Cellular structures are highly evaluated due to their high material efficiency. Both theoretical and experimental studies have done on periodic cellular structures. However, the mechanical performance can be stochastically distributed in the cellular architecture. This thesis presents the design and manufacturing of variable stiffness cellular architecture to achieve optimized topology by changing the unit cell parameters. The author applies image analysis technique to extract and digitize the information from the performance distribution map. Two types of cellular cells are studied for their relationship of stiffness and relative density. The methods of voxelization for both cells are also given in this study. This proposed methodology is then implemented to design a customized mattress and compare with current existing mattress. With the study of the unit cells and voxelization technique, our designed mattress aligns body curve better which provides more recuperation of the body during sleep.

"Global illumination (GI) rendering simulates the propagation of light through a 3D volume and its interaction with surfaces, dramatically increasing the fidelity of computer generated images. While off-line GI algorithms such as ray tracing and radiosity can generate physically accurate images, their rendering speeds are too slow for real-time applications. The many-light method is one of many novel emerging real-time global illumination algorithms. However, it requires many shadow maps to be generated for Virtual Point Light (VPL) visibility tests, which reduces its efficiency. Prior solutions restrict either the number or accuracy of shadow map updates, which may lower the accuracy of indirect illumination or prevent the rendering of fully dynamic scenes. In this thesis, we propose a hybrid real-time GI algorithm that utilizes an efficient Sparse Voxel Octree (SVO) ray marching algorithm for visibility tests instead of the shadow map generation step of the many-light algorithm. Our technique achieves high rendering fidelity at about 50 FPS, is highly scalable and can support thousands of VPLs generated on the fly. A survey of current real-time GI techniques as well as details of our implementation using OpenGL and Shader Model 5 are also presented."

This thesis presents an efficient computational voxelization approach that utilizes the graphics pipeline. Our approach is hybrid in that it performs a precise gap-free computational voxelization, employs fixed-function components of the GPU, and utilizes the stages of the graphics pipeline to improve parallelism. This approach makes use of the latest features of OpenGL and fully supports both conservative and thin voxelization. In contrast to other computational voxelization approaches, this approach is implemented entirely in OpenGL, and achieves both triangle and fragment parallelism through its use of both the geometry and fragment shaders. A novel approach utilizing the graphics pipeline to complement geometric triangle intersection computations is presented. By exploiting features of the existing graphics pipeline we are able to rapidly compute accurate scene voxelization in a manner that integrates well with existing OpenGL applications, is robust across many different models, and eschews the need for complex work/load-balancing schemes. / Graduation date: 2013

Context. Producing NavMeshes for pathfinding in computer games is a time-consuming process. Recast and Detour is a pair of stateof-the-art libraries that allows automation of NavMesh generation. It builds on a technique called Scene Voxelization, where triangle geometry is converted to voxels in heightfields. The algorithm is expensive in terms of execution time. A fast voxelization algorithm could be useful in real-time applications where geometry is dynamic. In recent years, voxelization implementations on the GPU have been shown to outperform CPU implementations in certain configurations. Objectives. The objective of this thesis is to find a GPU-based alternative to Recast’s voxelization algorithm, and determine when the GPU-based solution is faster than the reference. Methods. This thesis proposes a GPU-based alternative to Recast’s voxelization algorithm, designed to be an interchangeable step in Recast’s pipeline, in a real-time application where geometry is dynamic. Experiments were conducted to show how accurately the algorithm generates heightfields, how fast the execution time is in certain con- figurations, and how the algorithm scales with different sets of input data. Results. The proposed algorithm, when run on an AMD Radeon RX 480 GPU, was shown to be both accurate and fast in certain configurations. At low voxelfield resolutions, it outperformed the reference algorithm on typical Recast reference models. The biggest performance gain was shown when the input contained large numbers of small triangles. The algorithm performs poorly when the input data has triangles that are big in relation to the size of the voxels, and an optional optimization was presented to address this issue. Another optimization was presented that further increases performance gain when many instances of the same mesh are voxelized. Conclusions. The objectives of the thesis were met. A fast, GPUbased algorithm for voxelization in Recast was presented, and conclusions about when it can outperform the reference algorithm were drawn. Possibilities for even greater performance gains were identified for future research.

