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.

In this paper, we survey the state of the art in collision detection between general geometric models. The set of models include polygonal objects, spline or algebraic surfaces, CSG models, and deformable bodies. We present a number of techniques and systems available for contact determination. We also describe several N-body algorithms to reduce the number of pairwise intersection tests. 1 Introduction The goal of collision detection (also known as interference detection or contact determination) is to automatically report a geometric contact when it is about to occur or has actually occurred. The geometric models may be polygonal objects, splines, or algebraic surfaces. The problem is encountered in computer-aided design and machining (CAD/CAM), robotics and automation, manufacturing, computer graphics, animation and computer simulated environments. Collision detection enables simulationbased design, tolerance verification, engineering analysis, assembly and dis-assembly, motion pla...

This paper presents a method for approximating polyhedral objects to support a timecritical collision-detection algorithm. The approximations are hierarchies of spheres, and they allow the time-critical algorithm to progressively refine the accuracy of its detection, stopping as needed to maintain the real-time performance essential for interactive applications. The key to this approach is a preprocess that automatically builds tightly fitting hierarchies for rigid and articulated objects. The preprocess uses medial-axis surfaces, which are skeletal representations of objects. These skeletons guide an optimization technique that gives the hierarchies accuracy properties appropriate for collision detection. In a sample application, hierarchies built this way allow the time-critical collision-detection algorithm to have acceptable accuracy, improving significantly on that possible with hierarchies built by previous techniques. The performance of the time-critical algorithm in this appli...

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The need to perform fast and accurate proximity queries arises frequently in physically-based modeling, simulation, animation, real-time interaction within a virtual environment, and game dynamics. The set of proximity queries include intersection detection, tolerance verification, exact and approximate minimum distance computation, and (disjoint) contact determination. Specialized data structures and algorithms have often been designed to perform each type of query separately. We present a unified approach to perform any of these queries seamlessly for general, rigid polyhedral objects with boundary representations which are orientable 2-manifolds. The proposed method involves a hierarchical data structure built upon a surface decomposition of the models. Furthermore, the incremental query algorithm takes advantage of coherence between successive frames. It has been applied to complex benchmarks and compares very favorably with earlier algorithms and systems.

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.

Typical high-level directives for locomotion of human-like characters are useful for interactive games and simulations as well as for off-line production animation. In this paper, we present a new scheme for planning natural-looking locomotion of a biped figure to facilitate rapid motion prototyping and task-level motion generation. Given start and goal positions in a virtual environment, our scheme gives a sequence of motions to move from the start to the goal using a set of live-captured motion clips. Based on a novel combination of probabilistic path planning and hierarchical displacement mapping, our scheme consists of three parts: roadmap construction, roadmap search, and motion generation. We randomly sample a set of valid footholds of the biped figure from the environment to construct a directed graph, called a roadmap, that guides the locomotion of the figure. Every edge of the roadmap is associated with a live-captured motion clip. Augmenting the roadmap with a posture transition graph, we traverse it to obtain the sequence of input motion clips and that of target footprints. We finally adapt the motion sequence to the constraints specified by the footprint sequence to generate a desired locomotion.

We consider the problem of designing traditional (e.g. vibratory bowl) feeders for singulating and orienting industrial parts. Our ultimate goal is to prototype new designs using analytically- and geometrically-based methods. We have developed a tool for designing industrial parts feeders based on dynamic simulation. Our tool allows us to automatically perform multiple feeder design experiments, and to evaluate their outcomes. These results can then be used to compute the probabilities of a Markov model for the feeder. To demonstrate our technique, we present preliminary results for the design of two simple feeders. Our findings suggest that using dynamic simulation is a promising approach for designing parts feeders. 1 Introduction Vibratory bowl feeders and hopper feeders have proliferated industry as a cost-effective means for reliably orienting parts. These feeders and their transfer conveyorsaccount for nearly one-third of the cost and failure risk of an assembly system [8] . H...

Computer haptics, an emerging field of research that is analogous to computer graphics, is concerned with the generation and rendering of haptic virtual objects. In this paper, we propose an efficient haptic rendering method for displaying the feel of 3-D polyhedral objects in virtual environments (VEs). Using this method and a haptic interface device, the users can manually explore and feel the shape and surface details of virtual objects. The main component of our rendering method is the "neighborhood watch" algorithm that takes advantage of precomputed connectivity information for detecting collisions between the end effector of a force-reflecting robot and polyhedral objects in VEs. We use a hierarchical database, multithreading techniques, and efficient search procedures to reduce the computational time such that the haptic servo rate after the first contact is essentially independent of the number of polygons that represent the object. We also propose efficient methods for displaying surface properties of objects such as haptic texture and friction. Our haptic-texturing techniques and friction model can add surface details onto convex or concave 3-D polygonal surfaces. These haptic-rendering techniques can be extended to display dynamics of rigid and deformable objects. 1

The straight skeleton of a polygon is a variant of the medial axis, introduced by Aichholzer et al., defined by a shrinking process in which each edge of the polygon moves inward at a fixed rate. We construct the straight skeleton of an n-gon with r reflex vertices in time O(n 1+" +n 8=11+" r 9=11+" ), for any fixed " ? 0, improving the previous best upper bound of O(nr log n). Our algorithm simulates the sequence of collisions between edges and vertices during the shrinking process, using a technique of Eppstein for maintaining extrema of binary functions to reduce the problem of finding successive interactions to two dynamic range query problems: (1) maintain a changing set of triangles in IR 3 and answer queries asking which triangle would be first hit by a query ray, and (2) maintain a changing set of rays in IR 3 and answer queries asking for the lowest intersection of any ray with a query triangle. We also exploit a novel characterization of the straight skeleton as a ...