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

Implementation and Analysis of an Image-Based Global Illumination Framework for Animated Environments

We describe a new framework for efficiently computing and storing global illumination effects for complex, animated environments. The new framework allows the rapid generation of sequences representing any arbitrary path in a view space within an environment in which both the viewer and objects move. The global illumination is stored as time sequences of range-images at base locations that span the view space. We present algorithms for determining locations for these base images, and the time steps required to adequately capture the effects of object motion. We also present algorithms for computing the global illumination in the base images that exploit spatial and temporal coherence by considering direct and indirect illumination separately. We discuss an initial implementation using the new framework. Results and analysis of our implementation demonstrate the effectiveness of the individual phases of the approach; we conclude with an application of the complete framework to a complex environment that includes object motion

APPLICATION OF VARIATIONAL CALCULUS IN THE RADIOSITY METHOD

The original radiosity method searches for the radiosity distribution in a piecewise constant function form. Using this stepwise constant assumption about the radiosity distribution, the integral equation describing the energy transfer is transformed to a linear equation system. Higher order radiosity method means the approximation of the radiosity distri- bution by more complex functions, as for example, by piecewise linear, harmonic, wavelet, etc. function series with unknown coefficients. Due to higher order approximation, the number of the unknown variables can be significantly smaller than the number of constant steps in the original method. This paper discusses the conversion of the integral equation to an equivalent variational problem which can result in a linear equation system for the unknown coefficients. Three function bases are examined in detail in this framework: piecewise constant, piecewise linear and harmonic approximations

Efficient representations of large radiosity matrices

The radiosity equation can be expressed as a linear system, where light interactions between patches of the scene are considered. Its resolution has been one of the main subjects in computer graphics, which has lead to the development of methods focused on different goals. For instance, in inverse lighting problems, it is convenient to solve the radiosity equation thousands of times for static geometries. Also, this calculation needs to consider many (or infinite) light bounces to achieve accurate global illumination results. Several methods have been developed to solve the linear system by finding approximations or other representations of the radiosity matrix, because the full storage of this matrix is memory demanding. Some examples are hierarchical radiosity, progressive refinement approaches, or wavelet radiosity. Even though these methods are memory efficient, they may become slow for many light bounces, due to their iterative nature. Recently, efficient methods have been developed for the direct resolution of the radiosity equation. In this case, the challenge is to reduce the memory requirements of the radiosity matrix, and its inverse. The main objective of this thesis is exploiting the properties of specific problems to reduce the memory requirements of the radiosity problem. Hereby, two types of problems are analyzed. The first problem is to solve radiosity for scenes with a high spatial coherence, such as it happens to some architectural models. The second involves scenes with a high occlusion factor between patches. For the high spatial coherence case, a novel and efficient error-bounded factorization method is presented. It is based on the use of multiple singular value decompositions along with a space filling curve, which allows to exploit spatial coherence. This technique accelerates the factorization of in-core matrices, and allows to work with out-of-core matrices passing only one time over them. In the experimental analysis, the presented method is applied to scenes up to 163K patches. After a precomputation stage, it is used to solve the radiosity equation for fixed geometries and infinite bounces, at interactive times. For the high occlusion problem, city models are used. In this case, the sparsity of the radiosity matrix is exploited. An approach for radiative exchange computation is proposed, where the inverse of the radiosity matrix is approximated. In this calculation, near-zero elements are removed, leading to a highly sparse result. This technique is applied to simulate daylight in urban environments composed by up to 140k patches.La ecuación de radiosidad tiene por objetivo el cálculo de la interacción de la luz con los elementos de la escena. Esta se puede expresar como un sistema lineal, cuya resolución ha derivado en el desarrollo de diversos métodos gráficos para satisfacer propósitos específicos. Por ejemplo, en problemas inversos de iluminación para geometrías estáticas, se debe resolver la ecuación de radiosidad miles de veces. Además, este cálculo debe considerar muchos (infinitos) rebotes de luz, si se quieren obtener resultados precisos de iluminación global. Entre los métodos desarrollados, se destacan aquellos que generan aproximaciones u otras representaciones de la matriz de radiosidad, debido a que su almacenamiento requiere grandes cantidades de memoria. Algunos ejemplos de estas técnicas son la radiosidad jerárquica, el refinamiento progresivo y la radiosidad basada en wavelets. Si bien estos métodos son eficientes en cuanto a memoria, pueden ser lentos cuando se requiere el cálculo de muchos rebotes de luz, debido a su naturaleza iterativa. Recientemente se han desarrollado métodos eficientes para la resolución directa de la ecuación de radiosidad, basados en el pre-cómputo de la inversa de la matriz de radiosidad. En estos casos, el desafío consiste en reducir los requerimientos de memoria y tiempo de ejecución para el cálculo de la matriz y de su inversa. El principal objetivo de la tesis consiste en explotar propiedades específicas de ciertos problemas de iluminación para reducir los requerimientos de memoria de la ecuación de radiosidad. En este contexto, se analizan dos casos diferentes. El primero consiste en hallar la radiosidad para escenas con alta coherencia espacial, tal como ocurre en algunos modelos arquitectónicos. El segundo involucra escenas con un elevado factor de oclusión entre parches. Para el caso de alta coherencia espacial, se presenta un nuevo método de factorización de matrices que es computacionalmente eficiente y que genera aproximaciones cuyo error es configurable. Está basado en el uso de múltiples descomposiciones en valores singulares (SVD) junto a una curva de recubrimiento espacial, lo que permite explotar la coherencia espacial. Esta técnica acelera la factorización de matrices que entran en memoria, y permite trabajar con matrices que no entran en memoria, recorriéndolas una única vez. En el análisis experimental, el método presentado es aplicado a escenas de hasta 163 mil parches. Luego de una etapa de precómputo, se logra resolver la ecuación de radiosidad en tiempos interactivos, para geométricas estáticas e infinitos rebotes. Para el problema de alta oclusión, se utilizan modelos de ciudades. En este caso, se aprovecha la baja densidad de la matriz de radiosidad, y se propone una técnica para el cálculo aproximado de su inversa. En este cálculo, los elementos cercanos a cero son eliminados. La técnica es aplicada a la simulación de la luz natural en ambientes urbanos compuestos por hasta 140 mil parches

