A method for analytically calculating the forces between systems of rigid bodies in resting (non-colliding) contact is presented. The systems of bodies may either be in motion or static equilibrium and adjacent bodies may touch at multiple points. The analytic formulation of the forces between bodies in non-colliding contact can be modified to deal with colliding bodies. Accordingly, an improved method for analytically calculating the forces between systems of rigid bodies in colliding contact is also presented. Both methods can be applied to systems with arbitrary holonomic geometric constraints, such as linked figures. The analytical formulations used treat both holonomic and non-holonomic constraints in a consistent manner.

A formulation for the contact forces between curved surfaces in resting (non-colliding) contact is presented. In contrast to previous formulations, constraints on the allowable tangential movement between contacting surfaces are not required. Surfaces are restricted to be twice-differentiable surfaces without boundary. Only finitely many contact points between surfaces are allowed; however, the surfaces need not be convex. The formulation yields the contact forces between curved surfaces and polyhedra as well. Algorithms for performing collision detection during simulation on bodies composed of both polyhedra and strictly convex curved surfaces are also presented. The collision detection algorithms exploit the geometric coherence between successive time steps of the simulation to achieve efficient running times.

We introduce a promising new approach to rigid body dynamic simulation called impulse-based simulation. The method is well suited to modeling physical systems with large numbers of collisions, or with contact modes that change frequently. All types of contact (colliding, rolling, sliding, and resting) are modeled through a series of collision impulses between the objects in contact, hence the method is simpler and faster than constraint-based simulation. We have implemented an impulse-based simulator that can currently achieve interactive simulation times, and real time simulation seems within reach. In addition, the simulator has produced physically accurate results in several qualitative and quantitative experiments. After giving an overview of impulse-based dynamic simulation, we discuss collision detection and collision response in this context, and present

Abstract not found

We present efficient algorithms for collision detection and contact determination between geometric models, described by linear or curved boundaries, undergoing rigid motion. The heart of our collision detection algorithm is a simple and fast incremental method to compute the distance between two convex polyhedra. It utilizes convexity to establish some local applicability criteria for verifying the closest features. A preprocessing procedure is used to subdivide each feature's neighboring features to a constant size and thus guarantee expected constant running time for each test. The expected constant time performance is an attribute from exploiting the geometric coherence and locality. Let n be the total number of features, the expected run time is between O( p n) and O(n) ...

This paper develops a systematic approach to deriving dynamic models from parametrically defined solid primitives, global geometric deformations and local finiteelement deformations. Even though their kinematics is stylized by the particular solid primitive used, the models behave in a physically correct way with prescribed mass distributions and elasticities. We also propose efficient constraint methods for connecting these new dynamic primitives together to make articulated models. Our techniques make it possible to build and animate constrained, nonrigid, unibody or multibody objects in simulated physical environments at interactive rates.

Techniques are presented that are used to animate and ren-der particle systems with the Connection Machine CM-2, a data parallel supercomputer. A particle behavior language provides an animator with levels of control from kinematic spllne motions to physically based simulations. A parallel particle rendering system allows particles of different shapes, sizes, colors and transparencies to be rendered with anti-allasing, hidden surfaces, and motion-blur. One virtual pro-cessor is assigned to each primitive data element: one to each particle, and during the rendering process, one to each pixeLsized particle fragment, and to each pixel. These tools are used to model dynamic phenomena such as wind, snow, water, and fire. 2

An articulated figure is often modeled as a set of rigid segments connected with joints. Its configuration can be altered by varying the joint angles. Although it is straightforward to compute figure configurations given joint angles (forward kinematics), it is not so to find the joint angles for a desired configuration (inverse kinematics). Since the inverse kinematics problem is of special importance to an animator wishing to set a figure to a posture satisfying a set of positioning constraints, researchers have proposed many approaches. But when we try to follow these approaches in an interactive animation system where the object to operate on is as highly articulated as a realistic human figure, they fail in either generality or performance, and so a new approach is fostered. Our approach is based on nonlinear programming techniques. It has been used for several years in the spatial constraint system in the Jack TM human figure simulation software developed at the Compute...

Current linear-time simulation methods for articulated figures are based exclusively on reduced-coordinate formulations. This paper describes a general, non-iterative linear-time simulation method based instead on Lagrange multipliers. Lagrange multiplier methods are important for computer graphics applications because they bypass the difficult (and often intractable) problem of parameterizing a system’s degrees of freedom. Given a loop-free set of n equality constraints acting between pairs of bodies, the method takes O(n) time to compute the system’s dynamics. The method does not rely on matrix bandwidth, so no assumptions about the constraints’ topology are needed. Bodies need not be rigid, constraints can be of various dimensions, and unlike reduced-coordinate approaches, nonholonomic (e.g. velocity-dependent) constraints are allowed. An additional set of k one-dimensional constraints which induce loops and/or handle inequalities can be accommodated with cost O(kn). This makes it practical to simulate complicated, closedloop articulated figures with joint-limits and contact at interactive rates. A complete description of a sample implementation is provided in pseudocode. 1

Animation through the numerical simulation of physics-based graphics models offers unsurpassed realism, but it can be computationally demanding. Likewise, finding controllers that enable physics-based models to produce desired animations usually entails formidable computational cost. This paper demonstrates the possibility of replacing the numerical simulation and control of model dynamics with a dramatically more efficient alternative. In particular, we propose the NeuroAnimator, a novel approach to creating physically realistic animation that exploits neural networks. NeuroAnimators are automatically trained off-line to emulate physical dynamics through the observation of physics-based models in action. Depending on the model, its neural network emulator can yield physically realistic animation one or two orders of magnitude faster than conventional numerical simulation. Furthermore, by exploiting the network structure of the NeuroAnimator, we introduce a fast algorithm for learning controllers that enables either physics-based models or their neural network emulators to synthesize motions satisfying prescribed animation goals. We demonstrate NeuroAnimators for passive and active (actuated) rigid body, articulated, and deformable physics-based models.