Operations on Signed Distance Functions

We present a theoretical overview of signed distance functions and analyze how this representation changes when applying an offset transformation. First, we analyze the properties of signed distance and the sets they describe. Second, we introduce our main theorem regarding the distance to an offset set in (X, || · ||) strictly normed Banach spaces. An offset set of D ⊆ X is the set of points equidistant to D. We show when such a set can be represented by f(x) − c = 0, where c 6= 0 denotes the radius of the offset. Finally, we apply these results to gain a deeper insight into offsetting surfaces defined by signed distance functions

Entwicklung und Evaluation einer auf der Hauptkomponentenanalyse basierenden Bounding Volume Hierarchy

Die vorliegende Arbeit beschäftigt sich im übergeordneten Kontext mit den Bounding Volume Hierarchies zur Veinfachung des Intersection Testings beim Raytracing. Die derzeitige Problematik besteht vor allem in der immer noch zu optimierenden Laufzeit. Dementsprechend wird trotz der bereits bestehenden Beschleunigungsdatenstrukturen wie unter anderem der Bounding Volume Hierarchy versucht, effizientere Strukturen oder Erstellungsprozeduren zu entwickeln. Für die Bounding Volume Hierarchy bedeutet dies, dass vor allem hinsichtlich verschiedener Splitting-Methoden und Möglichkeiten für die Baumoptimierung geforscht wird. Explizit wird daher innerhalb dieser Arbeit untersucht, wie die Bounding Volume Hierarchy durch die Verwendung der Hauptkomponentenanalyse bei der Erstellung optimiert werden kann und wie effizient der daraus resultierende Ansatz gegenüber der klassischen Bounding Volume Hierarchy sowie deren Splitting-Methoden ist. Eine Evaluation anhand 12 verschiedener Szenen zeigte, dass der vorliegende Ansatz unter Verwendung der SAH-Methode wie auch mit der Middle-Methode 17.70% respektive 13.14% geringere Renderlaufzeiten als der distanzbasierte Ansatz aufweist. Des Weiteren konnte mittels der kombinierten Verwendung aus klassischer SAH-Methode und PCA-basierter SAH-Methode eine weitere Verbesserung um 6.65% gegenüber der SAH-Methode der PCA-BVH erreicht werden

Synchronized-tracing of implicit surfaces

Implicit surfaces are known for their ability to represent smooth objects of arbitrary topology thanks to hierarchical combinations of primitives using a structure called a blobtree. We present a new tile-based rendering pipeline well suited for modeling scenarios, i.e., no preprocessing is required when primitive parameters are updated. When using approximate signed distance fields, we rely on compact, smooth CSG operators - extended from standard bounded operators - to compute a tight volume of interest for all primitives of the blobtree. The pipeline relies on a low-resolution A-buffer storing the primitives of interest of a given screen tile. The A-buffer is then used during ray processing to synchronize threads within a subfrustum. This allows coherent field evaluation within workgroups. We use a sparse bottom-up tree traversal to prune the blobtree on-the-fly which allows us to decorrelate field evaluation complexity from the full blobtree size. The ray processing itself is done using the sphere-tracing algorithm. The pipeline scales well to surfaces consisting of thousands of primitives

Visual-auditory visualisation of dynamic multi-scale heterogeneous objects.

