A constructive theory of sampling for image synthesis using reproducing kernel bases

Sampling a scene by tracing rays and reconstructing an image from such pointwise samples is fundamental to computer graphics. To improve the efficacy of these computations, we propose an alternative theory of sampling. In contrast to traditional formulations for image synthesis, which appeal to nonconstructive Dirac deltas, our theory employs constructive reproducing kernels for the correspondence between continuous functions and pointwise samples. Conceptually, this allows us to obtain a common mathematical formulation of almost all existing numerical techniques for image synthesis. Practically, it enables novel sampling based numerical techniques designed for light transport that provide considerably improved performance per sample. We exemplify the practical benefits of our formulation with three applications: pointwise transport of color spectra, projection of the light energy density into spherical harmonics, and approximation of the shading equation from a photon map. Experimental results verify the utility of our sampling formulation, with lower numerical error rates and enhanced visual quality compared to existing techniques

B-splines for physically-based rendering

technical reportAlthough B-spline curves and surfaces have enjoyed a long established place in the graphics community as constructive modeling tools, the use of B-spline approximation techniques has received relatively little attention in rendering. In this work we explore the use of 4D and 5D tensor product B-spline functions to represent surface radiance, and establish that, when appropriately applied, they can be used effectively for static scenes with diffuse to moderately specular elements. Once computed, the surface radiance representation is view independent, can be evaluated quickly, and is equally suited for incorporation into ray tracing or scan-line rendering algorithms. Furthermore, we use B-spline approximation techniques to solve the problem of global illumination for general parametric surfaces with a wide range of reflectance and transmission properties. We conclude that addressing functional approximation aspects offers a fertile research ground relative to the already impressive gains that splines have made in other fields

A Final Reconstruction Approach for a Unified Global Illumination Algorithm

International audienceIn the past twenty years, many algorithms have been proposed to compute global illumination in synthetic scenes. Typically, such approaches can deal with specific lighting configurations, but often have difficulties with others. In this article, we present a final reconstruction step for a novel unified approach to global illumination, that automatically detects different types of light transfer and uses the appropriate method in a closely-integrated manner. With our approach, we can deal with difficult lighting configurations such as indirect nondiffuse illumination. The first step of this algorithm consists in a view-independent solution based on hierarchical radiosity with clustering, integrated with particle tracing. This first pass results in solutions containing directional effects such as caustics, which can be interactively rendered. The second step consists of a view-dependent final reconstruction that uses all existing information to compute higher quality, ray-traced images

Doctor of Philosophy

dissertationWhile boundary representations, such as nonuniform rational B-spline (NURBS) surfaces, have traditionally well served the needs of the modeling community, they have not seen widespread adoption among the wider engineering discipline. There is a common perception that NURBS are slow to evaluate and complex to implement. Whereas computer-aided design commonly deals with surfaces, the engineering community must deal with materials that have thickness. Traditional visualization techniques have avoided NURBS, and there has been little cross-talk between the rich spline approximation community and the larger engineering field. Recently there has been a strong desire to marry the modeling and analysis phases of the iterative design cycle, be it in car design, turbulent flow simulation around an airfoil, or lighting design. Research has demonstrated that employing a single representation throughout the cycle has key advantages. Furthermore, novel manufacturing techniques employing heterogeneous materials require the introduction of volumetric modeling representations. There is little question that fields such as scientific visualization and mechanical engineering could benefit from the powerful approximation properties of splines. In this dissertation, we remove several hurdles to the application of NURBS to problems in engineering and demonstrate how their unique properties can be leveraged to solve problems of interest