In recent years, voxel-based modelling has seen a reintroduction to computer game development through massive graphics hardware improvements. Never- theless, polygons continue to be the default building block of 3D objects, intro- ducing a need for the transformation of polygon meshes into voxel-based models; this process is known as voxelization. Efficient voxelization algorithms take ad- vantage of the flexibility and control offered by modern, programmable GPU pipelines. However, the variability in possible approaches poses the question of how different GPU-based implementations affect voxelization performance.This thesis explores the impact of GPU-based improvements by comparing four different implementations of a solid voxelization algorithm. The implemen- tations include a naive transition from the CPU to the GPU, a non-branching execution path approach, data pre-processing, and a combination of the two previous approaches. Benchmarking experiments run on four, standard polygo- nal models and three graphics cards (NVIDIA and AMD) provide runtime and memory usage data for each implementation. A comparative analysis is per- formed on the basis of this data to determine the performance impact of the GPU-based adjustments to the voxelization algorithm implementation.Results indicate that the non-branching execution path approach yields clear improvements over the naive implementation, while data pre-processing has in- consistent performance and a large initial performance cost; the combination of the two improvements unsurprisingly leads to combined results. Therefore, the conclusive recommendation is using the non-branching execution path technique for GPU-based improvements. / Voxel-baserad modellering har på senare år blivit återintroducerat till datorspelsutveckling tack vare massiva förbättringar i grafikhårdvara. Trots detta fortsätter polygoner att vara standarden för uppbyggnaden av 3D-objekt. Detta gör det nödvändigt att kunna transformera polygonytor till voxel-baserade modeller; denna process kallas för voxelisering. Effektiva voxeliseringsalgoritmer tar vara på den flexibilitet och kontroll som ges av moderna, programmerbara GPU-pipelines. Variationen i möjliga tillvägagångssätt gör det dock intressant att veta hur olika GPU-baserade implementationer påverkar prestandan av voxeliseringen. Denna avhandling undersöker påverkan av GPU-baserade förbättringar genom att jämföra fyra olika implementationer av en solid-voxeliseringsalgoritm. Implementationerna inkluderar en naiv övergång från CPU:n till GPU:n, en metod med en non-branching exekveringsväg, förbehandling av data, och en kombination av det två tidigare metoderna. Benchmarkingexperiment görs på fyra standardpolygonmodeller och tre grafikkort (NVIDIA och AMD) förser data för exekveringstid och minnesåtgång för varje implementation. En jämförande analys görs med detta data som grund för att bestämma den påverkan som de GPU-baserade ändringarna har på prestandan av voxeliseringsalgoritmens implementation. Resultaten indikerar att implementationen med en non-branching exekveringsväg ger klara förbättringar över den naiva implementationen, medans förbehandlingen av data presterar inkonsekvent och har en stor initial prestandakostnad; kombinationen av dem båda ledde, inte överraskande, till blandade resultat. Den slutgiltiga rekommendationen är således att använda tekniken med en non-branching exekveringsväg för GPU-baserade förbättringar.

This thesis presents a comparison between different algorithms for optimal scanline voxelization of 3D models.As the optimal scanline relies on line voxelization, three such algorithms were evaluated. These were Real Line Voxelization (RLV), Integer Line Voxelization (ILV) and a 3D Bresenham line drawing algorithm. RLV and ILV were both based on voxel traversal by Amanatides and Woo. The algorithms were evaluated based on runtime and the approximation error of the integer versions, ILV and Bresenham. The result was that RLV performed better in every case, with ILV being 20-250% slower and Bresenham being 20-500% slower. The error metric used was the Jaccard distance and generally started at 20% and grew up towards 25% for higher voxel resolutions. This was true for both ILV and Bresenham. The conclusion was that there is no reason to use any of the integer versions over RLV. As they both performed and approximated the original 3D model worse.

