Mesh simplification is an important task in Computer Graphics due to the ever increasing complexity of polygonal geometric models. Specifically in real-time rendering, there is a necessity that these models, which can be acquired through 3D scanning or through artistic conception, have to be simplified or optimized to be rendered on today's hardware while losing as little detail as possible. This thesis proposes a mesh simplification algorithm that works by identifying and simplifying features. Then it simplifies the remaining mesh with the simplified features frozen. The algorithm is called Quadric Error with Feature Curves (QEFC). Quadric Error with Feature Curves works as a tool that allows the user to interactively select a percentage of the most important points of the feature curves to be preserved along with the points determined by the Quadric Error Metric algorithm.

In this dissertation, we study the triangular mesh simplification process, describing its main characteristics. We discuss an adaptation for triangular meshes of a mesh simplification process based on Voronoi coverage proposed by Peixoto [2002]. Moreover, we use Fast Marching Method as a distance function over the mesh and some different strategies for simplified mesh vertices selection, like curvature based selection. The simplification process is done by constructing an intrinsic Voronoi diagram over the original mesh. We discuss some necessary conditions to obtain a mesh, as Voronoi dual, without any singularities and topologically equivalent to the original mesh. / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Nesta dissertação, estudaremos o processo de simplificaçãoo de malhas triangulares, caracterizando-o com suas particularidades. Discutiremos uma adaptação para superfícies triangulares do método de simplificação baseado em uma cobertura de Voronoi proposto por Peixoto [2002]. Além disso, utilizaremos o método Fast Marching como uma nova métrica e diferentes estratégias para seleção de vértices da malha simplificada, como a seleção por curvatura. A simplificação ocorre a partir de um diagrama de Voronoi intrínseco à malha. Discutiremos algumas condições necessárias para que a partir do dual desse diagrama, obtenha-se uma malha sem singularidades que seja equivalente a malha original.

<p>Captured and generated 3D data can be so large that it creates a problem for today's computers since they do not fit into the main or graphics card memory. Therefore methods for handling and rendering the data must be developed. This thesis presents a way to pre-process and render out-of-core height map data for real time use. The pre-processing uses a mesh decimation API called Simplygon developed by Donya Labs to optimize the geometry. From the height map a normal map can also be created and used at render time to increase the visual quality. In addition to the 3D data textures are also supported. To decrease the time to load an object the normal and texture maps can be compressed on the graphics card prior to rendering. Three different methods for covering gaps are explored of which one turns out to be insufficient for rendering cylindrical equidistant projected data.At render time two threads work in parallel. One thread is used to page the data from the hard drive to the main and graphics card memory. The other thread is responsible for rendering all data. To handle precision errors caused by spatial difference in the data each object receives a local origin and is then rendered relative to the camera. An atmosphere which handles views from both space and ground is computed on the graphics card.The result is an application adapted to current graphics card technology which can page out-of-core data and render a dataset covering the entire earth at 500 meters spatial resolution with a realistic atmosphere.</p>

Captured and generated 3D data can be so large that it creates a problem for today's computers since they do not fit into the main or graphics card memory. Therefore methods for handling and rendering the data must be developed. This thesis presents a way to pre-process and render out-of-core height map data for real time use. The pre-processing uses a mesh decimation API called Simplygon developed by Donya Labs to optimize the geometry. From the height map a normal map can also be created and used at render time to increase the visual quality. In addition to the 3D data textures are also supported. To decrease the time to load an object the normal and texture maps can be compressed on the graphics card prior to rendering. Three different methods for covering gaps are explored of which one turns out to be insufficient for rendering cylindrical equidistant projected data.At render time two threads work in parallel. One thread is used to page the data from the hard drive to the main and graphics card memory. The other thread is responsible for rendering all data. To handle precision errors caused by spatial difference in the data each object receives a local origin and is then rendered relative to the camera. An atmosphere which handles views from both space and ground is computed on the graphics card.The result is an application adapted to current graphics card technology which can page out-of-core data and render a dataset covering the entire earth at 500 meters spatial resolution with a realistic atmosphere.

Polygonal meshes are a common way of representing 3D surface models in many different areas of computer graphics and geometry processing. However, these models are becoming more and more complex which increases the cost of processing these models. In order to reduce this cost, mesh simplification algorithms are developed. Another important property of a polygonal mesh model is that whether it is regular or not. Regular meshes have many advantages over the irregular ones in terms of memory requirements, efficient processing, rendering etc. In this thesis work, both mesh simplification and regular remeshing algorithms are studied. Moreover, some of the popular mesh libraries are compared with respect to their approaches and performance to the mesh simplification. In addition, mesh models with disk topology are remeshed and converted to regular ones.

This thesis presents a new system that reconstructs the 3D representation of dental casts. To maintain the integrity of the 3D representation, a standard model is built to cover the blind spots that the camera cannot reach. The standard model is obtained by scanning a real human mouth model with a laser scanner. Then the model is simplified by an algorithm which is based on iterative contraction of vertex pairs. The simplified standard model uses a local parametrization method to obtain the curvature information. The system uses a digital camera and a square tube mirror in front of the camera to capture multi-view images. The mirror is made of stainless steel in order to avoid double reflections. The reflected areas of the image are considered as images taken by the virtual cameras. Only one camera calibration is needed since the virtual cameras have the same intrinsic parameters as the real camera. Depth is computed by a simple and accurate geometry based method once the corresponding points are identified. Correspondences are selected using a feature point based stereo matching process, including fast normalized cross-correlation and simulated annealing.

