Local collision avoidance algorithms in crowd simulation often ignore agents beyond a neighborhood of a certain size. This cutoff can result in sharp changes in trajectory when large groups of agents enter or exit these neighborhoods. In this work, we exploit the insight that exact collision avoidance is not necessary between agents at such large distances, and propose a novel algorithm for extending existing collision avoidance algorithms to perform approximate, long-range collision avoidance. Our formulation performs long-range collision avoidance for distant agent groups to efficiently compute trajectories that are smoother than those obtained with state-of-the-art techniques and at faster rates. Comparison to real-world data demonstrates that crowds simulated with our algorithm exhibit an improved speed sensitivity to density similar to human crowds. Another issue often sidestepped in existing work is that discrete and continuum collision avoidance algorithms have different regions of applicability. For example, low-density crowds cannot be modeled as a continuum, while high-density crowds can be expensive to model using discrete methods. We formulate a hybrid technique for crowd simulation which can accurately and efficiently simulate crowds at any density with seamless transitions between continuum and discrete representations. Our approach blends results from continuum and discrete algorithms, based on local density and velocity variance. In addition to being robust across a variety of group scenarios, it is also highly efficient, running at interactive rates for thousands of agents on portable systems.

We present a novel approach for wave-based sound propagation suitable for large, open spaces spanning hundreds of meters, with a small memory footprint. The scene is decomposed into disjoint rigid objects. The free-field acoustic behavior of each object is captured by a compact per-object transfer function relating the amplitudes of a set of incoming equivalent sources to outgoing equivalent sources. Pairwise acoustic interactions between objects are computed analytically to yield compact inter-object transfer functions. The global sound field accounting for all orders of interaction is computed using these transfer functions. The runtime system uses fast summation over the outgoing equivalent source amplitudes for all objects to auralize the sound field for a moving listener in real time. We demonstrate realistic acoustic effects such as diffraction, low-passed sound behind obstructions, focusing, scattering, high-order reflections, and echoes on a variety of scenes.

It is a common artifact of multi-agent motion planning for groups of agents, following similar paths, to converge to a line. This occurs because the agents' immediate goals, also known as waypoints, are frequently a common point in space. Contention for the point goal causes agents to line up and generally interferes with agent motion. By extending the definition of an immediate point goal to a line segment, which we call a "way portal", we enable the agents to better utilize the space available to them in responding to dynamic constraints. We present a novel multi-agent navigation algorithm to efficiently compute the trajectories of autonomous agents using these way portals. We have incorporated the concept into a velocity obstacle-based local navigation model and present a new segment optimization algorithm that efficiently computes a new agent velocity with respect to the way portal. We show how way portal data is extracted from current global navigation data structures, such as navigation meshes. The algorithm is relatively simple to implement and has a small run-time cost (approximately 3 μs per agent.) We highlight its performance in different game-like scenarios and observe improved agent behavior and better utilization of free space.

We present a novel approach to direct and control virtual crowds using navigation fields. Our method guides one or more agents toward desired goals based on guidance fields. The system allows the user to specify these fields by either sketching paths directly in the scene via an intuitive authoring interface or by importing motion flow fields extracted from crowd video footage. We propose a novel formulation to blend input guidance fields to create singularity-free, goal-directed navigation fields. Our method can be easily combined with the most current local collision avoidance methods and we use two such methods as examples to highlight the potential of our approach. We illustrate its performance on several simulation scenarios.

We present a method to control the behavior of elastic, deformable material in a dynamic simulation. We introduce dynamic morph targets, the equivalent in dynamic simulation to the geometric morph targets in (quasi-static) modeling. Dynamic morph targets define the pose-dependent physical state of soft objects, including surface deformation and elastic and inertial properties. Given these morph targets, our algorithm then derives a dynamic model that can be simulated in time-pose-space, interpolating the dynamic morph targets at the input poses. Our method easily integrates with current modeling and animation pipelines: at different poses, an artist simply provides a set of dynamic morph targets. Whether these input states are physically plausible is completely up to the artist. The resulting deformable models expose fully dynamic, pose-dependent behavior, driven by the artist-provided morph targets, complete with inertial effects.

Large dense crowds show aggregate behavior with reduced individual freedom of movement. We present a novel, scalable approach for simulating such crowds, using a dual representation both as discrete agents and as a single continuous system. In the continuous setting, we introduce a novel variational constraint calledunilateral incompressibility, to model the large-scale behavior of the crowd, and accelerate inter-agent collision avoidance in dense scenarios. This approach makes it possible to simulate very large, dense crowds composed of up to a hundred thousand agents at near-interactive rates on desktop computers.

