We present warp-canceling corotation , a nonlinear finite element formulation for elastodynamic simulation that achieves fast performance by making only partial or delayed changes to the simulation's linearized system matrices. Coupled with an algorithm for incremental updates to a sparse Cholesky factorization, the method realizes the stability and scalability of a sparse direct method without the need for expensive refactorization at each time step. This finite element formulation combines the widely used corotational method with stiffness warping so that changes in the per-element rotations are initially approximated by inexpensive per-node rotations. When the errors of this approximation grow too large, the per-element rotations are selectively corrected by updating parts of the matrix chosen according to locally measured errors. These changes to the system matrix are propagated to its Cholesky factor by incremental updates that are much faster than refactoring the matrix from scratch. A nested dissection ordering of the system matrix gives rise to a hierarchical factorization in which changes to the system matrix cause limited, well-structured changes to the Cholesky factor. We show examples of simulations that demonstrate that the proposed formulation produces results that are visually comparable to those produced by a standard corotational formulation. Because our method requires computing only partial updates of the Cholesky factor, it is substantially faster than full refactorization and outperforms widely used iterative methods such as preconditioned conjugate gradients. Our method supports a controlled trade-off between accuracy and speed, and unlike most iterative methods its performance does not slow for stiffer materials but rather it actually improves.

Monte Carlo ray tracing of soft shadows produced by area lighting and intricate geometries, such as the shadows through plant leaves or arrays of blockers, is a critical challenge. The final image often has relatively smooth shadow patterns, since it integrates over the light source. However, Monte Carlo rendering exhibits considerable noise even at high sample counts because of the large variance of the integrand due to the intricate shadow function. This article develops an efficient diffuse soft shadow technique for mid to far occluders that relies on a new 4D cache and sheared reconstruction filter. For this, we first derive a frequency analysis of shadows for planar area lights and complex occluders. Our analysis subsumes convolution soft shadows for parallel planes as a special case. It allows us to derive 4D sheared filters that enable lower sampling rates for soft shadows. While previous sheared-reconstruction techniques were able primarily to index samples according to screen position, we need to perform reconstruction at surface receiver points that integrate over vastly different shapes in the reconstruction domain. This is why we develop a new light-field-like 4D data structure to store shadowing values and depth information. Any ray tracing system that shoots shadow rays can easily incorporate our method to greatly reduce sampling rates for diffuse soft shadows.

This paper describes a method for animating the appearance of clothing, such as pants or a shirt, that fits closely to a figure's body. Compared to flowing cloth, such as loose dresses or capes, these types of garments involve nearly continuous collision contact and small wrinkles, that can be troublesome for traditional cloth simulation methods. Based on the observation that the wrinkles in close-fitting clothing behave in a predominantly kinematic fashion, we have developed an example-based wrinkle synthesis technique. Our method drives wrinkle generation from the pose of the figure's kinematic skeleton. This approach allows high quality clothing wrinkles to be combined with a coarse cloth simulation that computes the global and dynamic aspects of the clothing motion. While the combined results do not exactly match a high-resolution reference simulation, they do capture many of the characteristic fine-scale features and wrinkles. Further, the combined system runs at interactive rates, making it suitable for applications where high-resolution offline simulations would not be a viable option. The wrinkle synthesis method uses a precomputed database built by simulating the high-resolution clothing as the articulated figure is moved over a range of poses. In principle, the space of poses is exponential in the total number of degrees of freedom; however clothing wrinkles are primarily affected by the nearest joints, allowing each joint to be processed independently. During synthesis, mesh interpolation is used to consider the influence of multiple joints, and combined with a coarse simulation to produce the final results at interactive rates.

We present a visualization technique for simulated fluid dynamics data that visualizes the gradient of the velocity field in an intuitive way. Our work is inspired by rheoscopic particles, which are small, flat particles that, when suspended in fluid, align themselves with the shear of the flow. We adopt the physical principles of real rheoscopic particles and apply them, in model form, to 3D velocity fields. By simulating the behavior and reflectance of these particles, we are able to render 3D simulations in a way that gives insight into the dynamics of the system. The results can be rendered in real time, allowing the user to inspect the simulation from all perspectives. We achieve this by a combination of precomputations and fast ray tracing on the GPU. We demonstrate our method on several different simulations, showing their complex dynamics in the process.

A new approach to the 3D human motion tracking problem is proposed, which combines several particle filters with a physical simulation of a flexible body model. The flexible body model allows the partitioning of the state space of the human model into much smaller subsets, while finding a solution considering all the partial results of the particle filters. The flexible model also creates the necessary interaction between the different particle filters and allows effective semi-hierarchical tracking of the human body. The physical simulation does not require inverse kinematics calculations and is hence fast and easy to implement. Furthermore the system also builds an appearance model on-the-fly which allows it to work without a foreground segmentation. The system is able to start tracking automatically with a convenient initialization procedure. The implementation runs with 10 Hz on a regular PC using a stereo camera and is hence suitable for Human-Robot Interaction applications.