The multi-scale phenomena analysis is an area of active research that is connecting simulations with experiments to get a correct insight into the compound dynamic structure. Visualisation is a challenging task due to a large amount of data and a wide range of complex data representations. The analysis of dynamic multi-scale phenomena requires a combination of geometric modelling and rendering techniques for the analysis of the changes in the internal structure in the case of data coming from different sources of various nature. Moreover, the area often addresses the limitations of solely visual data representation and considers the introduction of other sensory stimuli as a well-known tool to enhance visual analysis. However, there is a lack of software tools allowing perform an advanced real-time analysis of heterogeneous phenomena properties. The hardware-accelerated volume rendering allows getting insight into the internal structure of complex multi-scale phenomena. The technique is convenient for detailed visual analysis and highlights the features of interest in complex structures and is an area of active research. However, the conventional volume visualisation is limited to the use of transfer functions that operate on homogeneous material and, as a result, does not provide flexibility in geometry and material distribution modelling that is crucial for the analysis of heterogeneous objects. Moreover, the extension to visual-auditory analysis emphasises the necessity to review the entire conventional volume visualisation pipeline. The multi-sensory feedback highly depends on the use of modern hardware and software advances for real-time modelling and evaluation. In this work, we explore the aspects of the design of visual-auditory pipelines for the analysis of dynamic multi-scale properties of heterogeneous objects that can allow overcoming well-known problems of complex representations solely visual analysis. We consider the similarities between light and sound propagation as a solution to the problem. The approach benefits from a combination of GPU accelerated ray-casting, geometry, optical and auditory properties modelling. We discuss how the modern GPU techniques application in those areas allows introducing a unified approach to the visual-auditory analysis of dynamic multi-scale heterogeneous objects. Similarly to the conventional volume rendering technique based on light propagation, we model auditory feedback as a result of initial impulse propagation through 3D space and its digital representation as a sampled sound wave obtained with the ray-casting procedure. The auditory stimuli can complement visual ones in the analysis of the dynamic multi-scale heterogeneous object. We propose a framework that facilitates the design of dynamic multi-scale heterogeneous objects visual-auditory pipeline and discuss the framework application for two case studies. The first is a molecular phenomena study that is a result of molecular dynamics simulation and quantum simulation. The second explores microstructures in digital fabrication with an arbitrary irregular lattice structure. For considered case studies, the visual-auditory techniques facilitate the interactive analysis of both spatial structure and internal multi-scale properties of volume nature in complex heterogeneous objects. A GPU-accelerated framework for visual-auditory analysis of heterogeneous objects can be applied and extend beyond this research. Thus, to specify the main direction of such extension from the point of view of the potential users, strengthen the value of this research as well as to evaluate the vision of the application of the techniques described above, we carry out a preliminary evaluation. The user study aims to compare our expectations on the visual-auditory approach with the views of the potential users of this system if it is implemented as a software product. A preliminary evaluation study was carried out with limitations imposed by 2020/2021 restrictions. However, it confirms that the main direction for the visual-auditory analysis of heterogeneous objects has been identified correctly and visual and auditory stimuli can complement each other in the analysis of both volume and spatial distribution properties of heterogeneous phenomena. The user reviews also highlight the necessary enhancements that should be introduced to the approach in terms of the design of more complex user interfaces and consideration of additional application cases. To provide a more detailed picture on evaluation results and recommendations introduced, we also identify the key factors that define the user vision of the approach further enhancement and its possible application areas, such as users experience in the area of complex physical phenomena analysis or multi-sensory area. The discussed in this work aspects of heterogeneous objects analysis task, theoretical and practical solutions allow considering the application, further development and enhancement of the results in multidisciplinary areas of GPU accelerated High-performance visualisation pipelines design and multi-sensory analysis

Toward robust and efficient physically-based rendering

Le rendu fondé sur la physique est utilisé pour le design, l'illustration ou l'animation par ordinateur. Ce type de rendu produit des images photo-réalistes en résolvant les équations qui décrivent le transport de la lumière dans une scène. Bien que ces équations soient connues depuis longtemps, et qu'un grand nombre d'algorithmes aient été développés pour les résoudre, il n'en existe pas qui puisse gérer de manière efficace toutes les scènes possibles. Plutôt qu'essayer de développer un nouvel algorithme de simulation d'éclairage, nous proposons d'améliorer la robustesse de la plupart des méthodes utilisées à ce jour et/ou qui sont amenées à être développées dans les années à venir. Nous faisons cela en commençant par identifier les sources de non-robustesse dans un moteur de rendu basé sur la physique, puis en développant des méthodes permettant de minimiser leur impact. Le résultat de ce travail est un ensemble de méthodes utilisant différents outils mathématiques et algorithmiques, chacune de ces méthodes visant à améliorer une partie spécifique d'un moteur de rendu. Nous examinons aussi comment les architectures matérielles actuelles peuvent être utilisées à leur maximum afin d'obtenir des algorithmes plus rapides, sans ajouter d'approximations. Bien que les contributions présentées dans cette thèse aient vocation à être combinées, chacune d'entre elles peut être utilisée seule : elles sont techniquement indépendantes les unes des autres.Physically-based rendering is used for design, illustration or computer animation. It consists in producing photorealistic images by solving the equations which describe how light travels in a scene. Although these equations have been known for a long time and many algorithms for light simulation have been developed, no algorithm exists to solve them efficiently for any scene. Instead of trying to develop a new algorithm devoted to light simulation, we propose to enhance the robustness of most methods used nowadays and/or which can be developed in the years to come. We do this by first identifying the sources of non-robustness in a physically-based rendering engine, and then addressing them by specific algorithms. The result is a set of methods based on different mathematical or algorithmic methods, each aiming at improving a different part of a rendering engine. We also investigate how the current hardware architectures can be used at their maximum to produce more efficient algorithms, without adding approximations. Although the contributions presented in this dissertation are meant to be combined, each of them can be used in a standalone way: they have been designed to be internally independent of each other