Object Hierarchies for Efficient Rendering

This thesis covers the efficient visualization of complex 3d scenes using various rendering methods such as photo-realistic and real-time rendering. Especially the important role of bounding volume hierarchies is discussed in detail in the context of illumination and visibility algorithms. We present a novel approach for automatic generation of object hierarchies and apply the resulting data structure to several rendering techniques. In the field of ray tracing we describe a novel ray acceleration method that combines objects hierarchies and regular grids. We demonstrate how radiosity computations may benefit from available scene hierarchies to determine the radiant flux between object clusters. Finally, we present an adaptive interactive rendering algorithm that may dramatically reduce the number of visibility tests in an occlusion culling framework for interactive real-time visualization.Diese Dissertation untersucht unterschiedliche Verfahren zur effizienten Visualisierung grosser dreidimensionaler Szenengeometrien, sowohl im Bereich des Photorealismus wie auch bei der Echtzeit-Visualisierung. Hierbei wird insbesondere die Nützlichkeit von Hüllkörperhierarchien bei der Beleuchtungsrechnung und bei der Beantwortung von Sichtbarkeitsfragen herausgearbeitet. Ein neuartiges, kostenbasiertes Verfahren zur automatischen Konstruktion von Objekthierarchien wird präsentiert sowie dessen Anwendung für alle gängigen Darstellungsverfahren. Zusätzlich beschreibt diese Disseration im Bereich Ray Tracing ein neues Verfahren zur Szenenstrukturierung, welches die Vorteile von Hüllkörperhierarchien und regulären Gittern kombiniert. Im Bereich der Radiosity wird gezeigt, wie sich Szenenhierarchien ideal zur Berechnung des Lichtflusses zwischen Objekt-Clustern nutzen lassen und im Bereich Echtzeit-Rendering wird ein adaptives Verfahren vorgestellt, dass die Zahl teurer Sichtbarkeitstests beim Occlusion-Culling deutlich reduziert

Efficient global illumination for dynamic scenes

The production of high quality animations which feature compelling lighting effects is computationally a very heavy task when traditional rendering approaches are used where each frame is computed separately. The fact that most of the computation must be restarted from scratch for each frame leads to unnecessary redundancy. Since temporal coherence is typically not exploited, temporal aliasing problems are also more difficult to address. Many small errors in lighting distribution cannot be perceived by human observers when they are coherent in temporal domain. However, when such a coherence is lost, the resulting animations suffer from unpleasant flickering effects. In this thesis, we propose global illumination and rendering algorithms, which are designed specifically to combat those problems. We achieve this goal by exploiting temporal coherence in the lighting distribution between the subsequent animation frames. Our strategy relies on extending into temporal domain wellknown global illumination and rendering techniques such as density estimation path tracing, photon mapping, ray tracing, and irradiance caching, which have been originally designed to handle static scenes only. Our techniques mainly focus on the computation of indirect illumination, which is the most expensive part of global illumination modelling.Die Erstellung von hochqualitativen 3D-Animationen mit anspruchsvollen Lichteffekten ist für traditionelle Renderinganwendungen, bei denen jedes Bild separat berechnet wird, sehr aufwendig. Die Tatsache jedes Bild komplett neu zu berechnen führt zu unnötiger Redundanz. Wenn temporale Koherenz vernachlässigt wird, treten unter anderem auch schwierig zu behandelnde temporale Aliasingprobleme auf. Viele kleine Fehler in der Beleuchtungsberechnung eines Bildes können normalerweise nicht wahr genommen werden. Wenn jedoch die temporale Koherenz zwischen aufeinanderfolgenden Bildern fehlt, treten störende Flimmereffekte auf. In dieser Arbeit stellen wir globale Beleuchtungsalgorithmen vor, die die oben genannten Probleme behandeln. Dies erreichen wir durch Ausnutzung von temporaler Koherenz zwischen aufeinanderfolgenden Einzelbildern einer Animation. Unsere Strategy baut auf die klassischen globalen Beleuchtungsalgorithmen wie "Path tracing", "Photon Mapping" und "Irradiance Caching" auf und erweitert diese in die temporale Domäne. Dabei beschränken sich unsereMethoden hauptsächlich auf die Berechnung indirekter Beleuchtung, welche den zeitintensivsten Teil der globalen Beleuchtungsberechnung darstellt