111 research outputs found

    Surface Deformation Potentials on Meshes for Computer Graphics and Visualization

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    Shape deformation models have been used in computer graphics primarily to describe the dynamics of physical deformations like cloth draping, collisions of elastic bodies, fracture, or animation of hair. Less frequent is their application to problems not directly related to a physical process. In this thesis we apply deformations to three problems in computer graphics that do not correspond to physical deformations. To this end, we generalize the physical model by modifying the energy potential. Originally, the energy potential amounts to the physical work needed to deform a body from its rest state into a given configuration and relates material strain to internal restoring forces that act to restore the original shape. For each of the three problems considered, this potential is adapted to reflect an application specific notion of shape. Under the influence of further constraints, our generalized deformation results in shapes that balance preservation of certain shape properties and application specific objectives similar to physical equilibrium states. The applications discussed in this thesis are surface parameterization, interactive shape editing and automatic design of panorama maps. For surface parameterization, we interpret parameterizations over a planar domain as deformations from a flat initial configuration onto a given surface. In this setting, we review existing parameterization methods by analyzing properties of their potential functions and derive potentials accounting for distortion of geometric properties. Interactive shape editing allows an untrained user to modify complex surfaces, be simply grabbing and moving parts of interest. A deformation model interactively extrapolates the transformation from those parts to the rest of the surface. This thesis proposes a differential shape representation for triangle meshes leading to a potential that can be optimized interactively with a simple, tailored algorithm. Although the potential is not physically accurate, it results in intuitive deformation behavior and can be parameterized to account for different material properties. Panorama maps are blends between landscape illustrations and geographic maps that are traditionally painted by an artist to convey geographic surveyknowledge on public places like ski resorts or national parks. While panorama maps are not drawn to scale, the shown landscape remains recognizable and the observer can easily recover details necessary for self location and orientation. At the same time, important features as trails or ski slopes appear not occluded and well visible. This thesis proposes the first automatic panorama generation method. Its basis is again a surface deformation, that establishes the necessary compromise between shape preservation and feature visibility.Potentiale zur Flächendeformation auf Dreiecksnetzen für Anwendungen in der Computergrafik und Visualisierung Deformationsmodelle werden in der Computergrafik bislang hauptsächlich eingesetzt, um die Dynamik physikalischer Deformationsprozesse zu modellieren. Gängige Beispiele sind Bekleidungssimulationen, Kollisionen elastischer Körper oder Animation von Haaren und Frisuren. Deutlich seltener ist ihre Anwendung auf Probleme, die nicht direkt physikalischen Prozessen entsprechen. In der vorliegenden Arbeit werden Deformationsmodelle auf drei Probleme der Computergrafik angewandt, die nicht unmittelbar einem physikalischen Deformationsprozess entsprechen. Zu diesem Zweck wird das physikalische Modell durch eine passende Änderung der potentiellen Energie verallgemeinert. Die potentielle Energie entspricht normalerweise der physikalischen Arbeit, die aufgewendet werden muss, um einen Körper aus dem Ruhezustand in eine bestimmte Konfiguration zu verformen. Darüber hinaus setzt sie die aktuelle Verformung in Beziehung zu internen Spannungskräften, die wirken um die ursprüngliche Form wiederherzustellen. In dieser Arbeit passen wir für jedes der drei betrachteten Problemfelder die potentielle Energie jeweils so an, dass sie eine anwendungsspezifische Definition von Form widerspiegelt. Unter dem Einfluss weiterer Randbedingungen führt die so verallgemeinerte Deformation zu einer Fläche, die eine Balance zwischen der Erhaltung gewisser Formeigenschaften und Zielvorgaben der Anwendung findet. Diese Balance entspricht dem Equilibrium einer physikalischen Deformation. Die drei in dieser Arbeit diskutierten Anwendungen sind Oberflächenparameterisierung, interaktives Bearbeiten von Flächen und das vollautomatische Erzeugen von Panoramakarten im Stile von Heinrich Berann. Zur Oberflächenparameterisierung interpretieren wir Parameterisierungen über einem flachen Parametergebiet als Deformationen, die ein ursprünglich ebenes Flächenstück in eine gegebene Oberfläche verformen. Innerhalb dieses Szenarios vergleichen wir dann existierende Methoden zur planaren Parameterisierung, indem wir die resultierenden potentiellen Energien analysieren, und leiten weitere Potentiale her, die die Störung geometrischer Eigenschaften wie Fläche und Winkel erfassen. Verfahren zur interaktiven Flächenbearbeitung ermöglichen schnelle und intuitive Änderungen an einer komplexen Oberfläche. Dazu wählt der Benutzer Teile der Fläche und bewegt diese durch den Raum. Ein Deformationsmodell extrapoliert interaktiv die Transformation der gewählten Teile auf die restliche Fläche. Diese Arbeit stellt eine neue differentielle Flächenrepräsentation für diskrete Flächen vor, die zu einem einfach und interaktiv zu optimierendem Potential führt. Obwohl das vorgeschlagene Potential nicht physikalisch korrekt ist, sind die resultierenden Deformationen intuitiv. Mittels eines Parameters lassen sich außerdem bestimmte Materialeigenschaften einstellen. Panoramakarten im Stile von Heinrich Berann sind eine Verschmelzung von Landschaftsillustration und geographischer Karte. Traditionell werden sie so von Hand gezeichnet, dass bestimmt Merkmale wie beispielsweise Skipisten oder Wanderwege in einem Gebiet unverdeckt und gut sichtbar bleiben, was große Kunstfertigkeit verlangt. Obwohl diese Art der Darstellung nicht maßstabsgetreu ist, sind Abweichungen auf den ersten Blick meistens nicht zu erkennen. Dadurch kann der Betrachter markante Details schnell wiederfinden und sich so innerhalb des Gebietes orientieren. Diese Arbeit stellt das erste, vollautomatische Verfahren zur Erzeugung von Panoramakarten vor. Grundlage ist wiederum eine verallgemeinerte Oberflächendeformation, die sowohl auf Formerhaltung als auch auf die Sichtbarkeit vorgegebener geographischer Merkmale abzielt