Fitted BVH for Fast Raytracing of Metaballs

International audienceRaytracing metaballs is a problem that has numerous applications in the rendering of dynamic soft objects such as fluids. However, current techniques are either limited in the visual effects that they can render or their performance drops as the number of metaballs and their density increase. We present a new acceleration structure based on BVH and kd-tree for efficient raytracing of a large number of metaballs. This structure is built from an adapted SAH using a fast greedy algorithm and allows the visualization of several hundreds of thousands metaballs at interactive-to-real-time framerates. Our method can handle arbitrary rays to simulate any complex secondary effects such as reflections or soft shadows, and is robust with respect to the density of metaballs. We achieve this performance thanks to a balanced CPU-GPU (using CUDA) implementation of the animation, structure creation, and rendering

Curve Skeleton and Moments of Area Supported Beam Parametrization in Multi-Objective Compliance Structural Optimization

This work addresses the end-to-end virtual automation of structural optimization up to the derivation of a parametric geometry model that can be used for application areas such as additive manufacturing or the verification of the structural optimization result with the finite element method. A holistic design in structural optimization can be achieved with the weighted sum method, which can be automatically parameterized with curve skeletonization and cross-section regression to virtually verify the result and control the local size for additive manufacturing. is investigated in general. In this paper, a holistic design is understood as a design that considers various compliances as an objective function. This parameterization uses the automated determination of beam parameters by so-called curve skeletonization with subsequent cross-section shape parameter estimation based on moments of area, especially for multi-objective optimized shapes. An essential contribution is the linking of the parameterization with the results of the structural optimization, e.g., to include properties such as boundary conditions, load conditions, sensitivities or even density variables in the curve skeleton parameterization. The parameterization focuses on guiding the skeletonization based on the information provided by the optimization and the finite element model. In addition, the cross-section detection considers circular, elliptical, and tensor product spline cross-sections that can be applied to various shape descriptors such as convolutional surfaces, subdivision surfaces, or constructive solid geometry. The shape parameters of these cross-sections are estimated using stiffness distributions, moments of area of 2D images, and convolutional neural networks with a tailored loss function to moments of area. Each final geometry is designed by extruding the cross-section along the appropriate curve segment of the beam and joining it to other beams by using only unification operations. The focus of multi-objective structural optimization considering 1D, 2D and 3D elements is on cases that can be modeled using equations by the Poisson equation and linear elasticity. This enables the development of designs in application areas such as thermal conduction, electrostatics, magnetostatics, potential flow, linear elasticity and diffusion, which can be optimized in combination or individually. Due to the simplicity of the cases defined by the Poisson equation, no experts are required, so that many conceptual designs can be generated and reconstructed by ordinary users with little effort. Specifically for 1D elements, a element stiffness matrices for tensor product spline cross-sections are derived, which can be used to optimize a