The purpose of this project was to construct a 3D scanner capable of scanning smaller objects and visualize them in a computer with satisfying accuracy. The goal was then to generate an STL file able to be 3D printed in an attempt at reverse engineering. Components, materials and tools were provided by KTH to the best of their ability and abudget of 1000 SEK was given to purchase components not available at KTH. The scanner was designed using Solid Edge and utilizes two stepper motors to scan objects. One motor is used to rotate a platform that the object is placed upon and the second stepper motor is used to move an elevator on which a distance sensor is mounted. By keeping track of the elevator’s height in conjunction with the rotation of the object, the distance measured by the sensor can be converted into a point in a Cartesian coordinate system. Several different methods were tested in order to see how results varied. Firstly, the density of scanned points was increased, meaning that the sensor returned values more often as the stepper motor was rotating. Secondly, multiple measurements were made for a single point to determine an average distance and in that way reduce noise and uncertainty. Placing a single laser sensor perpendicular to the object rotating plate proved to be the optimal arrangement in terms of accuracy with the limited budget provided for this project. The scans are very time consuming which makes it important to decide whether to prioritize speed or accuracy. / Syftet med detta projekt var att konstruera en 3D-scanner kapabel att scanna mindre objekt och visualisera dem i en dator med tillfredsställande resultat. Målet var sedan att generera en STL-fil som går att skriva ut i 3D-skrivare för att försöka använda sig av reverse engineering. Komponenter, material och verktyg försågs av KTH så gott det gick och en budget på 1000 kr var tillgänglig för att inhandla komponenter som inte fanns på KTH. Skannern designades med hjälp av Solid Edge och använder sig av två stegmotorer för att skanna object. En motor användes för att rotera den plattform som objektet placerades på och den andra stegmotorn användes för att flytta en hiss varpå en avståndssensor monterades. Genom att hålla koll på hissens höjd i kombination med rotationen av objektet kan avståndet som sensorn uppmäter konvertera still en punkt i det kartesiska koordinatsystemet. Ett flertal metoder testades för att undersöka hur resultaten varierade. För det första ökades densiteten av skannade punkter, det vill säga sensorn returnerade värden oftare än stegmotorn roterade. För det andra genomfördes ett flertal mätningar för varje enskild punkt för att bestämma ett medelavstånd och på så sätt minimera brus och osäkerhet. Att placera en enstaka lasersensor vinkelrätt mot objektroterande plattan visade sig vara det optimala arrangemanget för noggrannhet med den begränsade budgeten för det här projektet. Inskanningarna är väldigt tidskrävande vilket gör det viktigt att bestämma sig för att prioritera snabbhet eller noggrannhet.

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This project, completed in collaboration with Piktiv AB, aimed to develop an automated surface hole-filling feature for static meshes in Unreal Engine 4.27, with the goal of making repaired surfaces visually indistinguishable from their surrounding areas. The solution was primarily designed to address holes that arose from, but were not limited to, the use of Reduction Settings within Unreal Engine on static meshes. The functionality encompassed four key stages: boundary detection, where all holes on the mesh were identified; triangulation, which involved patching the hole using vertices from the boundary; refinement, entailing the addition of vertices and triangles to the patched area to mimic the density of the surrounding surface; and fairing, which smoothed the patched surface. Additionally, the project introduced a straightforward method for determining the texture coordinates of newly added vertices and a technique for ensuring that triangle normals correctly faced outward from the mesh. The Static Mesh Hole Filler, as implemented, demonstrates efficiency in filling an arbitrary amount of small, planar holes, which commonly result from polygon reduction using Reduction Settings in Unreal Engine. However, this function falls short in preserving unique texture details and maintaining the curvature of surfaces when dealing with larger holes. This limitation necessitates users to seek alternative methods for effectively repairing the mesh.

There is a constant development and continuous progress in the wireless technology field as it is in the all fields of information and communication technologies. One of the latest trends is the wireless mesh network. This type of network brings new features into the wireless field such as multihop, self-configuration, self-organization and self-healing. This enables the usage of wireless networks in new fields and industries or the upgrade of current implementations to meet new market demands. This thesis summarizes theoretical findings from this field from the users' point of view and functionality dimension. This is followed by a summary of possible applications, available technologies and known standards. The second half of the thesis consists of a requirement analysis of a chosen user group (the Fire Rescue Service of the Czech Republic) focusing on application of wireless mesh network for rescue operations. The analysis also includes test criteria and principles for test procedures for this application.

