We present an algorithm for fast, physically accurate simulation of deformable objects suitable for real time animation and virtual environment interaction. We describe the boundary integral equation formulation of static linear elasticity as well as the related Boundary Element Method (BEM) discretization technique. In addition, we show how to exploit the coherence of typical interactions to achieve low latency; the boundary formulation lends itself well to a fast update method when a few boundary conditions change. The algorithms are described in detail with examples from ArtDefo, our implementation.

Abstract — This paper presents a new radiosity algorithm that allows the simultaneous computation of energy exchanges between surface elements, scattering volume distributions, and groups of surfaces, or object clusters. The new technique is based on a hierarchical formulation of the zonal method, and efficiently integrates volumes and surfaces. In particular no initial linking stage is needed, even for inhomogeneous volumes, thanks to the construction of a global spatial hierarchy. An analogy between object clusters and scattering volumes results in a powerful clustering radiosity algorithm, with no initial linking between surfaces and fast computation of average visibility information through a cluster. We show that the accurate distribution of the energy emitted or received at the cluster level can produce even better results than isotropic clustering at a marginal cost. The resulting algorithm is fast and, more importantly, truly progressive as it allows the quick calculation of approximate solutions with a smooth convergence towards very accurate simulations. I.

This paper focuses on efficient rendering based on pre-computed light transport, with realistic materials and shadows under allfrequency direct lighting such as environment maps. The basic difficulty is representation and computation in the 6D space of light direction, view direction, and surface position. While image-based and synthetic methods for real-time rendering have been proposed, they do not scale to high sampling rates with variation of both lighting and viewpoint. Current approaches are therefore limited to lower dimensionality (only lighting or viewpoint variation, not both) or lower sampling rates (low frequency lighting and materials) . We propose a new mathematical and computational analysis of pre-computed light transport. We use factored forms, separately pre-computing and representing visibility and material properties. Rendering then requires computing triple product integrals at each vertex, involving the lighting, visibility and BRDF. Our main contribution is a general analysis of these triple product integrals, which are likely to have broad applicability in computer graphics and numerical analysis. We first determine the computational complexity in a number of bases like point samples, spherical harmonics and wavelets. We then give efficient linear and sublinear-time algorithms for Haar wavelets, incorporating non-linear wavelet approximation of lighting and BRDFs. Practically, we demonstrate rendering of images under new lighting and viewing conditions in a few seconds, significantly faster than previous techniques.

In this paper we develop a computational model of visual masking based on psychophysical data. The model predicts how the presence of one visual pattern affects the detectability of another. The model allows us to choose texture patterns for computer graphics images that hide the effects of faceting, banding, aliasing, noise and other visual artifacts produced by sources of error in graphics algorithms. We demonstrate the utility of the model by choosing a texture pattern to mask faceting artifacts caused by polygonal tesselation of a flat-shaded curved surface. The model predicts how changes in the contrast, spatial frequency, and orientation of the texture pattern, or changes in the tesselation of the surface will alter the masking effect. The model is general and has uses in geometric modeling, realistic image synthesis, scientific visualization, image compression, and image-based rendering.

In a distribution ray tracer, the crucial part of the direct lighting calculation is the sampling strategy for shadow ray testing. Monte Carlo integration with importance sampling is used to carry out this calculation. Importance sampling involves the design of integrand-specific probability density functions which are used to generate sample points for the numerical quadrature. Probability density functions are presented that aid in the direct lighting calculation from luminaires of various simple shapes. A method for defining a probability density function over a set of luminaires is presented that allows the direct lighting calculation to be carried out with one sample, regardless of the number of luminaires. CR Categories and Subject Descriptors: G.1.4 [Mathematical Computing]: Quadrature and Numerical Differentiation; I.3.0 [Computer Graphics]: General; I.3.7 [Computer Graphics]: Three-Dimensional Graphics and Realism. Additional Key Words and Phrases: direct lighting, importanc...