variety of lattice structures and automatically convert them into free-form surfaces. For 2D elements, non-local trigonometric interpolation functions are used, which should significantly increase interpretability of the density distribution. To further improve the optimization, a parameter-free mesh deformation is embedded so that the compliances can be further reduced by locally shifting the node positions. Finally, the proposed end-to-end optimization and parameterization is applied to verify a linear elasto-static optimization result for and to satisfy local size constraint for the manufacturing with selective laser melting of a heat transfer optimization result for a heat sink of a CPU. For the elasto-static case, the parameterization is adjusted until a certain criterion (displacement) is satisfied, while for the heat transfer case, the manufacturing constraints are satisfied by automatically changing the local size with the proposed parameterization. This heat sink is then manufactured without manual adjustment and experimentally validated to limit the temperature of a CPU to a certain level.:TABLE OF CONTENT III I LIST OF ABBREVIATIONS V II LIST OF SYMBOLS V III LIST OF FIGURES XIII IV LIST OF TABLES XVIII 1. INTRODUCTION 1 1.1 RESEARCH DESIGN AND MOTIVATION 6 1.2 RESEARCH THESES AND CHAPTER OVERVIEW 9 2. PRELIMINARIES OF TOPOLOGY OPTIMIZATION 12 2.1 MATERIAL INTERPOLATION 16 2.2 TOPOLOGY OPTIMIZATION WITH PARAMETER-FREE SHAPE OPTIMIZATION 17 2.3 MULTI-OBJECTIVE TOPOLOGY OPTIMIZATION WITH THE WEIGHTED SUM METHOD 18 3. SIMULTANEOUS SIZE, TOPOLOGY AND PARAMETER-FREE SHAPE OPTIMIZATION OF WIREFRAMES WITH B-SPLINE CROSS-SECTIONS 21 3.1 FUNDAMENTALS IN WIREFRAME OPTIMIZATION 22 3.2 SIZE AND TOPOLOGY OPTIMIZATION WITH PERIODIC B-SPLINE CROSS-SECTIONS 27 3.3 PARAMETER-FREE SHAPE OPTIMIZATION EMBEDDED IN SIZE OPTIMIZATION 32 3.4 WEIGHTED SUM SIZE AND TOPOLOGY OPTIMIZATION 36 3.5 CROSS-SECTION COMPARISON 39 4. NON-LOCAL TRIGONOMETRIC INTERPOLATION IN TOPOLOGY OPTIMIZATION 41 4.1 FUNDAMENTALS IN MATERIAL INTERPOLATIONS 43 4.2 NON-LOCAL TRIGONOMETRIC SHAPE FUNCTIONS 45 4.3 NON-LOCAL PARAMETER-FREE SHAPE OPTIMIZATION WITH TRIGONOMETRIC SHAPE FUNCTIONS 49 4.4 NON-LOCAL AND PARAMETER-FREE MULTI-OBJECTIVE TOPOLOGY OPTIMIZATION 54 5. FUNDAMENTALS IN SKELETON GUIDED SHAPE PARAMETRIZATION IN TOPOLOGY OPTIMIZATION 58 5.1 SKELETONIZATION IN TOPOLOGY OPTIMIZATION 61 5.2 CROSS-SECTION RECOGNITION FOR IMAGES 66 5.3 SUBDIVISION SURFACES 67 5.4 CONVOLUTIONAL SURFACES WITH META BALL KERNEL 71 5.5 CONSTRUCTIVE SOLID GEOMETRY 73 6. CURVE SKELETON GUIDED BEAM PARAMETRIZATION OF TOPOLOGY OPTIMIZATION RESULTS 75 6.1 FUNDAMENTALS IN SKELETON SUPPORTED RECONSTRUCTION 76 6.2 SUBDIVISION SURFACE PARAMETRIZATION WITH PERIODIC B-SPLINE CROSS-SECTIONS 78 6.3 CURVE SKELETONIZATION TAILORED TO TOPOLOGY OPTIMIZATION WITH PRE-PROCESSING 82 6.4 SURFACE RECONSTRUCTION USING LOCAL STIFFNESS DISTRIBUTION 86 7. CROSS-SECTION SHAPE PARAMETRIZATION FOR PERIODIC B-SPLINES 96 7.1 PRELIMINARIES IN B-SPLINE CONTROL GRID ESTIMATION 97 7.2 CROSS-SECTION EXTRACTION OF 2D IMAGES 101 7.3 TENSOR SPLINE PARAMETRIZATION WITH MOMENTS OF AREA 105 7.4 B-SPLINE PARAMETRIZATION WITH MOMENTS OF AREA GUIDED CONVOLUTIONAL NEURAL NETWORK 110 8. FULLY AUTOMATED COMPLIANCE OPTIMIZATION AND CURVE-SKELETON PARAMETRIZATION FOR A CPU HEAT SINK WITH SIZE CONTROL FOR SLM 115 8.1 AUTOMATED 1D THERMAL COMPLIANCE MINIMIZATION, CONSTRAINED SURFACE RECONSTRUCTION AND ADDITIVE MANUFACTURING 118 8.2 AUTOMATED 2D THERMAL COMPLIANCE MINIMIZATION, CONSTRAINT SURFACE RECONSTRUCTION AND ADDITIVE MANUFACTURING 120 8.3 USING THE HEAT SINK PROTOTYPES COOLING A CPU 123 9. CONCLUSION 127 10. OUTLOOK 131 LITERATURE 133 APPENDIX 147 A PREVIOUS STUDIES 147 B CROSS-SECTION PROPERTIES 149 C CASE STUDIES FOR THE CROSS-SECTION PARAMETRIZATION 155 D EXPERIMENTAL SETUP 15

