A parallel progressive radiosity algorithm based on patch data circulation

Cataloged from PDF version of article.Current research on radiosity has concentrated on increasing the accuracy and the speed of the solution. Although algorithmic and meshing techniques decrease the execution time, still excessive computational power is required for complex scenes. Hence, parallelism can be exploited for speeding up the method further. This paper aims at providing a thorough examination of parallelism in the basic progressive refinement radiosity, and investigates its parallelization on distributed-memory parallel architectures. A synchronous scheme, based on static task assignment, is proposed to achieve better coherence for shooting patch selections. An efficient global circulation scheme is proposed for the parallel light distribution computations, which reduces the total volume of concurrent communication by an asymptotical factor. The proposed parallel algorithm is implemented on an Intel's iPSC/2 hypercube multicomputer. Load balance qualities of the proposed static assignment schemes are evaluated experimentally. The effect of coherence in the parallel light distribution computations on the shooting patch selection sequence is also investigated. Theoretical and experimental evaluation is also presented to verify that the proposed parallelization scheme yields equally good performance on multicomputers implementing the simplest (e.g. ring) as well as the richest (e.g. hypercube) interconnection topologies. This paper also proposes and presents a parallel load re-balancing scheme which enhances our basic parallel radiosity algorithm to be usable in the parallelization of radiosity methods adopting adaptive subdivision and meshing techniques. (C) 1996 Elsevier Science Lt

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

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

Fast hierarchical low-rank view factor matrices for thermal irradiance on planetary surfaces

We present an algorithm for compressing the radiosity view factor model commonly used in radiation heat transfer and computer graphics. We use a format inspired by the hierarchical off-diagonal low rank format, where elements are recursively partitioned using a quadtree or octree and blocks are compressed using a sparse singular value decomposition -- the hierarchical matrix is assembled using dynamic programming. The motivating application is time-dependent thermal modeling on vast planetary surfaces, with a focus on permanently shadowed craters which receive energy through indirect irradiance. In this setting, shape models are comprised of a large number of triangular facets which conform to a rough surface. At each time step, a quadratic number of triangle-to-triangle scattered fluxes must be summed; that is, as the sun moves through the sky, we must solve the same view factor system of equations for a potentially unlimited number of time-varying righthand sides. We first conduct numerical experiments with a synthetic spherical cap-shaped crater, where the equilibrium temperature is analytically available. We also test our implementation with triangle meshes of planetary surfaces derived from digital elevation models recovered by orbiting spacecrafts. Our results indicate that the compressed view factor matrix can be assembled in quadratic time, which is comparable to the time it takes to assemble the full view matrix itself. Memory requirements during assembly are reduced by a large factor. Finally, for a range of compression tolerances, the size of the compressed view factor matrix and the speed of the resulting matrix vector product both scale linearly (as opposed to quadratically for the full matrix), resulting in orders of magnitude savings in processing time and memory space.Comment: 21 pages, 10 figure

Parallel hierarchical global illumination

Solving the global illumination problem is equivalent to determining the intensity of every wavelength of light in all directions at every point in a given scene. The complexity of the problem has led researchers to use approximation methods for solving the problem on serial computers. Rather than using an approximation method, such as backward ray tracing or radiosity, we have chosen to solve the Rendering Equation by direct simulation of light transport from the light sources. This paper presents an algorithm that solves the Rendering Equation to any desired accuracy, and can be run in parallel on distributed memory or shared memory computer systems with excellent scaling properties. It appears superior in both speed and physical correctness to recent published methods involving bidirectional ray tracing or hybrid treatments of diffuse and specular surfaces. Like progressive radiosity methods, it dynamically refines the geometry decomposition where required, but does so without the excessive storage requirements for ray histories. The algorithm, called Photon, produces a scene which converges to the global illumination solution. This amounts to a huge task for a 1997-vintage serial computer, but using the power of a parallel supercomputer significantly reduces the time required to generate a solution. Currently, Photon can be run on most parallel environments from a shared memory multiprocessor to a parallel supercomputer, as well as on clusters of heterogeneous workstations