    Quad Meshing

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    Triangle meshes have been nearly ubiquitous in computer graphics, and a large body of data structures and geometry processing algorithms based on them has been developed in the literature. At the same time, quadrilateral meshes, especially semi-regular ones, have advantages for many applications, and significant progress was made in quadrilateral mesh generation and processing during the last several years. In this State of the Art Report, we discuss the advantages and problems of techniques operating on quadrilateral meshes, including surface analysis and mesh quality, simplification, adaptive refinement, alignment with features, parametrization, and remeshing

    3D to 2D surface mesh parameterisation for the purposes of unstructured transmission line modelling method simulations

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    Small scale fabrication processes have led to the advent of very thin flexible devices such as RFID tags, flexible PCBs and smart clothing. In a geometrical sense, these present themselves as curved two dimensional surfaces embedded in a three dimensional domain. When simulating electromagnetic behaviour on these surfaces at low frequencies, a full 3D field model is not always necessary. Using 3D algorithms to solve these problems can result in a large portion of the computer memory and runtime being used to mesh and simulate areas of the domain that present little electromagnetic activity. The theme of this thesis is concerned with the improvement of the runtime and memory consumption of electromagnetic simulations of these surfaces. The main contributions of this work are presented as an investigation into the feasibility of applying a 2D Unstructured Transmission Line Modelling method (UTLM) simulation to open, curved surfaces embedded in 3D space, by providing a one-to-one mapping of the geometry to a 2D flat plane. First, an investigation into the various methods of how a computer represents unstructured meshes in its memory is presented, and how this affects the runtime of the simulation. The underlying mesh data structures used to represent the geometrical problem space can have a huge impact on the efficiency and memory consumption of the simulation. This investigation served to demonstrate that it is not just simply the optimisation of the simulation algorithms that facilitate improvements to the runtime and memory consumption of a simulation. How a computer understands the connectivity of the mesh can have far greater impacts to the computational resources available. The concepts of surface parameterisation are then introduced; a process of mapping curved surfaces embedded in a three dimensional domain to a flat two dimensional plane. By providing a one-to-one mapping of the geometry from the 3D domain to the 2D flat plane, a low frequency 2D unstructured TLM simulation can be applied, negating the need for 3D algorithms. Because this mapping is one-to-one, the results of the simulation can then be mapped back to 3D space for visualisation. Parameterisations will almost always introduce distortion to angle and area, and minimising this distortion is paramount to maintaining an accurate simulation. Test cases were used to measure the extent of this distortion, and the investigation concluded that Angle Based Flattening (ABF) and Least Squares Conformal Mapping (LSCM) methods resulted in the best quality parameterisations. Simulations were then conducted on these test cases as a demonstration of how UTLM can be performed on 2D surfaces, embedded in a 3D domain