Overlapping Multi-Processing and Graphics Hardware Acceleration: Performance Evaluation

Colloque avec actes et comité de lecture.Recently, multi-processing has been shown to deliver good performance in rendering. However, in some applications, processors spend too much time executing tasks that could be more efficiently done through intensive use of new graphics hardware. We present in this paper a novel solution combining multi-processing and advanced graphics hardware, where graphics pipelines are used both for classical visualization tasks and to advantageously perform geometric calculations while remaining computations are handled by multi-processors. The experiment is based on an implementation of a new parallel wavelet radiosity algorithm. The application is executed on the SGI Origin2000 connected to the SGI InfiniteReality2 rendering pipeline. A performance evaluation is presented. Keeping in mind that the approach can benefit all available workstations and super-computers, from small scale (2 processors and 1 graphics pipeline) to large scale ($p$ processors and $n$ graphics pipelines), we highlight some important bottlenecks that impede performance. However, our results show that this approach could be a promising avenue for scientific and engineering simulation and visualization applications that need intensive geometric calculations

Bernstein Polynomials for Radiative Transfer Computations

In this paper we propose using planar and spherical Bernstein polynomials over triangular domain for radiative transfer computations. In the planar domain, we propose using piecewise Bernstein basis functions and symmetric Gaussian quadrature formulas over triangular elements for high quality radiosity solution. In the spherical domain, we propose using piecewise Bernstein basis functions over a geodesic triangulation to represent the radiance function. The representation is intrinsic to the unit sphere, and may be efficiently stored, evaluated, and subdivided by the de Casteljau algorithm. The computation of other fundamental radiometric quantities such as vector irradiance and reflected radiance may be reduced to the integration of the piecewise Bernstein basis functions on the unit sphere. The key result of our work is a simple geometric integration algorithm based on adaptive domain subdivision for the Bernstein-Bézier polynomials over a geodesic triangle on the unit sphere

