Parallel hierarchical radiosity rendering

The radiosity equation is examined, and is found to contain a previously unexploited symmetry. This symmetry is formalized, and a solution method previously unusable in the field of computer graphics (conjugate gradients) is shown to be superior to all methods currently in use. A detailed analysis of all solution techniques previously applied to the radiosity problem is conducted, and results presented;So-called hierarchical methods have reduced the operational complexity of the N-body problem from O(N[superscript]2) to O(N log N) assuming a pre-set error tolerance. An algorithm following the same basic tenets has been applied to radiosity rendering by other researchers, and has reduced the operational complexity from O(N[superscript]2) to (arguably) O(N);Shortcomings in the state-of-the-art hierarchical radiosity method are pointed out, and enhancements are offered. A consistent treatment of various types of error is found to be absent from present methods. Catastrophic error is possible in the visibility assessment between two polygons. A self-consistency check is possible during the solution process, but never exploited;Until now, supercomputer-class computers have not been used to solve radiosity problems at a production-quality level even though realistic image synthesis has always been a prodigious consumer of computer time. A state-of-the-art hierarchical radiosity code is implemented on an nCUBE-2 parallel computer, and discussed in detail. The algorithm is found to have ample sources of parallelism, in both data- and operational modes. Its performance is analyzed in detail;The hierarchical method has only been applied to realistic image synthesis since 1991. Not surprisingly, many avenues of further research are open. Some are pointed out, and include: analytic determination of coupling factors, quantifying discretization error, incorporating specular light reflection modes into the hierarchical treatment, and exploring what other important physical problems might benefit from the hierarchical approach

Hardware Acceleration of Progressive Refinement Radiosity using Nvidia RTX

A vital component of photo-realistic image synthesis is the simulation of indirect diffuse reflections, which still remain a quintessential hurdle that modern rendering engines struggle to overcome. Real-time applications typically pre-generate diffuse lighting information offline using radiosity to avoid performing costly computations at run-time. In this thesis we present a variant of progressive refinement radiosity that utilizes Nvidia's novel RTX technology to accelerate the process of form-factor computation without compromising on visual fidelity. Through a modern implementation built on DirectX 12 we demonstrate that offloading radiosity's visibility component to RT cores significantly improves the lightmap generation process and potentially propels it into the domain of real-time.Comment: 114 page

Hierarchical N-Body problem on graphics processor unit

Galactic simulation is an important cosmological computation, and represents a classical N-body problem suitable for implementation on vector processors. Barnes-Hut algorithm is a hierarchical N-Body method used to simulate such galactic evolution systems. Stream processing architectures expose data locality and concurrency available in multimedia applications. On the other hand, there are numerous compute-intensive scientific or engineering applications that can potentially benefit from such computational and communication models. These applications are traditionally implemented on vector processors. Stream architecture based graphics processor units (GPUs) present a novel computational alternative for efficiently implementing such high-performance applications. Rendering on a stream architecture sustains high performance, while user-programmable modules allow implementing complex algorithms efficiently. GPUs have evolved over the years, from being fixed-function pipelines to user programmable processors. In this thesis, we focus on the implementation of Barnes-Hut algorithm on typical current-generation programmable GPUs. We exploit computation and communication requirements present in Barnes-Hut algorithm to expose their suitability for user-programmable GPUs. Our implementation of the Barnes-Hut algorithm is formulated as a fragment shader targeting the selected GPU. We discuss implementation details, design issues, results, and challenges encountered in programming the fragment shader

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

Edge Asymptotics for the Radiosity Equation over Polyhedral Boundaries

In the present paper we consider the radiosity equation over the boundary of a polyhedral domain. Similarly to corresponding results on the double layer potential equation, the solution of the second kind integral equation with non-compact integral operator is piecewise continuous. The partial derivatives, however, are not bounded. In the present paper we derive the first term in the asymptotic expansion of the solution in the vicinity of an edge. Note that, knowing this term, optimal mesh gradings can be designed for the numerical solution of this equation

