In this paper we present a new Monte Carlo rendering algorithm that seamlessly integrates the ideas of

We present a new clustering algorithm for global illumination in complex environments. The new algorithm extends previous work on clustering for radiosity to allow for nondiffuse (glossy) reflectors. We represent clusters as points with directional distributions of outgoing and incoming radiance and importance, and we derive an error bound for transfers between these clusters. The algorithm groups input surfaces into a hierarchy of clusters, and then permits clusters to interact only if the error bound is below an acceptable tolerance. We show that the algorithm is asymptotically more efficient than previous clustering algorithms even when restricted to ideally diffuse environments. Finally, we demonstrate the performance of our method on two complex glossy environments.

The problem of global illumination in computer graphics is described by a second kind Fredholm integral equation. Due to the complexity of this equation, Monte Carlo methods provide an interesting tool for approximating solutions to this transport equation. For the case of the radiosity equation, we present the deterministic method of quasi-random walks. This method very efficiently uses low discrepancy sequences for integrating the Neumann series and consistently outperforms stochastic techniques. The method of quasi-random walks also is applicable to transport problems in settings other than computer graphics.

Monte Carlo techniques have been widely used in rendering algorithms for local integration. For example, to compute the contribution of a patch to the luminance of another. In the present paper we propose an algorithm based on Integral geometry where Monte Carlo is applied globally. We give some results of the implementation to validate the proposition and we study the error of the technique, as well as its complexity. 1. INTRODUCTION Monte Carlo methods in radiative heat transfer, and thereafter in radiosity, can be classified in two: those that ignore the form-factor matrix and only need a final solution, and those which explicitly give the form factor matrix and solve a posteriori the equations system. [Shamsundar73], [Pattanaik92] and [Shirley90] fall into the first category, while [Weiner65] belongs to the second. The first category is more suitable for a quick solution, while the second allows the possibility of changing the problem's initial conditions of illumination. As [Sie...

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 . . . . . . . . . . . . . . . . .

The ability to perform interactive walkthroughs of global illumination solutions including glossy effects is a challenging open problem. In this paper we overcome certain limitations of previous approaches. We first introduce a novel, memory- and compute-efficient representation of incoming illumination, in the context of a hierarchical radiance clustering algorithm. We then represent outgoing radiance with an adaptive hierarchical basis, in a manner suitable for interactive display. Using appropriate refinement and display strategies, we achieve walkthroughs of glossy solutions at interactive rates for non-trivial scenes. In addition, our implementation has been developed to be portable and easily adaptable as an extension to existing, diffuse-only, hierarchical radiosity systems. We present results of the implementation of glossy global illumination in two independent global illumination systems.

This text discusses a few aspects of reflectance models in physically based rendering: ffl The first section presents the definition of the bidirectional reflection distribution function (brdf) of a surface and its physical properties. ffl On a more practical level, the next section discusses models to represent brdfs and their desired properties in general for Monte Carlo algorithms. ffl The third section goes into details about a specific reflectance model, the modified Phong brdf, with its definition, its properties and its use. We show how this model can be correctly integrated in importance sampling schemes for physically based Monte Carlo rendering algorithms. ffl The fourth section is devoted to alternative parameter spaces in which reflectance models can be sampled, either deterministically or stochastically. ffl The last section discusses an important implementational issue, more specifically the problem of verifying the implementation of a reflectance model. Keywords : ...

. Particle tracing allows physically correct simulation of all kinds of light interaction in a scene, but can be a computationally expensive task. Use of visual importance is a powerful technique to improve the efficiency of global illumination calculations. We describe a three pass solution for global illumination calculation extending the two pass approach proposed by Jensen. In the first pass particle tracing of importance is performed to create a global data structure, called importance map. Based on this data structure importance driven photon tracing is used in the second pass to construct a photon map containing information about the global illumination in the scene. In the last pass the image is rendered by distributed ray tracing using the photon map. The photon tracing process, improved by the use of importance information, creates photon maps with an up to 8-times higher photon density in important regions of the scene. This allows a better use of memory and computation time...

Stochastic radiosity methods have become a standard tool for generating global illumination solutions for very large scenes. Unfortunately, these methods need scene descriptions that are premeshed to a very fine resolution, in order to compute an adequate solution of the global illumination. The algorithm proposed in this paper uses a stochastic Galerkin approach to incrementally calculate the illumination function. By tracking the illumination function at different levels of resolution it is possible to get a measure for the quality of the representation, and thus adaptively subdivide in places with inadequate accuracy. With this technique a hierarchical mesh is generated, that is based on the stochastic evaluation of global illumination. Keywords: radiosity, stochastic, Monte Carlo, hierarchical, Galerkin, density estimation 1 Introduction Calculating the global illumination for a given scene is a very time-consuming task. In order to speed up the calculation, stochastic methods ha...

An equation adjoint tothe luminance equation for describing the global illumination can be formulated using the notion of a surface potential to illuminate the region of interest. This adjoint equation which we shall call as the potential equation, is fundamental to the adjoint radiosity equation used to devise the importance driven radiosity algorithm. In this paper we rst brie y derive the adjoint system of integral equations and then show that the adjoint linear equations used in the above algorithm are basically discrete formulations of the same. We also show that the importance entity of the linear equations is basically the potential function integrated over a patch. Further we prove that the linear operators in the two equations are indeed transposes of each other. 1.