Vertex classification for non-uniform geometry reduction.

Complex models created from isosurface extraction or CAD and highly accurate 3D models produced from high-resolution scanners are useful, for example, for medical simulation, Virtual Reality and entertainment. Often models in general require some sort of manual editing before they can be incorporated in a walkthrough, simulation, computer game or movie. The visualization challenges of a 3D editing tool may be regarded as similar to that of those of other applications that include an element of visualization such as Virtual Reality. However the rendering interaction requirements of each of these applications varies according to their purpose. For rendering photo-realistic images in movies computer farms can render uninterrupted for weeks, a 3D editing tool requires fast access to a model's fine data. In Virtual Reality rendering acceleration techniques such as level of detail can temporarily render parts of a scene with alternative lower complexity versions in order to meet a frame rate tolerable for the user. These alternative versions can be dynamic increments of complexity or static models that were uniformly simplified across the model by minimizing some cost function. Scanners typically have a fixed sampling rate for the entire model being scanned, and therefore may generate large amounts of data in areas not of much interest or that contribute little to the application at hand. It is therefore desirable to simplify such models non-uniformly. Features such as very high curvature areas or borders can be detected automatically and simplified differently to other areas without any interaction or visualization. However a problem arises when one wishes to manually select features of interest in the original model to preserve and create stand alone, non-uniformly reduced versions of large models, for example for medical simulation. To inspect and view such models the memory requirements of LoD representations can be prohibitive and prevent storage of a model in main memory. Furthermore, although asynchronous rendering of a base simplified model ensures a frame rate tolerable to the user whilst detail is paged, no guarantees can be made that what the user is selecting is at the original resolution of the model or of an appropriate LoD owing to disk lag or the complexity of a particular view selected by the user. This thesis presents an interactive method in the con text of a 3D editing application for feature selection from any model that fits in main memory. We present a new compression/decompression of triangle normals and colour technique which does not require dedicated hardware that allows for 87.4% memory reduction and allows larger models to fit in main memory with at most 1.3/2.5 degrees of error on triangle normals and to be viewed interactively. To address scale and available hardware resources, we reference a hierarchy of volumes of different sizes. The distances of the volumes at each level of the hierarchy to the intersection point of the line of sight with the model are calculated and these distances sorted. At startup an appropriate level of the tree is automatically chosen by separating the time required for rendering from that required for sorting and constraining the latter according to the resources available. A clustered navigation skin and depth buffer strategy allows for the interactive visualisation of models of any size, ensuring that triangles from the closest volumes are rendered over the navigation skin even when the clustered skin may be closer to the viewer than the original model. We show results with scanned models, CAD, textured models and an isosurface. This thesis addresses numerical issues arising from the optimisation of cost functions in LoD algorithms and presents a semi-automatic solution for selection of the threshold on the condition number of the matrix to be inverted for optimal placement of the new vertex created by an edge collapse. We show that the units in which a model is expressed may inadvertently affect the condition of these matrices, hence affecting the evaluation of different LoD methods with different solvers. We use the same solver with an automatically calibrated threshold to evaluate different uniform geometry reduction techniques. We then present a framework for non-uniform reduction of regular scanned models that can be used in conjunction with a variety of LoD algorithms. The benefits of non-uniform reduction are presented in the context of an animation system. (Abstract shortened by UMI.)