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This thesis deals with the global illumination in the scene by using Voxel Cone Tracing method. It is based on the voxelization of a triangle mesh scene. The voxels can be stored to a full regular 3D grid (texture) or to the hierarchic Sparse Voxel Octree for saving of the memory space. This voxel representation is further used for computations of the global indirect illumination in real time within normal triangle mesh scenes for more realistic final image. Values from the voxels are obtained by tracing cones from the pixels which we want to get illumination for.

On retrouve dans la nature un nombre impressionnant de matériaux semi-transparents tels le marbre, le jade ou la peau, ainsi que plusieurs liquides comme le lait ou les jus. Que ce soit pour le domaine cinématographique ou le divertissement interactif, l'intérêt d'obtenir une image de synthèse de ce type de matériau demeure toujours très important. Bien que plusieurs méthodes arrivent à simuler la diffusion de la lumière de manière convaincante a l'intérieur de matériaux semi-transparents, peu d'entre elles y arrivent de manière interactive. Ce mémoire présente une nouvelle méthode de diffusion de la lumière à l'intérieur d'objets semi-transparents hétérogènes en temps réel. Le coeur de la méthode repose sur une discrétisation du modèle géométrique sous forme de voxels, ceux-ci étant utilisés comme simplification du domaine de diffusion. Notre technique repose sur la résolution de l'équation de diffusion à l'aide de méthodes itératives permettant d'obtenir une simulation rapide et efficace. Notre méthode se démarque principalement par son exécution complètement dynamique ne nécessitant aucun pré-calcul et permettant une déformation complète de la géométrie. / We find in nature several semi-transparent materials such as marble, jade or skin, as well as liquids such as milk or juices. Whether it be for digital movies or video games, having an efficient method to render these materials is an important goal. Although a large body of previous academic work exists in this area, few of these works provide an interactive solution. This thesis presents a new method for simulating light scattering inside heterogeneous semi-transparent materials in real time. The core of our technique relies on a geometric mesh voxelization to simplify the diffusion domain. The diffusion process solves the diffusion equation in order to achieve a fast and efficient simulation. Our method differs mainly from previous approaches by its completely dynamic execution requiring no pre-computations and hence allowing complete deformations of the geometric mesh.

On retrouve dans la nature un nombre impressionnant de matériaux semi-transparents tels le marbre, le jade ou la peau, ainsi que plusieurs liquides comme le lait ou les jus. Que ce soit pour le domaine cinématographique ou le divertissement interactif, l'intérêt d'obtenir une image de synthèse de ce type de matériau demeure toujours très important. Bien que plusieurs méthodes arrivent à simuler la diffusion de la lumière de manière convaincante a l'intérieur de matériaux semi-transparents, peu d'entre elles y arrivent de manière interactive. Ce mémoire présente une nouvelle méthode de diffusion de la lumière à l'intérieur d'objets semi-transparents hétérogènes en temps réel. Le coeur de la méthode repose sur une discrétisation du modèle géométrique sous forme de voxels, ceux-ci étant utilisés comme simplification du domaine de diffusion. Notre technique repose sur la résolution de l'équation de diffusion à l'aide de méthodes itératives permettant d'obtenir une simulation rapide et efficace. Notre méthode se démarque principalement par son exécution complètement dynamique ne nécessitant aucun pré-calcul et permettant une déformation complète de la géométrie. / We find in nature several semi-transparent materials such as marble, jade or skin, as well as liquids such as milk or juices. Whether it be for digital movies or video games, having an efficient method to render these materials is an important goal. Although a large body of previous academic work exists in this area, few of these works provide an interactive solution. This thesis presents a new method for simulating light scattering inside heterogeneous semi-transparent materials in real time. The core of our technique relies on a geometric mesh voxelization to simplify the diffusion domain. The diffusion process solves the diffusion equation in order to achieve a fast and efficient simulation. Our method differs mainly from previous approaches by its completely dynamic execution requiring no pre-computations and hence allowing complete deformations of the geometric mesh.