Radiation techniques for urban thermal simulation with the Finite Element Method

Modern societies are increasingly organized in cities. In the present times, more than half of the world’s population lives in urban settlements. In this context, architectural and building scale works have the need of extending their scope to the urban environment. One of the main challenges of these times is understanting all the thermal exchanges that happen in the city. The radiative part appears as the less developed one; its characterization and interaction with built structures has gained attention for building physics, architecture and environmental engineering. Providing a linkage between these areas, the emerging field of urban physics has become important for tackling studies of such nature. Urban thermal studies are intrinsically linked to multidisciplinary work approaches. Performing full-scale measurements is hard, and prototype models are difficult to develop. Therefore, computational simulations are essential in order to understand how the city behaves and to evaluate projected modifications. The methodological and algorithmic improvement of simulation is one of the mainlines of work for computational physics and many areas of computer science. The field of computer graphics has addressed the adaptation of rendering algorithms to daylighting using physically-based radiation models on architectural scenes. The Finite Element Method (FEM) has been widely used for thermal analysis. The maturity achieved by FEM software allows for treating very large models with a high geometrical detail and complexity. However, computing radiation exchanges in this context implies a hard computational challenge, and forces to push the limits of existing physical models. Computer graphics techniques can be adapted to FEM to estimate solar loads. In the thermal radiation range, the memory requirements for storing the interaction between the elements grows because all the urban surfaces become radiation sources. In this thesis, a FEM-based methodology for urban thermal analysis is presented. A set of radiation techniques (both for solar and thermal radiation) are developed and integrated into the FEM software Cast3m. Radiosity and ray tracing are used as the main algorithms for radiation computations. Several studies are performed for different city scenes. The FEM simulation results are com-pared with measured temperature results obtained by means of urban thermography. Post-processing techniques are used to obtain rendered thermograms, showing that the proposed methodology pro-duces accurate results for the cases analyzed. Moreover, its good computational performance allows for performing this kind of study using regular desktop PCs.Las sociedades modernas están cada vez más organizadas en ciudades. Más de la mitad de la población mundial vive en asentamientos urbanos en la actualidad. En este contexto, los trabajos a escala arquitectónica y de edificio deben extender su alcance al ambiente urbano. Uno de los mayores desafíos de estos tiempos consiste en entender todos los intercambios térmicos que suceden en la ciudad. La parte radiativa es la menos desarrollada; su caracterización y su interacción con edificaciones ha ganado la atención de la física de edificios, la arquitectura y la ingeniería ambiental. Como herramienta de conexión entre estas áreas, la física urbana es un área que resulta importante para atacar estudios de tal naturaleza. Los estudios térmicos urbanos están intrinsecamente asociados a trabajos multidisciplinarios. Llevar a cabo mediciones a escala real resulta difícil, y el desarrollo de prototipos de menor escala es complejo. Por lo tanto, la simulación computacional es esencial para entender el comportamiento de la ciudad y para evaluar modificaciones proyectadas. La mejora metodológica y algorítmica de las simulaciones es una de las mayores líneas de trabajo para la física computacional y muchas áreas de las ciencias de la computación. El área de la computación gráfica ha abordado la adaptación de algoritmos de rendering para cómputo de iluminación natural, utilizando modelos de radiación basados en la física y aplicándolos sobre escenas arquitectónicas. El Método de Elementos Finitos (MEF) ha sido ampliamente utilizado para análisis térmico. La madurez alcanzada por soluciones de software MEF permite tratar grandes modelos con un alto nivel de detalle y complejidad geométrica. Sin embargo, el cómputo del intercambio radiativo en este contexto implica un desafío computacional, y obliga a empujar los límites de las descripciones físicas conocidas. Algunas técnicas de computación gráfica pueden ser adaptadas a MEF para estimar las cargas solares. En el espectro de radiación térmica, los requisitos de memoria necesarios para almacenar la interacción entre los elementos crecen debido a que todas las superficies urbanas se transforman en fuentes emisoras de radiación. En esta tesis se presenta una metodología basada en MEF para el análisis térmico de escenas urbanas. Un conjunto de técnicas de radiación (para radiación solar y térmica) son desarrolladas e integradas en el software MEF Cast3m. Los algoritmos de radiosidad y ray tracing son utilizados para el cómputo radiativo. Se presentan varios estudios que utilizan diferentes modelos de ciudades. Los resultados obtenidos mediante MEF son comparados con temperaturas medidas por medio de termografías urbanas. Se utilizan técnicas de post-procesamiento para renderizar imágenes térmicas, que permiten concluir que la metodología propuesta produce resultados precisos para los casos analizados. Asimismo, su buen desempeño computacional posibilita realizar este tipo de estudios en computadoras personales

Numerical Solutions of the Radiosity Equation by the Galerkin Method for the Spherical Pyramid (Mars Project)

The Radiosity of a surface is the rate at which energy leaves that surface. It includes the energy emitted by a surface as well as the energy reflected. In this thesis, a spherical shaped interior space was designed on a spacecraft, which one day might land on Mars. The Radiosity model was used to determine the brightness inside the space. A global Galerkin method is used to solve the Radiosity Equation for several spherical shapes. This research is based on the study of the Radiosity Equation for occluded surfaces using the Collocation Method by Atkinson and Chein. The previous research was done on the Sphere, Perturbation of the Sphere, Ellipsoid and the Oval of Cassini. The convergence errors between true solutions and approximated numerical solutions for different reflectivity values and emissivity functions were presented

Doctor of Philosophy

dissertationReal-time global illumination is the next frontier in real-time rendering. In an attempt to generate realistic images, games have followed the film industry into physically based shading and will soon begin integrating global illumination techniques. Traditional methods require too much memory and too much time to compute for real-time use. With Modular and Delta Radiance Transfer we precompute a scene-independent, low-frequency basis that allows us to calculate complex indirect lighting calculations in a much lower dimensional subspace with a reduced memory footprint and real-time execution. The results are then applied as a light map on many different scenes. To improve the low frequency results, we also introduce a novel screen space ambient occlusion technique that allows us to generate a smoother result with fewer samples. These three techniques, low and high frequency used together, provide a viable indirect lighting solution that can be run in milliseconds on today's hardware, providing a useful new technique for indirect lighting in real-time graphics