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

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

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

Efficient Object-Based Hierarchical Radiosity Methods

The efficient generation of photorealistic images is one of the main subjects in the field of computer graphics. In contrast to simple image generation which is directly supported by standard 3D graphics hardware, photorealistic image synthesis strongly adheres to the physics describing the flow of light in a given environment. By simulating the energy flow in a 3D scene global effects like shadows and inter-reflections can be rendered accurately. The hierarchical radiosity method is one way of computing the global illumination in a scene. Due to its limitation to purely diffuse surfaces solutions computed by this method are view independent and can be examined in real-time walkthroughs. Additionally, the physically based algorithm makes it well suited for lighting design and architectural visualization. The focus of this thesis is the application of object-oriented methods to the radiosity problem. By consequently keeping and using object information throughout all stages of the algorithms several contributions to the field of radiosity rendering could be made. By introducing a new meshing scheme, it is shown how curved objects can be treated efficiently by hierarchical radiosity algorithms. Using the same paradigm the radiosity computation can be distributed in a network of computers. A parallel implementation is presented that minimizes communication costs while obtaining an efficient speedup. Radiosity solutions for very large scenes became possible by the use of clustering algorithms. Groups of objects are combined to clusters to simulate the energy exchange on a higher abstraction level. It is shown how the clustering technique can be improved without loss in image quality by applying the same data-structure for both, the visibility computations and the efficient radiosity simulation.Eines der Schwerpunktthemen in der Computergraphik ist die effiziente Erzeugung von fotorealistischen Bildern. Im Gegensatz zur einfachen Bilderzeugung, die bereits durch gaengige 3D-Grafikhardware unterstuetzt wird, gehorcht die fotorealistische Bildsynthese physikalischen Gesetzen, die die Lichtausbreitung innerhalb einer bestimmten Umgebung beschreiben. Durch die Simulation der Energieausbreitung in einer dreidimensionalen Szene koennen globale Effekte wie Schatten und mehrfache Reflektionen wirklichkeitstreu dargestellt werden. Die hierarchische Radiositymethode (Hierarchical Radiosity) ist eine Moeglichkeit, um die globale Beleuchtung innerhalb einer Szene zu berechnen. Da diese Methode auf die Verwendung von rein diffus reflektierenden Oberflaechen beschraenkt ist, sind damit errechnete Loesungen blickwinkelunabhaengig und lassen sich in Echtzeit am Bildschirm durchwandern. Zudem ist dieser Algorithmus aufgrund der verwendeten physikalischen Grundlagen sehr gut zur Beleuchtungssimulation und Architekturvisualisierung geeignet. Den Schwerpunkt dieser Doktorarbeit stellt die Anwendung objektbasierter Methoden auf das Radiosityproblem dar. Durch konsequente Ausnutzung von Objektinformationen waehrend aller Berechnungsschritte konnten verschiedene Verbesserungen im Rahmen der hierarchischen Radiositymethode erzielt werden. Gekruemmte Objekte koennen aufgrund eines neuen Flaechenunterteilungsverfahrens nun effizient durch den hierarchischen Radiosityalgorithmus dargestellt werden. Dieses Verfahren ermoeglicht ebenso eine effiziente Parallelisierung des hierarchischen Radiosityalgorithmus. Es wird ein parallele Implementierung vorgestellt, die unter Minimierung der Kommunikationskosten eine effiziente Geschwindigkeitssteigerung erzielt. Radiosityberechnungen fuer sehr grosse Szenen sind nur durch Verwendung sogenannter Clustering-Algorithmen moeglich. Dabei werden Gruppen von Objekten zu Clustern kombiniert um den Energieaustausch zwischen Oberflaechen stellvertretend auf einem hoeheren Abstraktionsniveau durchzufuehren. Durch Verwendung derselben Datenstruktur fuer Sichtbarkeitsberechnungen und fuer die Steuerung der Radiositysimulation wird gezeigt, wie das Clusteringverfahren ohne Qualitaetsverluste verbessert werden kann

Parallelization of hierarchical radiosity algorithms on distributed memory computers

Ankara : Department of Computer Engineering and Information Science and the Institute of Engineering and Science of Bilkent Univ., 1998.Thesis (Master's) -- Bilkent University, 1998.Includes bibliographical references leaves 93-97.Şireli, Ahmet ReşatM.S

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 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

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