Hierarchical spacetime control

Specifying the motion of an animated linked figure such that it achieves given tasks (e.g., throwing a ball into a basket) and performs the tasks in a realistic fashion (e.g., gracefully, and following physical laws such as gravity) has been an elusive goal for computer animators. The spacetime constraints paradigm has been shown to be a valuable approach to this problem, but it suffers from computational complexity growth as creatures and tasks approach those one would like to animate. The complexity is shown to be, in part, due to the choice of finite basis with which to represent the trajectories of the generalized degrees of freedom. This paper describes new features to the spacetime constraints paradigm to address this problem.The functions through time of the generalized degrees of freedom are reformulated in a hierarchical wavelet representation. This provides a means to automatically add detailed motion only where it is required, thus minimizing the number of discrete variables. In addition the wavelet basis is shown to lead to better conditioned systems of equations and thus faster convergence.Engineering and Applied Science

Polyhedral Geometry and the Two-plane Parameterization

Recently the light-field and lumigraph systems have been proposed as general methods of representing the visual information present in a scene. These methods represent this information as a 4D function of light over the domain of directed lines. These systems use the intersection points of the lines on two planes to parameterize the lines in space. This paper explores the structure of the two-plane parameterization in detail. In particular we analyze the association between the geometry of the scene and subsets of the 4D data. The answers to these questions are essential to understanding the relationship between a lumigraph, and the geometry that it attempts to represent. This knowledge is potentially important for a variety of applications such as extracting shape from lumigraph data, and lumigraph compression.Engineering and Applied Science

Time Critical Lumigraph Rendering

It was illustrated in 1996 that the light leaving the convex hull of an object (or entering a convex region of empty space) can be fully characterized by a 4D function over the space of rays crossing a surface surrounding the object (or surrounding the empty space). Methods to represent this function and quickly render individual images from this representation given an arbitrary cameras were also described. This paper extends the work outlined by (Gortler et al) by demonstrating a taxonomy of methods to accelerate the rendering process by trading off quality for time. Given the specific limitation of a given hardware configuration, we discuss methods to tailor a critical time rendering strategy using these methods.Engineering and Applied Science

A geometrical approach to computing free-energy landscapes from short-ranged potentials

Particles interacting with short-ranged potentials have attracted increasing interest, partly for their ability to model mesoscale systems such as colloids interacting via DNA or depletion. We consider the free-energy landscape of such systems as the range of the potential goes to zero. In this limit, the landscape is entirely defined by geometrical manifolds, plus a single control parameter. These manifolds are fundamental objects that do not depend on the details of the interaction potential and provide the starting point from which any quantity characterizing the system—equilibrium or nonequilibrium—can be computed for arbitrary potentials. To consider dynamical quantities we compute the asymptotic limit of the Fokker–Planck equation and show that it becomes restricted to the low-dimensional manifolds connected by “sticky” boundary conditions. To illustrate our theory, we compute the low-dimensional manifolds for Graphic identical particles, providing a complete description of the lowest-energy parts of the landscape including floppy modes with up to 2 internal degrees of freedom. The results can be directly tested on colloidal clusters. This limit is a unique approach for understanding energy landscapes, and our hope is that it can also provide insight into finite-range potentials.Engineering and Applied Science

Wavelet Radiosity

Radiosity methods have been shown to be an effective means to solve the global illumination problem in Lambertian diffuse environments. These methods approximate the radiosity integral equation by projecting the unknown radiosity function into a set of basis functions with limited support resulting in a set of n linear equations where n is the number of discrete elements in the scene. Classical radiosity methods required the evaluation of n2 interaction coefficients. Efforts to reduce the number of required coefficients without compromising error bounds have focused on raising the order of the basis functions, meshing, accounting for discontinuities, and on developing hierarchical approaches, which have been shown to reduce the required interactions to O(n). In this paper we show that the hierarchical radiosity formulation is an instance of a more general set of methods based on wavelet theory. This general framework offers a unified view of both higher order element approaches to radiosity and the hierarchical radiosity methods. After a discussion of the relevant theory, we discuss a new set of linear time hierarchical algorithms based on wavelets such as the multiwavelet family and a flatlet basis which we introduce. Initial results of experimentation with these basis sets are demonstrated and discussed.Engineering and Applied Science

Radiosity and Relaxation Methods

To date, there has been some confusion in the computer graphics community about how the progressive radiosity (PR) method relates to standard numerical methods for solving linear systems of equations. We show that PR is actually equivalent to the combination of two numerical analysis techniques known as Southwell relaxation and Jacobi iteration. A new overshooting method similar to over relaxation can accelerate the convergence of the iterative radiosity methods.Engineering and Applied Science

Simplifying the Representation of Radiance from Multiple Emitters

International audienceIn recent work radiance function properties and discontinuity meshing have been used to construct high quality interpolants representing radiance. Such approaches do not consider the combined effect of multiple sources and thus perform unnecessary discontinuity meshing calculations and often construct interpolants with too fine subdivision. In this research we present an extended structured sampling algorithm that treats scenes with shadows and multiple sources. We then introduce an algorithm which simplifies the mesh based on the interaction of multiple sources. For unoccluded regions an a posteriori simplification technique is used. For regions in shadow, we first compute the maximal umbral/penumbral and penumbral/light boundaries. This construction facilitates the determination of whether full discontinuity meshing is required or whether it can be avoided due to the illumination from another source. An estimate of the error caused by potential simplification is used for this decision. Thus full discontinuitymesh calculation is only incurred in regions where it is necessary resulting in a more compact representation of radiance

Functional electrical stimulation driven by a brain–computer interface in acute and subacute stroke patients impacts beta power and long-range temporal correlation

Functional electrical stimulation (FES) is a standard rehabilitation approach applied by therapists to aid motor recovery in a paretic limb post-stroke. Information pertaining to the timing of a movement attempt can be obtained from changes in the power of oscillatory electrophysiological activity in motor cortical regions, derived from scalp electroencephalographic (EEG) recordings. The use of a brain–computer interface (BCI), to enable delivery of FES within a tight temporal window with a movement attempt detected in scalp EEG, is associated with greater motor recovery than conventional FES application in patients in the chronic phase post-stroke. We hypothesized that the heightened neural plasticity early post-stroke could further enhance motor recovery and that motor improvements would be accompanied by changes in the motor cortical sensorimotor rhythm after compared with before treatment. Here we assessed clinical outcome and changes in the sensorimotor rhythm in patients following subcortical stroke affecting the non-dominant hemisphere from a study comparing timing of FES delivery using a BCI, with a Sham group, receiving FES with no such temporal relationship. The BCI group showed greater clinical improvement following the treatment, particularly early post-stroke, and a greater decrease in beta oscillatory power and long-range temporal correlation over contralateral (ipsilesional) motor cortex. The electrophysiological changes are consistent with a reduction in compensatory processes and a transition towards a subcritical state when movement is triggered at the time of movement detection based on motor cortical oscillations