We describe a method for replacing certain stages of rigid body simulation with a statistically-based approximation. We begin by collecting statistical data regarding changes in linear and angular momentum for collisions of a given object. From this data we extract a statistical “signature” for the object, giving a compact representation of the object’s response to collision events. During object simulation, both the collision detection and the collision response calculations are replaced by simpler calculations based on the statistical signature. Using this approach, we are able to achieve significant improvement in the performance of rigid body simulation. The statistical behavior of the simulation is maintained, including achieving valid resting positions. We present results from a variety of simulations that demonstrate the method and its performance improvement. The method is appropriate for rigid body simulation situations requiring significant performance improvement, and allowing for some loss in fidelity
Category: Rigid bodies
Fluid Simulation with Articulated Bodies
We present an algorithm for creating realistic animations of characters that are swimming through fluids. Our approach combines dynamic simulation with data-driven kinematic motions (motion capture data) to produce realistic animation in a fluid. The interaction of the articulated body with the fluid is performed by incorporating joint constraints with rigid animation and by extending a solid/fluid coupling method to handle articulated chains. Our solver takes as input the current state of the simulation and calculates the angular and linear accelerations of the connected bodies needed to match a particular motion sequence for the articulated body. These accelerations are used to estimate the forces and torques that are then applied to each joint. Based on this approach, we demonstrate simulated swimming results for a variety of different strokes, including crawl, backstroke, breaststroke and butterfly. The ability to have articulated bodies interact with fluids also allows us to generate simulations of simple water creatures that are driven by simple controllers.
Accurate Tangential Velocities for Solid-Fluid Coupling
We propose a novel method for obtaining more accurate tangential velocities for solid fluid coupling. Our method works for both rigid and deformable objects as well as both volumetric objects and thin shells. The fluid can be either one phase such as smoke or two phase such as water with a free surface. The coupling between the solid and the fluid can either be one-way with kinematic solids or fully two-way coupled. The only previous scheme that was general enough to handle both two-way coupling and thin shells required a mass lumping strategy that did not allow for freely flowing tangential velocities. Similar to that previous work, our method prevents leaking of fluid across a thin shell, however unlike that work our method does not couple the tangential velocities in any fashion, allowing for the proper slip independently on each side of the body. Moreover, since it accurately and directly treats the tangential velocity, it does not rely on grid refinement to obtain a reasonable solution. Therefore, it gives a highly improved result on coarse meshes.
Direct Forcing for Lagrangian Rigid-Fluid Coupling
We propose a novel boundary handling algorithm for particle-based fluids. Based on a predictor-corrector scheme for both velocity and position, one- and two-way coupling with rigid bodies can be realized. The proposed algorithm offers significant improvements over existing penalty-based approaches. Different slip conditions can be realized and non-penetration is enforced. Direct forcing is employed to meet the desired boundary conditions and to ensure valid states after each simulation step. We have performed various experiments in 2D and 3D. They illustrate one- and two-way coupling of rigid bodies and fluids, the effects of hydrostatic and dynamic forces on a rigid body as well as different slip conditions. Numerical experiments and performance measurements are provided.
Staggered Projections for Frictional Contact in Multibody Systems
We present a new discrete velocity-level formulation of frictional contact dynamics that reduces to a pair of coupled projections and introduce a simple fixed-point property of this coupled system. This allows us to construct a novel algorithm for accurate frictional contact resolution based on a simple staggered sequence of projections. The algorithm accelerates performance using warm starts to leverage the potentially high temporal coherence between contact states and provides users with direct control over frictional accuracy. Applying this algorithm to rigid and deformable systems, we obtain robust and accurate simulations of frictional contact behavior not previously possible, at rates suitable for interactive haptic simulations, as well as large-scale animations. By construction, the proposed algorithm guarantees exact, velocity-level contact constraint enforcement and obtains long-term stable and robust integration. Examples are given to illustrate the performance, plausibility and accuracy of the obtained solutions.
Staggered Projections for Frictional Contact in Multibody Systems
Efficient Contact Modeling using Compliance Warping
Precise contact modeling is essential when simulating rigid or deformable objects in interaction. Yet, most recent work in computer graphics has focused on the computation of the motion or deformation of objects, and little has been done to model the interaction between simulated objects. In this paper, we propose a novel and very efficient approach for precise computation of contact response between various types of objects commonly used in computer animation. Our approach represents the objects motion as a free motion and a corrective motion. The corrective motion uses an efficient contact model, based on an approximation of the behavior model, but still follows Signorini and Coulomb laws for contact and friction modeling. Our approach guarantees no interpenetration at the end of the time step, and only introduces a minimal error in the objects motion. We illustrate our approach using an approximate (warped) compliance in the case of non-linear deformable models. This speeds-up the contact response by several orders of magnitude, thus allowing the simulation of scenes with many complex interacting objects.
Real-time Animation of Sand-Water Interaction
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.
Magnets in Motion
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.
Algoryx and Phun, CMLabs
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.
PixeLux's DMM
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.”