No / Modern manufacturing involves multiple stages of complex process chains where Finite Element Analysis is frequently used as a simulation method on a discretized mesh to provide an accurate estimation of factors such as stresses, strains, and displacements. The choice of the most suitable element type and density is dependent on the individual manufacturing process or treatment applied at each stage of the process chain. To map between unalike Finite Element meshes, differing in density and/or element type, an Octree spatial index was evaluated as a solution for highly performant mapping. Compared to existing solutions, the Octree spatial index introduces parallelism within index creation and provides a strategy to perform the most complex interpolation technique, Element Shape Function, in a more computationally efficient manner.

The subject of this thesis is an implementation of realistic rendering of voxel scenes using a graphics card. This work explains the fundamentals of realistic rendering and voxel representation of visual data. It also presents selected hierarchical structures usable for acceleration and describes the desing of a solution focusing on the representation of voxel data and their rendering. The thesis describes libraries created as part of the project and algorithms. It also evaluates time and memory requirements of the application along with graphical output.

Detailed and exact collision detection for large amounts of objects has for a long time been a non real-time affair because of the immense amount of computations necessary. This was however not only because of the complexity of the algorithms but also because discussed of the computations would not have had to be done in the first place. This paper has through literature research and empirical testing examined two different broad phase approaches to object culling in a three dimensional environment. The aim of such a broad phase algorithm is to decrease the amount of computation heavy narrow phase collision detection checks and thus enhancing application performance. Potential weaknesses of these approaches were addressed and possible solutions discussed. Performance comparisons were made to give a better overview of what kind of performance enhancements can be expected and to give a theoretical base for further research.

To handle broken 3D models can be a very time consuming problem. Several methods aiming for automatic mesh repair have been presented in the recent years. This thesis gives an extensive evaluation of automatic mesh repair algorithms, presents a mesh repair pipeline and describes an implemented automatic mesh repair algorithm. The presented pipeline for automatic mesh repair includes three main steps: octree generation, surface reconstruction and ray casting. Ray casting is for removal of hidden objects. The pipeline also includes a pre processing step for removal of intersecting triangles and a post processing step for error detection. The implemented algorithm presented in this thesis is a volumetric method for mesh repair. It generates an octree in which data from the input model is saved. Before creation of the output, the octree data will be patched to remove inconsistencies. The surface reconstruction is done with a method called Manifold Dual Contouring. First new vertices are created from the information saved in the octree. Then there is a possibility to cluster vertices together for decimation of the output. Thanks to a special Manifold criterion, the output is guaranteedto be manifold. Furthermore the output will have sharp and clear edges and corners thanks to the use of Singular Value Decomposition during determination of the positions of the new vertices.

In recent years several depth cameras have emerged on the consumer market, creating many interesting possibilities forboth professional and recreational usage. One example of such a camera is the Microsoft Kinect sensor originally usedwith the Microsoft Xbox 360 game console. In this master thesis a system is presented that utilizes this device in order to create an as accurate as possible 3D reconstruction of an indoor environment. The major novelty of the presented system is the data structure based on signed distance fields and voxel octrees used to represent the observed environment. / Under de senaste åren har flera olika avståndskameror lanserats på konsumentmarkanden. Detta har skapat många intressanta applikationer både i professionella system samt för underhållningssyfte. Ett exempel på en sådan kamera är Microsoft Kinect som utvecklades för Microsofts spelkonsol Xbox 360. I detta examensarbete presenteras ett system som använder Kinect för att skapa en så exakt rekonstruktion i 3D av en innomhusmiljö som möjligt. Den främsta innovationen i systemet är en datastruktur baserad på signed distance fields (SDF) och octrees, vilket används för att representera den rekonstruerade miljön.