An adaptive mesh redistribution method for efficient and accurate simulation of multi dimensional hyperbolic conservation laws is developed. The algorithm consists of two coupled steps; evolution of the governing PDE followed by a redistribution of the computational nodes. The second step, i.e. mesh redistribution is carried out at each time step iteratively with the primary aim of adapting the grid to the computed solution in order to maximize accuracy while minimizing the computational overheads. The governing hyperbolic conservation laws, originally defined on the physical domain, are transformed on to a simplified computational domain where the position of the nodes remains independent of time. The transformed governing hyperbolic equations are recast in a strong conservative form and are solved directly on the computational domain without the need for interpolation that is typically associated with standard mesh redistribution algorithms. Several standard test cases involving numerical solution of scalar and system of hyperbolic conservation laws in one and two dimensions are presented in order to demonstrate the accuracy and computational efficiency of the proposed technique.

Técnicas para gerar malhas triangulares ou tetraedrais a partir de imagens, ou assumem como entrada uma imagem pré-processada, ou geram uma malha sem distinguir as diferentes estruturas contidas na imagem. O pré-processamento e a ausência de estruturas bem definidas podem apresentar dificuldades na utilização das malhas geradas em algumas aplicações, tais como simulações numéricas. Neste trabalho, apresentamos uma nova técnica que elimina a necessidade do pré-processamento embutindo a segmentação dentro do processo de geração de malha. Além disto, a técnica proposta considera critérios de qualidade nas malhas geradas, mostrando-se apropriada para aplicações de simulação numérica assim como modelagem de imagens com malhas / Techniques devoted to generate triangular or tetrahedral meshes from images either take as starting point a pre-processed image or generate a mesh without distinguishing different structures contained in the image. The pre-process and the absence of well defined structures may impose difficulties in using the resulting mesh in some applications as, for example, numerical simulations. In this work, we present a new technique that aims at eliminating the need for pre-processing by building the segmentation into the mesh generation process. Furthermore, the proposed technique consider quality criteria in the generated meshes, being appropriated for applications in numerical simulation as well as in image modeling

Com a popularização de equipamentos tradicionais de captura de imagens, como câmeras digitais, e o avanço tecnológico dos dispositivos não invasivos, como tomografia e ressonância, cresce também a necessidade e consequente uso de métodos numéricos para simulação de fenômenos físicos em domínios definidos por imagens. Um dos pré-requisitos para a aplicação de tais métodos numéricos consiste na discretização do domínio em questão, num processo denominado geração de malhas. Embora diversos métodos de geração de malha tenham sido propostos para discretizar domínios definidos por primitivas geométricas, pouco tem sido feito no sentido de gerar uma decomposição diretamente a partir de imagens. Neste trabalho, apresentamos uma abordagem de geração de malhas de qualidade a partir de domínios definidos por imagens com textura. Mais especificamente, a pesquisa descrita nesta tese contribui com a melhoria do algoritmo Imesh, ao sanar três de suas principais limitações: tratamento de imagens com texturas; controle do nível de refinamento da malha e suporte a outros tipos de elementos. Estas contribuições flexibilizam o processo de geração da malha, e ainda ampliam o domínio de aplicações do algoritmo Imesh, à medida que são considerados domínios definidos por imagens com textura e o uso de métodos numéricos para elementos não simpliciais torna-se possível. O algoritmo de melhoria da malha gerada utiliza uma abordagem inovadora de remalhamento baseada em templates e guiada por retalhos de Bézier / With the spreading of traditional image capturing devices, such as digital cameras, and the technological advancement of more specific imaging devices such as CT and MRI, also increased the need and the following use of numerical methods for simulation of physical phenomena in domains defined by images. One of the prerequisites for the application of such numerical methods is the discretization of the corresponding domain, in a process called mesh generation. Although several methods of mesh generation have been proposed to discretize domains defined by geometric primitives, little has been done to generate a decomposition directly from images. We present an approach to generate quality meshes from domains defined by images with texture. More specifically, the research described in this thesis contributes to the improvement of the Imesh algorithm, removing three of its main limitations: treatment textured images, control of the level of the mesh refinement and support for other types of non-simplicial elements. These contributions provide flexibility to the mesh generation process, and extend the range of applications of Imesh by both handling textured images and considering the use of numerical methods for non-simplicial elements. The mesh quality improvement algorithm uses a new approach based on mesh templates and it is guided by Bezier patches

