We present an algorithm to efficiently and robustly process collisions, contact and friction in cloth simulation. It works with any technique for simulating the internal dynamics of the cloth, and allows true modeling of cloth thickness. We also show how our simulation data can be post-processed with a collision-aware subdivision scheme to produce smooth and interference free data for rendering.

We consider the simulation of nonconvex rigid bodies focusing on interactions such as collision, contact, friction (kinetic, static, rolling and spinning) and stacking. We advocate representing the geometry with both a triangulated surface and a signed distance function defined on a grid, and this dual representation is shown to have many advantages. We propose a novel approach to time integration merging it with the collision and contact processing algorithms in a fashion that obviates the need for ad hoc threshold velocities. We show that this approach matches the theoretical solution for blocks sliding and stopping on inclined planes with friction. We also present a new shock propagation algorithm that allows for efficient use of the propagation (as opposed to the simultaneous) method for treating contact. These new techniques are demonstrated on a variety of problems ranging from simple test cases to stacking problems with as many as 1000 nonconvex rigid bodies with friction as shown in Figure 1.

This dissertation was presented by Gary D. Hart It was defended on

The layout of large scenes can be a time-consuming and tedious task. In most current systems, the user must position each of the objects by hand, one at a time. This paper presents a constraint-based automatic placement system, which allows the user to quickly and easily lay out complex scenes. The system

Figure 1: Staggered Projections resolves frictional contact between a wide range of rigid and deformable models at rates suitable for (a) interactive haptic simulations, as well as accurate animations that capture important frictional contact phenomena such as: (b) large-deformation frictional contact with reduced StVK models, (c) large-scale, frictional stacking and jamming of large numbers of objects without constraint drift, (d) and long term stable simulation of difficult, frictionally dependent structures. 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.

We develop a method for reliable simulation of elastica in complex contact scenarios. Our focus is on firmly establishing three parameter-independent guarantees: that simulations of well-posed problems (a) have no interpenetrations, (b) obey causality, momentum- and energy-conservation laws, and (c) complete in finite time. We achieve these guarantees through a novel synthesis of asynchronous variational integrators, kinetic data structures, and a discretization of the contact barrier potential by an infinite sum of nested quadratic potentials. In a series of two- and threedimensional examples, we illustrate that this method more easily handles challenging problems involving complex contact geometries, sharp features, and sliding during extremely tight contact.

Most of well-known approaches for rigid body simulations are formulated in the contact-space. Thanks to Gauss ’ principle of least constraints, the frictionless dynamics problems are formulated in a motion-space. While the two formulations are mathematically equivalent, they are not computationally equivalent. The motion-space formulation is better conditionned, always sparse, needs less memory, and avoids some unnecessary computations. A preliminary experimental comparison suggests that an algorithm operating in the motionspace takes advantage of sparsity to perform increasingly better than a contact-space algorithm as the average number of contact points per object increases. 1

In this paper a new method for handling collisions and permanent contacts between rigid bodies is presented. Constraint-based methods for computing contact forces with friction provide a high degree of accuracy. The computation is often transformed into an optimization problem and solved with techniques like linear or quadratic programming. Impulse-based methods compute impulses to prevent colliding bodies from interpenetrating. The determination of these impulses is simple and fast. The impulse-based methods are very efficient but they are less accurate than the constraint-based methods because they resolve only one contact between two colliding bodies at the same time. The presented method uses a constraint-based approach. It can handle multiple contacts between two colliding bodies at the same time. For every collision and contact a non-penetration constraint is defined. These constraints are satisfied by iteratively computing impulses. In the same iteration loop impulses for dynamic and static friction are determined. The new method provides the accuracy of a constraint-based method and is efficient and easy to implement like an impulse-based one.

Abstract—A suite of algorithms is presented for contact resolution in rigid body simulation under the Coulomb friction model: Given a set of rigid bodies with many contacts among them, resolve dynamic contacts (collisions) and static (persistent) contacts. The suite consists of four algorithms: 1) partial sequential collision resolution, 2) final resolution of collisions through the solution of a single convex QP (positive semidefinite quadratic program), 3) resolution of static contacts through the solution of a single convex QP, 4) freezing of “stationary ” bodies. This suite can generate realistic-looking results for simple examples yet, for the first time, can also tractably resolve contacts for a simulation as large as 1,000 cubes in an “hourglass. ” Freezing speeds up this simulation by more than 25 times. Thanks to excellent commercial QP technology, the contact resolution suite is simple to implement and can be “plugged into” any simulation algorithm to provide fast and realistic-looking animations of rigid bodies. Index Terms—Quadratic programming, computer graphics, physically-based modeling, simulation, animation. æ

In this paper, we propose a new approach to simulate the small intestine in a context of laparoscopic surgery. The ultimate aim of this work is to simulate the training of a basic surgical gesture in real-time: moving aside the intestine to reach hidden areas of the abdomen. The main problem posed by this kind of simulation is animating the intestine. The problem comes from the nature of the intestine: a very long tube which is not isotropically elastic, and is contained in a volume that is small when compared to the intestine's length. It coils extensively and collides with itself in many places.