Background. Real-time applications like video games use particle systems for special effects to add visual aesthetics and realism. However, when complex behaviour that requires interaction between particles and geometry is desired, problems arise. The developer has to choose between having consistent and precise collisions or higher performance. This thesis goes over two particle collision implementations that try to solve these problems. Objectives. The objective of this thesis is to create an application that has support for two collision methods and compare them on performance and accuracy to decide which one is more suitable for real-time applications. Methods. To answer the research questions proposed the implementation methodology was used, as a result of that, a 3D-application was created using the graphics API OpenGL to render. Two simple GPGPU implementations were made for each method, to have a more fair comparison. To be able to measure performance the application logs frame-time every frame. A fixed time-step was added in the main loop to allow the users to stop the application at a certain time to be able to capture images of the scene that will then be used for pixel comparison to measure accuracy. Results. Screen space particle collision is almost three times faster than the octree-based method. Both methods had different behavior in both the real-time simulation and at specific time-steps resulting in loss of accuracy from the screen space particle collision. Conclusions. The tests allowed the authors to show that the screen space particle collision is faster and scales better than the octree-based method. However, it did lack precision as shown by the comparison by the images taken from the test. For particle simulations that require consistent and accurate collision checks the octree-based method is better due to the fact that screen space particle collision can result in false collisions checks and has problems with hidden geometry.

In the past twenty years, our world has experienced a number of disasters, ranging from hurricanes to acts of terrorism. While both natural and anthropogenic disasters are inevitable, being able to simulate their progression and impact can provide guidance for preemptive measures to mitigate casualties and property damage. Specifically, computational fluid dynamics (CFD) simulations can be used to simulate wind forces associated with hurricanes or pressure waves associated with explosions. However, even a simple CFD simulation is time consuming and requires highly-specialized expertise. This paper aims to reduce the processing time by utilizing readily available geometry models, and a surface wrapping algorithm that allows for fast and seamless way of repairing geometry. Both of these processes are automated which also reduces the amount of training in various software packages.

Autonomous navigation of our rough-terrain rovers implies the need of a good representation of their near surrounding. In order to archive this we fuse several of their sensors into one representation called OctoMap. But moving obstacles can produce artefacts, leading to untraversable re- gions. Furthermore the map itself is increasing in size while discovering new places. Even though we are only interested in the near surrounding of the rovers. Our approach to these problems is the usage of timestamps within the map. If a certain region was not updated within a given interval, it will be set to free space or deleted from the map. This first option is an existing solution and the second option reflects our new alternative.

On s'interesse aux problèmes elliptiques avec coéficients variables à travers des interfaces intérieures. La solution et ses dérivées normales peuvent subir des variations significatives à travers les frontières intérieures. On présente une méthode compacte aux différences finies sur des maillages adaptés de type octree conçues pour une résolution en parallèle. L'idée principale est de minimiser l'erreur de troncature sur la discretisation locale, en fonction de la configuration du maillage, en rapprochant une convergence à l'ordre deux. On montrera des cas 2D et 3D des résultat liés à des applications concrètes. / We consider problems governed by a linear elliptic equation with varying coéficients across internal interfaces. The solution and its normal derivative can undergo significant variations through these internal boundaries. We present a compact finite-difference scheme on a tree-based adaptive grid that can be efficiently solved using a natively parallel data structure. The main idea is to optimize the truncation error of the discretization scheme as a function of the local grid configuration to achieve second order accuracy. Numerical illustrations relevant for actual applications are presented in two and three-dimensional configurations.

Le sujet de la thèse est le développement d'un outil numérique qui permet de modéliser l'écoulement autour des pales d'éoliennes. Nous nous sommes intéressés à la résolution des équations de Navier-Stokes en incompressible sur des maillages de type octree où les échelles plus petites en proche parois ont été modélisées par la méthode dite des wall functions. Un procédé d'adaptation automatique du maillage (AMR) a été développé pour affiner le maillage dans les zones où la vorticité est plus importante. Le modèle de structure d'une pale d'éolienne a été également implémenté et couplé avec le modèle fluide car une application de l'outil numérique est l'étude des effets des rafales de vent sur les pales d'éolienne. Un travail expérimental a été mené sur une éolienne avec une mesure de vent en amont. Ces données permettent ainsi de calibrer et valider les modèles numériques développés dans la thèse. / The subject of the thesis is the development of a numerical tool that allows to model the flow around wind blades. We are interested in the solving of incompressible Navier-Stokes equations on octree grids, where the smallest scales close to the wall have been modelled by the use of the so-called Wall Functions. An automatic Adaptive Mesh Refinement (AMR) process has been developed in order to refine the mesh in the areas where the vorticity is higher. The structural model of a real wind blade has also been implemented and coupled with the fluid model. Indeed, an application of the numerical tool is the study of the effects of wind gusts on blades. An experimental work has been conducted with an in-service wind turbine with the measurement of wind speed upstream. This data will allow to calibrate and validate the numerical models developed in the thesis.