Efficient global illumination calculation for inverse lighting problems

La luz es un elemento clave en la manera en que percibimos y experimentamos nuestro entorno. Como tal, es un objeto mas a modelar en el proceso de diseño, de forma similar a como ocurre con las formas y los materiales. Las intenciones de iluminacion (LI) son los objetivos y restricciones que el diseñador pretende alcanzar en el proceso del diseño de iluminaci´on: ¿qué superficies se deben iluminar con luz natural y cuales con luz artificial?, ¿qué zonas deben estar en sombra?, ¿cuales son las intensidades maximas y mínimas permitidas? Satisfacer las LI consiste en encontrar la ubicacion, forma e intensidad adecuada de las fuentes luminosas. Este tipo de problemas se define como un problema inverso de iluminacion (ILP) que se resuelve con tecnicas de optimizacion. En el contexto anterior, el objetivo de esta tesis consiste en proponer metodos eficientes para resolver ILP. Este objetivo es motivado por la brecha percibida entre los problemas habituales de diseño de iluminacion y las herramientas computacionales existentes para su resolucion. Las herramientas desarrolladas por la industria se especializan en evaluar configuraciones de iluminacion previamente diseñadas, y las desarrolladas por la academia resuelven problemas relativamente sencillos a costos elevados. Las propuestas cubren distintos aspectos del proceso de optimizacion, que van desde la formulacion del problema a su resolucion. Estan desarrolladas para el caso en que las superficies poseen reflexion e iluminacion difusas y se basan en el calculo de una aproximacion de rango bajo de la matriz de radiosidad. Algunos resultados obtenidos son: el calculo acelerado de la radiosidad de la escena en una unidad de procesamiento gr´afico (GPU); el uso de la heuristica \201Cvariable neighborhood search\201D (VNS) para la resolucion de ILP; el planteo de una estructura multinivel para tratar ILP de forma escalonada; y el uso de tecnicas para optimizar la configuracion de filtros de luz. Otros resultados obtenidos se basan en la formulacion de las LI en funcion de la media y desviacion estandar de las radiosidades halladas. Se propone un metodo para generar LI que contengan esos parametros estadisticos, y otro metodo para acelerar su evaluacion. Con estos resultados se logran tiempos de respuesta interactivos. Por último, las tecnicas anteriores adolecen de una etapa de pre-cómputo relativamente costosa, por tanto se propone acelerar el calculo de la inversa de la matriz de radiosidad a partir de una muestra de factores de forma. Los métodos aquí presentados fueron publicados en seis articulos, tres de ellos en congresos internacionales y tres en revistas arbitradas.Light is a key element that influences the way we perceive and experience our environment. As such, light is an object to be modeled in the design process, as happens with the forms and materials. The lighting intentions (LI) are the objectives and constraints that designers want to achieve in the process of lighting design: which surfaces should be illuminated with natural and which with artificial light?, which surfaces should be in shadow?, which are the maximum and minimum intensities allowed? The fulfillment of the LI consists in finding the location, shape and intensity appropriate for the light sources. This problem is defined as an inverse lighting problem (ILP), solved by optimization techniques. In the above context, the aim of this thesis is the proposal of efficient methods to solve ILP. This objective is motivated by the perceived gap between the usual problems of lighting design, and the computational tools developed for its resolution. The tools developed by the industry specialize in evaluating previously designed lighting configurations, and those developed by the academia solve relatively simple problems at a high computational cost. The proposals cover several aspects of the optimization process, ranging from the formulation of the problem to its resolution. They are developed for the case in which the surfaces have Lambertian reflection and illumination, and are based on the calculation of a low rank approximation to the radiosity matrix. Some results are: rapid calculation of radiosity of the scene in a graphics processing unit (GPU), the use of heuristics “variable neighborhood search” (VNS) for solving ILP, the proposition of a multilevel structure to solve ILP in a stepwise approach, and the use of these techniques to optimize the configuration of light filters. Other results are based on the formulation of LI that use the mean and standard deviation of the radiosity values found. A method is proposed for generating LI containing these parameters, and another method is developed to speed up their evaluations. With these results we achieve interactive response times. Finally, the above techniques suffer from a costly pre-computing stage and therefore, a method is proposed to accelerate the calculation of the radiosity inverse matrix based on a sample of the form factors. The methods presented here were published in six articles, three of them at international conferences and three in peer reviewed journals

Efficient From-Point Visibility for Global Illumination in Virtual Scenes with Participating Media

Sichtbarkeitsbestimmung ist einer der fundamentalen Bausteine fotorealistischer Bildsynthese. Da die Berechnung der Sichtbarkeit allerdings äußerst kostspielig zu berechnen ist, wird nahezu die gesamte Berechnungszeit darauf verwendet. In dieser Arbeit stellen wir neue Methoden zur Speicherung, Berechnung und Approximation von Sichtbarkeit in Szenen mit streuenden Medien vor, die die Berechnung erheblich beschleunigen, dabei trotzdem qualitativ hochwertige und artefaktfreie Ergebnisse liefern