Técnicas para gerar malhas triangulares ou tetraedrais a partir de imagens, ou assumem como entrada uma imagem pré-processada, ou geram uma malha sem distinguir as diferentes estruturas contidas na imagem. O pré-processamento e a ausência de estruturas bem definidas podem apresentar dificuldades na utilização das malhas geradas em algumas aplicações, tais como simulações numéricas. Neste trabalho, apresentamos uma nova técnica que elimina a necessidade do pré-processamento embutindo a segmentação dentro do processo de geração de malha. Além disto, a técnica proposta considera critérios de qualidade nas malhas geradas, mostrando-se apropriada para aplicações de simulação numérica assim como modelagem de imagens com malhas / Techniques devoted to generate triangular or tetrahedral meshes from images either take as starting point a pre-processed image or generate a mesh without distinguishing different structures contained in the image. The pre-process and the absence of well defined structures may impose difficulties in using the resulting mesh in some applications as, for example, numerical simulations. In this work, we present a new technique that aims at eliminating the need for pre-processing by building the segmentation into the mesh generation process. Furthermore, the proposed technique consider quality criteria in the generated meshes, being appropriated for applications in numerical simulation as well as in image modeling

Many physical problems lead to boundary value problems for partial differential equations, which can be solved with the finite element method. In order to construct adaptive solution algorithms or to measure the error one aims at reliable a posteriori error estimators. Many such estimators are known, as well as their theoretical foundation. Some boundary value problems yield so-called anisotropic solutions (e.g. with boundary layers). Then anisotropic finite element meshes can be advantageous. However, the common error estimators for isotropic meshes fail when applied to anisotropic meshes, or they were not investigated yet. For rectangular or cuboidal anisotropic meshes a modified error estimator had already been derived. In this paper error estimators for anisotropic tetrahedral or triangular meshes are considered. Such meshes offer a greater geometrical flexibility. For the Poisson equation we introduce a residual error estimator, an estimator based on a local problem, several Zienkiewicz-Zhu estimators, and an L_2 error estimator, respectively. A corresponding mathematical theory is given.For a singularly perturbed reaction-diffusion equation a residual error estimator is derived as well. The numerical examples demonstrate that reliable and efficient error estimation is possible on anisotropic meshes. The analysis basically relies on two important tools, namely anisotropic interpolation error estimates and the so-called bubble functions. Moreover, the correspondence of an anisotropic mesh with an anisotropic solution plays a vital role. AMS(MOS): 65N30, 65N15, 35B25

The objective of this PhD research programme is to investigate the effectiveness of a finite volume method incorporating radial basis functions for simulating nonlinear transport processes. The finite volume method is the favoured numerical technique for solving the advection-diffusion equations that arise in transport simulation. The method transforms the original problem into a system of nonlinear, algebraic equations through the process of discretisation. The accuracy of this discretisation determines to a large extent the accuracy of the final solution. A new method of discretisation is presented that employs radial basis functions (rbfs) as a means of local interpolation. When combined with Gaussian quadrature integration methods, the resulting finite volume discretisation leads to accurate numerical solutions without the need for very fine meshes, and the additional overheads they entail. The resulting nonlinear, algebraic system is solved efficiently using a Jacobian-free Newton-Krylov method. By employing the new method as an extension of existing shape function-based approaches, the number of nonlinear iterations required to obtain convergence can be reduced. Furthermore, information obtained from these iterations can be used to increase the efficiency of subsequent rbf-based iterations, as well as to construct an effective parallel reconditioner to further reduce the number of nonlinear iterations required. Results are presented that demonstrate the improved accuracy offered by the new method when applied to several test problems. By successively refining the meshes, it is also possible to demonstrate the increased order of the new method, when compared to a traditional shape function basedmethod. Comparing the resources required for both methods reveals that the new approach can be many times more efficient at producing a solution of a given accuracy.