An Integral geometry based method for fast form-factor computation

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.Postprint (published version

A Monte Carlo method for accelerating the computation of animated radiosity sequences

Realistic rendering animation is known to be an expensive processing task when physically-based global illumination methods are used in order to improve illumination details. This paper presents an acceleration technique to compute animations in radiosity environments. The technique is based on an interpolated approach that exploits temporal coherence in radiosity. A fast global Monte Carlo pre-processing step is introduced to the whole computation of the animated sequence to select important frames. These are fully computed and used as a base for the interpolation of all the sequence. The approach is completely view-independent. Once the illumination is computed, it can be visualized by any animated camera. Results present significant high speed-ups showing that the technique could be an interesting alternative to deterministic methods for computing non-interactive radiosity animations for moderately complex scenario

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 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

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

Efficient Many-Light Rendering of Scenes with Participating Media

We present several approaches based on virtual lights that aim at capturing the light transport without compromising quality, and while preserving the elegance and efficiency of many-light rendering. By reformulating the integration scheme, we obtain two numerically efficient techniques; one tailored specifically for interactive, high-quality lighting on surfaces, and one for handling scenes with participating media