    3D Shape Modeling Using High Level Descriptors

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    3D to 2D surface mesh parameterisation for the purposes of unstructured transmission line modelling method simulations

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    Small scale fabrication processes have led to the advent of very thin flexible devices such as RFID tags, flexible PCBs and smart clothing. In a geometrical sense, these present themselves as curved two dimensional surfaces embedded in a three dimensional domain. When simulating electromagnetic behaviour on these surfaces at low frequencies, a full 3D field model is not always necessary. Using 3D algorithms to solve these problems can result in a large portion of the computer memory and runtime being used to mesh and simulate areas of the domain that present little electromagnetic activity. The theme of this thesis is concerned with the improvement of the runtime and memory consumption of electromagnetic simulations of these surfaces. The main contributions of this work are presented as an investigation into the feasibility of applying a 2D Unstructured Transmission Line Modelling method (UTLM) simulation to open, curved surfaces embedded in 3D space, by providing a one-to-one mapping of the geometry to a 2D flat plane. First, an investigation into the various methods of how a computer represents unstructured meshes in its memory is presented, and how this affects the runtime of the simulation. The underlying mesh data structures used to represent the geometrical problem space can have a huge impact on the efficiency and memory consumption of the simulation. This investigation served to demonstrate that it is not just simply the optimisation of the simulation algorithms that facilitate improvements to the runtime and memory consumption of a simulation. How a computer understands the connectivity of the mesh can have far greater impacts to the computational resources available. The concepts of surface parameterisation are then introduced; a process of mapping curved surfaces embedded in a three dimensional domain to a flat two dimensional plane. By providing a one-to-one mapping of the geometry from the 3D domain to the 2D flat plane, a low frequency 2D unstructured TLM simulation can be applied, negating the need for 3D algorithms. Because this mapping is one-to-one, the results of the simulation can then be mapped back to 3D space for visualisation. Parameterisations will almost always introduce distortion to angle and area, and minimising this distortion is paramount to maintaining an accurate simulation. Test cases were used to measure the extent of this distortion, and the investigation concluded that Angle Based Flattening (ABF) and Least Squares Conformal Mapping (LSCM) methods resulted in the best quality parameterisations. Simulations were then conducted on these test cases as a demonstration of how UTLM can be performed on 2D surfaces, embedded in a 3D domain

