Category: Rigid bodies

Velocity-Based Shock Propagation for Multibody Dynamics Animation

Multibody dynamics are used in interactive and real-time applications, ranging from computer games to virtual prototyping, and engineering. All these areas strive towards faster and larger scale simulations. Particularly challenging are large-scale simulations with highly organized and structured stacking. We present a stable, robust, and versatile method for multibody dynamics simulation. Novel contributions include a new, explicit, fixed time-stepping scheme for velocity-based complementarity formulations using shock propagation with a simple reliable implementation strategy for an iterative complementarity problem solver specifically optimized for multibody dynamics.

Velocity-Based Shock Propagation for Multibody Dynamics Animation

Impulse-Based Dynamic Simulation in Linear Time

This paper describes an impulse-based dynamic simulation method for articulated bodies which has a linear time complexity. Existing linear-time methods are either based on a reduced-coordinate formulation or on Lagrange multipliers. The impulse-based simulation has advantages over these well-known methods. Unlike reduced-coordinate methods, it handles nonholonomic constraints like velocity-dependent ones and is very easy to implement. In contrast to Lagrange multiplier methods the impulse-based approach has no drift problem and an additional stabilisation is not necessary. The presented method computes a simulation step in O(n) time for acyclic multi-body systems containing equality constraints. Closed kinematic chains can be handled by dividing the model into different acyclic parts. Each of these parts is solved independently from each other. The dependencies between the single parts are solved by an iterative method. In the same way inequality constraints can be integrated in the simulation process in order to handle collisions and permanent contacts with dynamic and static friction.

Impulse-Based Dynamic Simulation in Linear Time

Many Worlds Browsing for Control of Multibody Dynamics

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.

We introduce Many-Worlds Browsing, a method which circumvents these limits by exploiting the speed of multibody simulators to compute numerous example simulations in parallel (offline and online), and allow the user to browse and modify them interactively. We demonstrate intuitive interfaces through which the user can select among the examples and interactively adjust those parts of the scene that don’t match his requirements. We show that using a combination of our techniques, unusual and interesting results can be generated for moderately sized scenes with under an hour of user time. Scalability is demonstrated by sampling much larger scenes using modest offline computations.

Many Worlds Browsing for Control of Multibody Dynamics

Hybrid Simulation of Deformable Solids

Although mesh-based methods are efficient for simulating simple hyperelasticity, maintaining and adapting a mesh-based representation is less appealing in more complex scenarios, e.g. collision, plasticity and fracture. Thus, meshless or point-based methods have enjoyed recent popularity due to their added flexibility in dealing with these situations. Our approach begins with an initial mesh that is either conforming (as generated by one’s favorite meshing algorithm) or non-conforming (e.g. a BCC background lattice). We then propose a framework for embedding arbitrary sample points into this initial mesh allowing for the straightforward handling of collisions, plasticity and fracture without the need for complex remeshing. A straightforward consequence of this new framework is the ability to naturally handle T-junctions alleviating the requirement for a manifold initial mesh. The arbitrarily added embedded points are endowed with full simulation capability allowing them to collide, interact with each other, and interact with the parent geometry in the fashion of a particle-centric simulation system. We demonstrate how this formulation facilitates tasks such as arbitrary refinement or resampling for collision processing, the handling of multiple and possibly conflicting constraints (e.g. when cloth is nonphysically pinched between two objects), the straightforward treatment of fracture, and sub-element resolution of elasticity and plasticity.

Hybrid Simulation of Deformable Solids

Continuous Collision Detection for Articulated Models using Taylor Models and Temporal Culling

“We present a fast continuous collision detection (CCD) algorithm for articulated models using Taylor models and temporal culling. Our algorithm is a generalization of conservative advancement (CA) from convex models [Mirtich 1996] to articulated models with non-convex links. Given the initial and final configurations of a moving articulated model, our algorithm creates a continuous motion with constant translational and rotational velocities for each link, and checks for interferences between the articulated model under continuous motion and other models in the environment and for self-collisions. If collisions occur, our algorithm reports the first time of contact (TOC) as well as collision witness features. We have implemented our CCD algorithm and applied it to several challenging scenarios including locomotion generation, articulated body dynamics and character motion planning. Our algorithm can perform CCDs including self-collisions for articulated models consisting of many links and tens of thousands of triangles in 1.22 ms on average running on a 3.6 GHz Pentium 4 PC. This is an improvement on the performance of prior algorithms of more than an order of magnitude.”

Continuous Collision Detection for Articulated Models using Taylor Models and Temporal Culling

A Fast Variational Framework for Accurate Solid-Fluid Coupling

“Physical simulation has emerged as a compelling animation technique, yet current approaches to coupling simulations of fluids and solids with irregular boundary geometry are inefficient or cannot handle some relevant scenarios robustly. We propose a new variational approach which allows robust and accurate solution on relatively coarse Cartesian grids, allowing possibly orders of magnitude faster simulation. By rephrasing the classical pressure projection step as a kinetic energy minimization, broadly similar to modern approaches to rigid body contact, we permit a robust coupling between fluid and arbitrary solid simulations that always gives a well-posed symmetric positive semi-definite linear system. We provide several examples of efficient fluid-solid interaction and rigid body coupling with sub-grid cell flow. In addition, we extend the framework with a new boundary condition for free-surface flow, allowing fluid to separate naturally from solids.”

A Fast Variational Framework for Accurate Solid-Fluid Coupling

Fracturing Rigid Materials

“We propose a novel approach to fracturing (and denting) brittle materials. To avoid the computational burden imposed by the stringent time step restrictions of explicit methods or with solving nonlinear systems of equations for implicit methods, we treat the material as a fully rigid body in the limit of infinite stiffness. In addition to a triangulated surface mesh and level set volume for collisions, each rigid body is outfitted with a tetrahedral mesh upon which finite element analysis can be carried out to provide a stress map for fracture criteria. We demonstrate that the commonly used stress criteria can lead to arbitrary fracture (especially for stiff materials) and instead propose the notion of a time averaged stress directly into the FEM analysis. When objects fracture, the virtual node algorithm provides new triangle and tetrahedral meshes in a straightforward and robust fashion. Although each new rigid body can be rasterized to obtain a new level set, small shards can be difficult to accurately resolve. Therefore, we propose a novel collision handling technique for treating both rigid bodies and rigid body thin shells represented by only a triangle mesh.”

Fracturing Rigid Materials