Visualized data often have dubious origins and quality. Di erent forms of uncertainty and errors are also introduced as the data are derived, transformed, interpolated, and nally rendered. In the absence of integrated presentation of data and uncertainty, the analysis of the visualization is incomplete at best and often leads to inaccurate or incorrect conclusions. This paper surveys techniques for presenting data together with uncertainty. These uncertainty visualization techniques present data in such a manner that users are made aware of the locations and degree of uncertainties in their data so as to make more informed analyses and decisions. The techniques include adding glyphs, adding geometry, modifying geometry, modifying attributes, animation, soni cation, and psycho-visual approaches. We present our results in uncertainty visualization for environmental visualization, surface interpolation, global illumination with radiosity, ow visualization, and gure animation. We also present a classi cation of the possibilities in uncertainty visualization, and locate our contributions within this classi cation.

This thesis presents a volumetric representation for the global illumination within a space based on the radiometric quantity irradiance. We call this representation the irradiance volume. Although irradiance is traditionally computed only for surfaces, its de nition can be naturally extended to all points and directions in space. The irradiance volume supports the reconstruction of believable approximations to the illumination in situations that overwhelm traditional global illumination algorithms. Atheoretical basis for the irradiance volume is discussed and the methods and issues involved with building the volume are described. The irradiance volume method is tested within several situations in which the use of traditional global illumination methods is impractical, and is shown to provide good performance.

In this paper we introduce a new approach to controlling error in hierarchical clustering algorithms for radiosity. The new method ensures that just enough work is done to meet the user's quality criteria. To this end the importance of traditionally ignored visibility error is identified, and the concept of features is introduced as a way to evaluate the quality of an image. A methodology to evaluate error based on features is presented, which leads to the development of a multi-resolution visibility algorithm. An algorithm to construct a suitable hierarchy for clustering and multi-resolution visibility is also proposed. Results of the implementation show that the multiresolution approach has the potential of providing significant computational savings depending on the choice of feature size the user is interested in. They also illustrate the relevance of the featurebased error analysis. The proposed algorithms are well suited to the development of interactive lighting simulation syste...

Contents Acknowledgements 3 Foreword 9 1 Introduction 11 2 PreviousWork 14 2.1 The Radiosity equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.1.1 Rendering Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.1.2 Rendering Equation for diffuse surfaces . . . . . . . . . . . . . . . . . . . . 16 2.1.3 The Radiosity system of equations . . . . . . . . . . . . . . . . . . . . . . . 17 2.1.4 Two forms of the Form Factor integral . . . . . . . . . . . . . . . . . . . . . 18 2.1.5 The Form Factor integral as a contour integral . . . . . . . . . . . . . . . . 18 2.1.6 Differential area to area Form Factor . . . . . . . . . . . . . . . . . . . . . . 19 2.2 Computing the Form Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.2.1 Deterministic numerical solutions . . . . . . . . . . . . . . . . . . . . . . . . 22 2.3 Monte Carlo evaluation of the Form Factor integral . . . . . . . . . . . . . . . . .

Figure 1: Left: An office which receives light through a window on the right wall while the rest of the scene is lit indirectly. Our method avoids explicit visibility computation and our GPU implementation enables the manipulation of the light or objects at 9 frames per second (fps). This includes four iterations of radiance and antiradiance per frame. Center: We can also include an animated character; indirect light is updated at 7.8 fps. Right: Our method naturally handles glossy surfaces; the glossy bust is lit indirectly, since the light points at the ceiling. We reformulate the rendering equation to alleviate the need for explicit visibility computation, thus enabling interactive global illumination on graphics hardware. This is achieved by treating visibility implicitly and propagating an additional quantity, called antiradiance, to compensate for light transmitted extraneously. Our new algorithm shifts visibility computation to simple local iterations by maintaining additional directional antiradiance information with samples in the scene. It is easy to parallelize on a GPU. By correctly treating discretization and filtering, we can compute indirect illumination in scenes with dynamic objects much faster than traditional methods. Our results show interactive update of indirect illumination with moving characters and lights.