model and dynamically simulate such Cosserat nets. We first derive the static equilibrium of the elastic rod model that supports both bending and twisting deformation modes. We further propose a
dynamic model that allows for the efficient simulation of elastic rods. We then focus on the simulation of the Cosserat nets by extending the elastic rod deformation model to branched and looped topologies.
To round out the discussion, we evaluate our deformation model. By comparing our deformation model to a reference model, we illustrate both the physical plausibility and the conceptual advantages of the proposed approach.

Cosserat Nets

I added Pixelux Entertainment’s link on the side.  They have developed a piece of software known as DMM (for  Digital Molecular Matter),  that “is a real-time finite element system that is being used in the “Force Unleashed”, an upcoming video game by LucasArts. [They] also have a plug-in that allows people to utilize FEA-based deformation and fracture within Maya as well as for [their] real-time engine.”

“This book is designed to give the reader a practical introduction to fluid simulation for graphics. The field of fluid dynamics, even just in animation, is vast and so not every topic will be covered, and many wonderful papers will sadly be passed over in the hope of distilling the essentials; this is far from a thorough survey. The focus of this book is animating fully three-dimensional incompressible flow—from understanding the math and the algorithms to actual implementation. However, there is also a small amount of material on height field simplifications which are important for efficiently modeling large bodies of water.”

Fluid simulation for computer graphics

The goal of this paper is to enable the interactive simulation of phenomena such as animated fluid characters. While full 3D fluid solvers achieve this with control algorithms, these 3D simulations are usually too costly for real-time environments. In order to achieve our goal, we reduce the problem from a three- to a two-dimensional one, and make use of the shallow water equations to simulate surface waves that can be solved very efficiently. In addition to a low runtime cost, stability is likewise crucial for interactive applications. Hence, we make use of an implicit time integration scheme to obtain a robust solver. To ensure a low energy dissipation, we apply an Implicit Newmark time integration scheme. We propose a general formulation of the underlying equations that is tailored towards the use with an Implicit Newmark integrator. Furthermore, we gain efficiency by making use of a direct solver. Due to the generality of our formulation, the fluid simulation can be coupled interactively with arbitrary external forces, such as forces caused by inertia or collisions. We will discuss the properties of our algorithm, and demonstrate its robustness with simulations on strongly deforming meshes.

Robust and Efficient Wave Simulations on Deforming Meshes

The error tolerance of human perception offers a range of opportunities to trade numerical accuracy for performance in physics-based simulation. However, most previous approaches either focus exclusively on understanding the tolerance of the human visual system or burden the application developer with case-specific implementations. In this paper, based on a detailed set of perceptual metrics, we propose a methodology to identify the maximum error tolerance of physics simulation. Then, we apply this methodology in the evaluation of two techniques. The first is the hardware optimization technique of precision reduction which reduces the size of floating point units (FPUs), allowing more of them to occupy the same silicon area. The increased number of FPUs can significantly improve the performance of future physics accelerators. A key benefit of our approach is that it is transparent to the application developer. The
second is the software optimization of choosing the largest timestep for simulation.

Fool Me Twice: Exploring and Exploiting Error Tolerance in Physics-Based Animation