The Virtual Mesh: A Geometric Abstraction for Efficiently Computing Radiosity

Article dans revue scientifique avec comité de lecture.International audienceIn this paper, we introduce a general-purpose method for computing radiosity on scenes made of parametric surfaces with arbitrary trimming curves. By contrast with past approaches that require a tessellation of the input surfaces (be it made up of triangles or patches with simple trimming curves) or some form of geometric approximation, our method takes fully advantage of the rich and compact mathematical representation of objects. At its core lies the \emph{virtual mesh}, an abstraction of the input geometry that allows complex shapes to be illuminated as if they were simple primitives. The virtual mesh is a collection of normalized square domains to which the input surfaces are mapped while preserving their energy properties. Radiosity values are then computed on these supports before being lifted back to the original surfaces. To demonstrate the power of our method, we describe a high-order wavelet radiosity implementation that uses the virtual mesh. Examples of objects and environments, designed for interactive applications or virtual reality, are presented. They prove that, by exactly integrating curved surfaces in the resolution process, the virtual mesh allows complex scenes to be rendered more quickly, more accurately and much more naturally than with previously known methods

Combining Higher-Order Wavelets and Discontinuity Meshing: a Compact Representation for Radiosity

Colloque avec actes et comité de lecture. internationale.International audienceThe radiosity method is used for global illumination simulation in diffuse scenes, or as an intermediate step in other methods. Radiosity computations using Higher-Order wavelets achieve a compact representation of the illumination on many parts of the scene, but are more expensive near discontinuities, such as shadow boundaries. Other methods use a mesh, based on the set of discontinuities of the illumination function. The complexity of this set of discontinuities has so far proven prohibitive for large scenes, mostly because of the difficulty to robustly manage a geometrically complex set of triangles. In this paper, we present a method for computing radiosity that uses higher-order wavelet functions as a basis, and introduces discontinuities only when they simplify the resulting mesh. The result is displayed directly, without post-processing

Wavelet Algorithms for Complex Models

Rapport interne.We present the result of experimentations and tests with Wavelet Radiosity. We have developed a powerful wavelet radiosity implementation where we can independantly modify every geometrical component of the scene (description of the input data, representation of spectral distribution, etc.) and every component of the global illumination algorithm (visibility algorithm, wavelet basis, etc.). This implementation has been tested on real world applications: an archaeological site reconstruction with daylight illumination, an opera house front with artificial illumination and the Soda Hall building inside illumination. In this paper, wepresent the results of our experiments, which are mostly about the interdependencies of the different parts of the general algorithm and the influence of each one on the final result. We also introduce several improvements to the wavelet radiosity algorithm that allow for higher rendering speed and lower memory use, thereby allowing rendering of architectural models of high complexity

Real-time Cinematic Design Of Visual Aspects In Computer-generated Images

Creation of visually-pleasing images has always been one of the main goals of computer graphics. Two important components are necessary to achieve this goal --- artists who design visual aspects of an image (such as materials or lighting) and sophisticated algorithms that render the image. Traditionally, rendering has been of greater interest to researchers, while the design part has always been deemed as secondary. This has led to many inefficiencies, as artists, in order to create a stunning image, are often forced to resort to the traditional, creativity-baring, pipelines consisting of repeated rendering and parameter tweaking. Our work shifts the attention away from the rendering problem and focuses on the design. We propose to combine non-physical editing with real-time feedback and provide artists with efficient ways of designing complex visual aspects such as global illumination or all-frequency shadows. We conform to existing pipelines by inserting our editing components into existing stages, hereby making editing of visual aspects an inherent part of the design process. Many of the examples showed in this work have been, until now, extremely hard to achieve. The non-physical aspect of our work enables artists to express themselves in more creative ways, not limited by the physical parameters of current renderers. Real-time feedback allows artists to immediately see the effects of applied modifications and compatibility with existing workflows enables easy integration of our algorithms into production pipelines