Visually pleasing real-time global illumination rendering for fully-dynamic scenes

Global illumination (GI) rendering plays a crucial role in the photo-realistic rendering of virtual scenes. With the rapid development of graphics hardware, GI has become increasingly attractive even for real-time applications nowadays. However, the computation of physically-correct global illumination is time-consuming and cannot achieve real-time, or even interactive performance. Although the realtime GI is possible using a solution based on precomputation, such a solution cannot deal with fully-dynamic scenes. This dissertation focuses on solving these problems by introducing visually pleasing real-time global illumination rendering for fully-dynamic scenes. To this end, we develop a set of novel algorithms and techniques for rendering global illumination effects using the graphics hardware. All these algorithms not only result in real-time or interactive performance, but also generate comparable quality to the previous works in off-line rendering. First, we present a novel implicit visibility technique to circumvent expensive visibility queries in hierarchical radiosity by evaluating the visibility implicitly. Thereafter, we focus on rendering visually plausible soft shadows, which is the most important GI effect caused by the visibility determination. Based on the pre-filtering shadowmapping theory, wesuccessively propose two real-time soft shadow mapping methods: "convolution soft shadow mapping" (CSSM) and "variance soft shadow mapping" (VSSM). Furthermore, we successfully apply our CSSM method in computing the shadow effects for indirect lighting. Finally, to explore the GI rendering in participating media, we investigate a novel technique to interactively render volume caustics in the single-scattering participating media.Das Rendern globaler Beleuchtung ist für die fotorealistische Darstellung virtueller Szenen von entscheidender Bedeutung. Dank der rapiden Entwicklung der Grafik-Hardware wird die globale Beleuchtung heutzutage sogar für Echtzeitanwendungen immer attraktiver. Trotz allem ist die Berechnung physikalisch korrekter globaler Beleuchtung zeitintensiv und interaktive Laufzeiten können mit "standard Hardware" noch nicht erzielt werden. Obwohl das Rendering auf der Grundlage von Vorberechnungen in Echtzeit möglich ist, kann ein solcher Ansatz nicht auf voll-dynamische Szenen angewendet werden. Diese Dissertation zielt darauf ab, das Problem der globalen Beleuchtungsberechnung durch Einführung von neuen Techniken für voll-dynamische Szenen in Echtzeit zu lösen. Dazu stellen wir eine Reihe neuer Algorithmen vor, die die Effekte der globaler Beleuchtung auf der Grafik-Hardware berechnen. All diese Algorithmen erzielen nicht nur Echtzeit bzw. interaktive Laufzeiten sondern liefern auch eine Qualität, die mit bisherigen offline Methoden vergleichbar ist. Zunächst präsentieren wir eine neue Technik zur Berechnung impliziter Sichtbarkeit, die aufwändige Sichbarkeitstests in hierarchischen Radiosity-Datenstrukturen vermeidet. Anschliessend stellen wir eine Methode vor, die weiche Schatten, ein wichtiger Effekt für die globale Beleuchtung, in Echtzeit berechnet. Auf der Grundlage der Theorie über vorgefilterten Schattenwurf, zeigen wir nacheinander zwei Echtzeitmethoden zur Berechnung weicher Schattenwürfe: "Convolution Soft Shadow Mapping" (CSSM) und "Variance Soft Shadow Mapping" (VSSM). Darüber hinaus wenden wir unsere CSSM-Methode auch erfolgreich auf den Schatteneffekt in der indirekten Beleuchtung an. Abschliessend präsentieren wir eine neue Methode zum interaktiven Rendern von Volumen-Kaustiken in einfach streuenden, halbtransparenten Medien