This report describes an algorithm for computing 3D object hierarchies fit for hlod optimization. The algorithm is used as a pre-processing stage in an hlod pipeline that automatically optimizes 3D models containing multiple meshes. The algorithm for generating hierarchies groups together meshes in a hierarchical tree using operations on bounding spheres of the meshes. The algorithm prioritizes grouping close objects together in the early stages, and relaxes its constraints toward the end, resulting in a tree structure with a single root node. The hierarchical tree is then used by computing proxy meshes, i.e. simplified stand-in meshes, for the inner nodes of the hierarchy. Finally, the resulting proxy meshes, together with the generated hierarchy and the original meshes, are used to render the model using a tree-traversing hlod switching algorithm that renders deeper parts of the tree containing more detailed meshes when more detail is needed. In addition, a minor change to the clustering algorithm is proposed. By swapping the bounding spheres to AABBs (Axis-Aligned Bounding Boxes) in the clustering stage, hierarchies with different properties are generated. This change is shown to generate hierarchies with similar rendering performance as the hierarchies made with bounding spheres, while at the same time resulting in lower space requirements for all proxy meshes. Overall, the proposed automatic hlod pipeline is shown to increase rendering performance for all evaluated scenes in most frames, while never yielding noticeably worse performance than the original model as well.

The use of realistic 3D avatars in Virtual Reality (VR) has gained significant traction in applications such as telecommunication and gaming, offering immersive experiences and face-to-face interactions. However, standalone VR devices often face limitations in computational resources and real-time rendering requirements, necessitating the optimization of 3D models through mesh simplification to enhance performance and ensure a smooth user experience. This thesis presents a pipeline that utilizes a Convolutional Neural Network to reconstruct realistic 3D human facial models in a static form from single RGB head images. The reconstructed models are then subjected to the Quadric Error Metrics simplification algorithm, enabling different levels of simplification to be achieved. An evaluation was conducted, utilizing 30 photos from the NoW dataset, to examine the trade-offs associated with employing mesh simplification on the generated facial models within the VR environment. The evaluation results demonstrate that reducing the polygon count improves frame rates and reduces GPU usage in VR, thereby enhancing overall performance. However, this improvement comes at the cost of increased simplification execution time and geometric errors, and decreased perceptual quality. This research contributes to the understanding of mesh simplification’s impact on human facial models within the VR context, providing insights into balancing model complexity and real-time rendering performance, particularly in resource-constrained environments such as mobile devices or cloud-based applications, as well as for models located farther away from the cameras. / Användningen av realistiska 3D-avatarer inom Virtuell Verklighet (VR) har fått betydande uppmärksamhet inom tillämpningar som telekommunikation och spel, vilket erbjuder en uppslukande upplevelse och ansikte mot ansikte-interaktioner. Dock möter fristående VR-enheter ofta begränsningar i beräkningsresurser och krav på realtidsrendering, vilket gör det nödvändigt att optimera 3D-modeller genom nätverksförenkling för att förbättra prestanda och säkerställa en smidig användarupplevelse. Denna avhandling presenterar en pipeline som använder sig av ett konvolutionellt neuralt nätverk för att rekonstruera realistiska 3D-modeller av mänskliga ansikten i en statisk form från enstaka RGB-bilder av huvudet. De rekonstruerade modellerna genomgår sedan nätverksförenkling med Quadric Error Metrics-algoritmen, vilket möjliggör olika nivåer av förenkling. En utvärdering genomfördes, med hjälp av 30 foton från NoW-datasetet, för att undersöka avvägningarna i samband med att använda nätverksförenkling på de genererade ansiktsmodellerna inom VR-miljön. Utvärderingsresultaten visar att minskning av polygonantal förbättrar bildhastigheten och minskar GPU-användningen inom VR, vilket förbättrar den övergripande prestandan. Dock sker denna förbättring på bekostnad av ökad tid för förenklingsexekvering och geometriska fel, samt minskad perceptuell kvalitet. Denna forskning bidrar till förståelsen av nätverksförenklingens påverkan på mänskliga ansiktsmodeller inom VR-sammanhanget och ger insikter om att balansera modellkomplexitet och realtidsrenderingsprestanda, särskilt i resursbegränsade miljöer som mobilenheter eller molnbaserade applikationer, samt för modeller som är längre bort från kamerorna.

Real-time rendering of massive 3D models has been recognized as a challenging task due to the limited computational power and memory available in a workstation. Most existing acceleration techniques, such as mesh simplification algorithms with hierarchical data structures, suffer from the nature of sequential executions. As data complexity increases due to the fundamental advances in modeling and simulation technologies, 3D models become complex and require gigabytes in storage. Consequently, visualizing such large datasets becomes a computationally intensive process where sequential solutions are unable to satisfy the demands of real-time rendering. Recently, the Graphics Processing Unit (GPU) has been praised as a massively parallel architecture not only for its significant improvements in performance but also because of its programmability for general-purpose computation. Today's GPUs allow researchers to solve problems by delivering fine-grained parallel implementations. In this dissertation, I concentrate on the design of parallel algorithms for real-time rendering of massive 3D polygonal models towards modern GPU architectures. As a result, the delivered rendering system supports high-performance visualization of 3D models composed of hundreds of millions of polygons on a single commodity workstation. / Ph. D.

To decrease the rendering time of a mesh, Level of Detail can be generated by reducing the number of polygons based on some geometrical error. While this works well for most meshes, it is not suitable for meshes with an associated texture atlas. By iteratively collapsing edges based on an extended version of Quadric Error Metric taking both spatial and texture coordinates into account, textured meshes can also be simplified. Results show that constraining edge collapses in the seams of a mesh give poor geometrical appearance when it is reduced to a few polygons. By allowing seam edge collapses and by using a pull-push algorithm to fill areas located outside the seam borders of the texture atlas, the appearance of the mesh is better preserved.