Ambient occlusion and directional (spherical harmonic) occlusion have become a staple of production rendering because they capture many visually important qualities of global illumination while being reusable across multiple artistic lighting iterations. However, ray-traced solutions for hemispherical occlusion require many rays per shading point (typically 256-1024) due to the full hemispherical angular domain. Moreover, each ray can be expensive in scenes with moderate to high geometric complexity. However, many nearby rays sample similar areas, and the final occlusion result is often low frequency. We give a frequency analysis of shadow light fields using distant illumination with a general BRDF and normal mapping, allowing us to share ray information even among complex receivers. We also present a new rotationally-invariant filter that easily handles samples spread over a large angular domain. Our method can deliver 4x speed up for scenes that are computationally bound by ray tracing costs.

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.

Motion blur is crucial for high-quality rendering, but is also very expensive. Our first contribution is a frequency analysis of motion-blurred scenes, including moving objects, specular reflections, and shadows. We show that motion induces a shear in the frequency domain, and that the spectrum of moving scenes can be approximated by a wedge. This allows us to compute adaptive space-time sampling rates, to accelerate rendering. For uniform velocities and standard axis-aligned reconstruction, we show that the product of spatial and temporal bandlimits or sampling rates is constant, independent of velocity. Our second contribution is a novel sheared reconstruction filter that is aligned to the first-order direction of motion and enables even lower sampling rates. We present a rendering algorithm that computes a sheared reconstruction filter per pixel, without any intermediate Fourier representation. This often permits synthesis of motion-blurred images with far fewer rendering samples than standard techniques require.

The ability to interactively edit BRDFs in their final placement within a computer graphics scene is vital to making informed choices for material properties. We significantly extend previous work on BRDF editing for static scenes (with fixed lighting and view) by developing a precomputed polynomial representation that enables interactive BRDF editing with global illumination. Unlike previous precomputation-based rendering techniques, the image is not linear in the BRDF when considering interreflections. We introduce a framework for precomputing a multibounce tensor of polynomial coefficients that encapsulates the nonlinear nature of the task. Significant reductions in complexity are achieved by leveraging the low-frequency nature of indirect light. We use a high-quality representation for the BRDFs at the first bounce from the eye and lower-frequency (often diffuse) versions for further bounces. This approximation correctly captures the general global illumination in a scene, including color-bleeding, near-field object reflections, and even caustics. We adapt Monte Carlo path tracing for precomputing the tensor of coefficients for BRDF basis functions. At runtime, the high-dimensional tensors can be reduced to a simple dot product at each pixel for rendering. We present a number of examples of editing BRDFs in complex scenes with interactive feedback rendered with global illumination.

In this paper, we use a linear complementarity problem (LCP) formulation of rigid body dynamics with unilateral contacts to obtain definitions for contact modes. We show how the complementary cones of the LCP correspond to each of the intuitive contact modes: slide right, slide left, roll and separate. These complementary cones allow us to make rigorous definitions for contact modes in three-dimensional systems, where our intuitive understanding fails.

Abstract Creating an information architecture for a bilingual Web site presents particular challenges beyond those that exist for single and multilanguage sites. This article reports work in progress on the development of a content‐based bilingual Web site to facilitate the sharing of resources and information between Speech and Language Therapists. The development of the information architecture is based on a combination of two aspects: an abstract structural analysis of existing bilingual Web designs focusing on the presentation of bilingual material, and a bilingual card‐sorting activity conducted with potential users. Issues for bilingual developments are discussed, and some observations are made regarding the use of card‐sorting activities.