    Appearance Preserving Rendering of Out-of-Core Polygon and NURBS Models

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    In Computer Aided Design (CAD) trimmed NURBS surfaces are widely used due to their flexibility. For rendering and simulation however, piecewise linear representations of these objects are required. A relatively new field in CAD is the analysis of long-term strain tests. After such a test the object is scanned with a 3d laser scanner for further processing on a PC. In all these areas of CAD the number of primitives as well as their complexity has grown constantly in the recent years. This growth is exceeding the increase of processor speed and memory size by far and posing the need for fast out-of-core algorithms. This thesis describes a processing pipeline from the input data in the form of triangular or trimmed NURBS models until the interactive rendering of these models at high visual quality. After discussing the motivation for this work and introducing basic concepts on complex polygon and NURBS models, the second part of this thesis starts with a review of existing simplification and tessellation algorithms. Additionally, an improved stitching algorithm to generate a consistent model after tessellation of a trimmed NURBS model is presented. Since surfaces need to be modified interactively during the design phase, a novel trimmed NURBS rendering algorithm is presented. This algorithm removes the bottleneck of generating and transmitting a new tessellation to the graphics card after each modification of a surface by evaluating and trimming the surface on the GPU. To achieve high visual quality, the appearance of a surface can be preserved using texture mapping. Therefore, a texture mapping algorithm for trimmed NURBS surfaces is presented. To reduce the memory requirements for the textures, the algorithm is modified to generate compressed normal maps to preserve the shading of the original surface. Since texturing is only possible, when a parametric mapping of the surface - requiring additional memory - is available, a new simplification and tessellation error measure is introduced that preserves the appearance of the original surface by controlling the deviation of normal vectors. The preservation of normals and possibly other surface attributes allows interactive visualization for quality control applications (e.g. isophotes and reflection lines). In the last part out-of-core techniques for processing and rendering of gigabyte-sized polygonal and trimmed NURBS models are presented. Then the modifications necessary to support streaming of simplified geometry from a central server are discussed and finally and LOD selection algorithm to support interactive rendering of hard and soft shadows is described

    Proceedings of the First International Workshop on Mathematical Foundations of Computational Anatomy (MFCA'06) - Geometrical and Statistical Methods for Modelling Biological Shape Variability

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    International audienceNon-linear registration and shape analysis are well developed research topic in the medical image analysis community. There is nowadays a growing number of methods that can faithfully deal with the underlying biomechanical behaviour of intra-subject shape deformations. However, it is more difficult to relate the anatomical shape of different subjects. The goal of computational anatomy is to analyse and to statistically model this specific type of geometrical information. In the absence of any justified physical model, a natural attitude is to explore very general mathematical methods, for instance diffeomorphisms. However, working with such infinite dimensional space raises some deep computational and mathematical problems. In particular, one of the key problem is to do statistics. Likewise, modelling the variability of surfaces leads to rely on shape spaces that are much more complex than for curves. To cope with these, different methodological and computational frameworks have been proposed. The goal of the workshop was to foster interactions between researchers investigating the combination of geometry and statistics for modelling biological shape variability from image and surfaces. A special emphasis was put on theoretical developments, applications and results being welcomed as illustrations. Contributions were solicited in the following areas: * Riemannian and group theoretical methods on non-linear transformation spaces * Advanced statistics on deformations and shapes * Metrics for computational anatomy * Geometry and statistics of surfaces 26 submissions of very high quality were recieved and were reviewed by two members of the programm committee. 12 papers were finally selected for oral presentations and 8 for poster presentations. 16 of these papers are published in these proceedings, and 4 papers are published in the proceedings of MICCAI'06 (for copyright reasons, only extended abstracts are provided here)

    Surface Remeshing and Applications

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    Due to the focus of popular graphic accelerators, triangle meshes remain the primary representation for 3D surfaces. They are the simplest form of interpolation between surface samples, which may have been acquired with a laser scanner, computed from a 3D scalar field resolved on a regular grid, or identified on slices of medical data. Typical methods for the generation of triangle meshes from raw data attempt to lose as less information as possible, so that the resulting surface models can be used in the widest range of scenarios. When such a general-purpose model has to be used in a particular application context, however, a pre-processing is often worth to be considered. In some cases, it is convenient to slightly modify the geometry and/or the connectivity of the mesh, so that further processing can take place more easily. Other applications may require the mesh to have a pre-defined structure, which is often different from the one of the original general-purpose mesh. The central focus of this thesis is the automatic remeshing of highly detailed surface triangulations. Besides a thorough discussion of state-of-the-art applications such as real-time rendering and simulation, new approaches are proposed which use remeshing for topological analysis, flexible mesh generation and 3D compression. Furthermore, innovative methods are introduced to post-process polygonal models in order to recover information which was lost, or hidden, by a prior remeshing process. Besides the technical contributions, this thesis aims at showing that surface remeshing is much more useful than it may seem at a first sight, as it represents a nearly fundamental step for making several applications feasible in practice
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