Unified processing of constraints for interactive simulation

International audienceThis paper introduces a generic way of dealing with a set of different constraints (bilateral, unilateral, dry friction) in the context of interactive simulation. We show that all the mentioned constraints can be handled within a unified framework: we define the notion of generalized constraints, which can be derived into most classical constraints types. The solving method is based on an implicit treatment of constraints that provides good stability for interactive applications using deformable models and rigid bodies. Each constraint law is expressed in constraint subspace, making constraint evaluation much easier. A global solution is calculated using an iterative process that takes into account the mechanical coupling between the constraints. Various examples, from basic to more complex, show the practical advantage of using generalized constraints, as a way of creating heterogeneously constrained systems, as well as the scalability of the proposed method

MICADO: Models of Interactive Constraints for the Assembling of 1D Deformable Objects

This paper introduces a set of Lagrangian constraints, allowing most needed interaction and combinations of one-dimensional deformable elements for creating complex structures. The proposed tools can potentially be used with a large set of available 1D-models. All constraints formulation are compatible with linear, displacement-based, integration schemes. The proposed constraints allow for real-time complex structure simulation, and also novel interactions between simulated objects. Various examples are provided, illustrating the benefit of the proposed numerical tools

Interactive Constrained Dynamics for Rigid and Deformable Objects

Following the continuous increase in computational power of consumer hardware, interactive virtual environments have been recently enriched with more and more complex deformable objects. However, many physics engines are still very limited in the way they handle interacting rigid and deformable objects. This paper proposes a constraint-based approach to real-time simulation of coupled rigid and deformable objects capable of providing two-way interactions. Similar techniques have seen widespread usage for either rigid or deformable objects, but not for the simultaneous simulation of both. By extending such approaches, we show not only how interaction is possible but also how it can be performed at real-time rates. We address contact response and also show how to implement typical constraints to enforce limitations in the degrees of freedom and to enhance the dynamical properties of deformable objects. The method is easily integrated into existing physics engines that use similar constraint solvers and is independent on the kind of deformable object paradigm chosen. The provided simulation results show that the method is fast and effective in handling contacts between rigid and deformable objects and in simulating friction and other kinds of constraints

Coupling, Conservation, and Performance in Numerical Simulations

This thesis considers three aspects of the numerical simulations, which arecoupling, conservation, and performance. We conduct a project and addressone challenge from each of these aspects.We propose a novel penalty force to enforce contacts with accurate Coulombfriction. The force is compatible with fully-implicit time integration and theuse of optimization-based integration. In addition to processing collisionsbetween deformable objects, the force can be used to couple rigid bodies todeformable objects or the material point method. The force naturally leads tostable stacking without drift over time, even when solvers are not run toconvergence. The force leads to an asymmetrical system, and we provide apractical solution for handling these.Next we present a new technique for transferring momentum and velocity betweenparticles and MAC grids based on the Affine-Particle-In-Cell (APIC) frameworkpreviously developed for co-locatedgrids. We extend the original APIC paper and show thatthe proposed transfers preserve linear and angular momentum and also satisfyall of the original APIC properties.Early indications in the original APIC paper suggested that APIC might besuitable for simulating high Reynolds fluids due to favorable retention ofvortices, but these properties were not studied further. We use twodimensional Fourier analysis to investigate dissipation in the limit \dt=0.We investigate dissipation and vortex retention numerically to quantify theeffectiveness of APIC compared with other transfer algorithms.Finally we present an efficient solver for problems typically seen inmicrofluidic applications.Microfluidic ``lab on a chip'' devices are small devices that operate on smalllength scales on small volumes of fluid. Designs for microfluidic chips aregenerally composed of standardized and often repeated components connected bylong, thin, straight fluid channels. We propose a novel discretizationalgorithm for simulating the Stokes equations on geometry with these features,which produces sparse linear systems with many repeated matrix blocks. Thediscretization is formally third order accurate for velocity and second orderaccurate for pressure in the $L^\infty$ norm. We also propose a novel linearsystem solver based on cyclic reduction, reordered sparse Gaussian elimination,and operation caching that is designed to efficiently solve systems withrepeated matrix blocks