We present an interactive algorithm for continuous collision detection between deformable models. We introduce multiple techniques to improve the culling efficiency and the overall performance of continuous collision detection. First, we present a novel formulation for continuous normal cones and use these normal cones to efficiently cull large regions of the mesh as part of self-collision tests. Second, we introduce the concept of "procedural representative triangles" to remove all redundant elementary tests between nonadjacent triangles. Finally, we exploit the mesh connectivity and introduce the concept of "orphan sets" to eliminate redundant elementary tests between adjacent triangle primitives. In practice, we can reduce the number of elementary tests by two orders of magnitude. These culling techniques have been combined with bounding volume hierarchies and can result in one order of magnitude performance improvement as compared to prior collision detection algorithms for deformable models. We highlight the performance of our algorithm on several benchmarks, including cloth simulations, N-body simulations, and breaking objects.

We present a new approach to accelerate collision detection for deformable models. Our formulation applies to all triangulated models and significantly reduces the number of elementary tests between features of the mesh, i.e., vertices, edges and faces. We introduce the notion of Representative-Triangles, standard geometric triangles augmented with mesh feature information and use this representation to achieve better collision query performance. The resulting approach can be combined with bounding volume hierarchies and works well for both inter-object and self-collision detection. We demonstrate the benefit of Representative-Triangles on continuous collision detection for cloth simulation and N-body collision scenarios. We observe up to a one-order of magnitude reduction in feature-pair tests and up to a 5X improvement in query time.

We present an interactive algorithm for continuous collision detection between deformable models. We introduce two techniques to improve the culling efficiency and reduce the number of potentially colliding triangle candidate pairs. First, we present a novel formulation for continuous normal cones and use these normal cones to efficiently cull large regions of the mesh from self-collision tests. Second, we exploit the mesh connectivity and introduce the concept of orphan sets to eliminate almost all redundant elementary tests between adjacent triangles. In particular, we can reduce the number of elementary tests by many orders of magnitude. These culling techniques have been combined with bounding volume hierarchies and can result in one order of magnitude performance improvement as compared to prior algorithms for deformable models. We highlight the performance of our algorithm on several benchmarks, including cloth simulations, N-body simulations and breaking objects.

Streamline integration of fields produced by computational fluid mechanics simulations is a commonly used tool for the investigation and analysis of fluid flow phenomena. Integration is often accomplished through the application of ordinary differential equation (ODE) integrators--integrators whose error characteristics are predicated on the smoothness of the field through which the streamline is being integrated--smoothness which is not available at the inter-element level of finite volume and finite element data. Adaptive error control techniques are often used to ameliorate the challenge posed by inter-element discontinuities. As the root of the difficulties is the discontinuous nature of the data, we present a complementary approach of applying smoothness-enhancing accuracy-conserving filters to the data prior to streamline integration. We investigate whether such an approach applied to uniform quadrilateral discontinuous Galerkin (high-order finite volume) data can be used to augment current adaptive error control approaches. We discuss and demonstrate through numerical example the computational trade-offs exhibited when one applies such a strategy.

We present a novel approach for efficient path planning and navigation of multiple virtual agents in complex dynamic scenes. We introduce a new data structure, Multi-agent Navigation Graph (MaNG), which is constructed using first- and second-order Voronoi diagrams. The MaNG is used to perform route planning and proximity computations for each agent in real time. Moreover, we use the path information and proximity relationships for local dynamics computation of each agent by extending a social force model [Helbing05]. We compute the MaNG using graphics hardware and present culling techniques to accelerate the computation. We also address undersampling issues and present techniques to improve the accuracy of our algorithm. Our algorithm is used for real-time multi-agent planning in pursuit-evasion, terrain exploration and crowd simulation scenarios consisting of hundreds of moving agents, each with a distinct goal.

We present a novel approach for real-time path planning of multiple virtual agents in complex dynamic scenes. We introduce a new data structure, Multi-agent Navigation Graph (MaNG), which is constructed from the first- and second-order Voronoi diagrams. The MaNG is used to perform route planning and proximity computations for each agent in real time. We compute the MaNG using graphics hardware and present culling techniques to accelerate the computation. We also address undersampling issues for accurate computation. Our algorithm is used for real-time multi-agent planning in pursuit-evasion and crowd simulation scenarios consisting of hundreds of moving agents, each with a distinct goal