Collision Detection and Merging of Deformable B-Spline Surfaces in Virtual Reality Environment

This thesis presents a computational framework for representing, manipulating and merging rigid and deformable freeform objects in virtual reality (VR) environment. The core algorithms for collision detection, merging, and physics-based modeling used within this framework assume that all 3D deformable objects are B-spline surfaces. The interactive design tool can be represented as a B-spline surface, an implicit surface or a point, to allow the user a variety of rigid or deformable tools. The collision detection system utilizes the fact that the blending matrices used to discretize the B-spline surface are independent of the position of the control points and, therefore, can be pre-calculated. Complex B-spline surfaces can be generated by merging various B-spline surface patches using the B-spline surface patches merging algorithm presented in this thesis. Finally, the physics-based modeling system uses the mass-spring representation to determine the deformation and the reaction force values provided to the user. This helps to simulate realistic material behaviour of the model and assist the user in validating the design before performing extensive product detailing or finite element analysis using commercially available CAD software. The novelty of the proposed method stems from the pre-calculated blending matrices used to generate the points for graphical rendering, collision detection, merging of B-spline patches, and nodes for the mass spring system. This approach reduces computational time by avoiding the need to solve complex equations for blending functions of B-splines and perform the inversion of large matrices. This alternative approach to the mechanical concept design will also help to do away with the need to build prototypes for conceptualization and preliminary validation of the idea thereby reducing the time and cost of concept design phase and the wastage of resources

Towards Predictive Rendering in Virtual Reality

The strive for generating predictive images, i.e., images representing radiometrically correct renditions of reality, has been a longstanding problem in computer graphics. The exactness of such images is extremely important for Virtual Reality applications like Virtual Prototyping, where users need to make decisions impacting large investments based on the simulated images. Unfortunately, generation of predictive imagery is still an unsolved problem due to manifold reasons, especially if real-time restrictions apply. First, existing scenes used for rendering are not modeled accurately enough to create predictive images. Second, even with huge computational efforts existing rendering algorithms are not able to produce radiometrically correct images. Third, current display devices need to convert rendered images into some low-dimensional color space, which prohibits display of radiometrically correct images. Overcoming these limitations is the focus of current state-of-the-art research. This thesis also contributes to this task. First, it briefly introduces the necessary background and identifies the steps required for real-time predictive image generation. Then, existing techniques targeting these steps are presented and their limitations are pointed out. To solve some of the remaining problems, novel techniques are proposed. They cover various steps in the predictive image generation process, ranging from accurate scene modeling over efficient data representation to high-quality, real-time rendering. A special focus of this thesis lays on real-time generation of predictive images using bidirectional texture functions (BTFs), i.e., very accurate representations for spatially varying surface materials. The techniques proposed by this thesis enable efficient handling of BTFs by compressing the huge amount of data contained in this material representation, applying them to geometric surfaces using texture and BTF synthesis techniques, and rendering BTF covered objects in real-time. Further approaches proposed in this thesis target inclusion of real-time global illumination effects or more efficient rendering using novel level-of-detail representations for geometric objects. Finally, this thesis assesses the rendering quality achievable with BTF materials, indicating a significant increase in realism but also confirming the remainder of problems to be solved to achieve truly predictive image generation

Integrated modeling and analysis methodologies for architecture-level vehicle design.

In order to satisfy customer expectations, a ground vehicle must be designed to meet a broad range of performance requirements. A satisfactory vehicle design process implements a set of requirements reflecting necessary, but perhaps not sufficient conditions for assuring success in a highly competitive market. An optimal architecture-level vehicle design configuration is one of the most important of these requirements. A basic layout that is efficient and flexible permits significant reductions in the time needed to complete the product development cycle, with commensurate reductions in cost. Unfortunately, architecture-level design is the most abstract phase of the design process. The high-level concepts that characterize these designs do not lend themselves to traditional analyses normally used to characterize, assess, and optimize designs later in the development cycle. This research addresses the need for architecture-level design abstractions that can be used to support ground vehicle development. The work begins with a rigorous description of hierarchical function-based abstractions representing not the physical configuration of the elements of a vehicle, but their function within the design space. The hierarchical nature of the abstractions lends itself to object orientation - convenient for software implementation purposes - as well as description of components, assemblies, feature groupings based on non-structural interactions, and eventually, full vehicles. Unlike the traditional early-design abstractions, the completeness of our function-based hierarchical abstractions, including their interactions, allows their use as a starting point for the derivation of analysis models. The scope of the research in this dissertation includes development of meshing algorithms for abstract structural models, a rigid-body analysis engine, and a fatigue analysis module. It is expected that the results obtained in this study will move systematic design and analysis to the earliest phases of the vehicle development process, leading to more highly optimized architectures, and eventually, better ground vehicles. This work shows that architecture level abstractions in many cases are better suited for life cycle support than geometric CAD models. Finally, substituting modeling, simulation, and optimization for intuition and guesswork will do much to mitigate the risk inherent in large projects by minimizing the possibility of incorporating irrevocably compromised architecture elements into a vehicle design that no amount of detail-level reengineering can undo

Numerical Simulation of Frictional Contact Problems using Nagata Patches in Surface Smoothing

Tese de doutoramento em Engenharia Mecânica, na especialidade de Tecnologias de Produção, apresentada ao Departamento de Engenharia Mecânica da Faculdade de Ciências e Tecnologia da Universidade de CoimbraAll movements in the world involve contact and friction, from walking to car driving. The contact mechanics has application in many engineering problems, including the connection of structural members by bolts or screws, design of gears and bearings, sheet metal or bulk forming, rolling contact of car tyres, crash analysis of structures, as well as prosthetics in biomedical engineering. Due to the nonlinear and non-smooth nature of contact mechanics (contact area is not known a priori), such problems are currently solved using the finite element method within the field of computational contact mechanics. However, most of the commercial finite element software packages presently available are not entirely capable to solve frictional contact problems, demanding for efficient and robust methods. Therefore, the main objective of this study is the development of algorithms and numerical methods to apply in the numerical simulation of 3D frictional contact problems between bodies undergoing large deformations. The presented original developments are implemented in the in-house finite element code DD3IMP. The formulation of quasi-static frictional contact problems between bodies undergoing large deformations is firstly presented in the framework of the continuum mechanics, following the classical scheme used in solid mechanics. The kinematic description of the deformable bodies is presented adopting an updated Lagrangian formulation. The mechanical behaviour of the bodies is described by an elastoplastic constitutive law in conjunction with an associated flow rule, allowing to model a wide variety of contact problems arising in industrial applications. The frictional contact between the bodies is established by means of two conditions: the principle of impenetrability and the Coulomb’s friction law, both imposed to the contact interface. The augmented Lagrangian method is applied for solving the constrained minimization incremental problem resulting from the frictional contact inequalities, yielding a mixed functional involving both displacements and contact forces. The spatial discretization of the bodies is performed with isoparametric solid finite elements, while the discretization of the contact interface is carried out using the classical Node-to-Segment technique, preventing the slave nodes from penetrating on the master surface. The geometrical part of the contact elements, defined by a slave node and the closest master segment, is created by the contact search algorithm based on the selection of the closest point on the master surface, defined by the normal projection of the slave node. In the particular case of contact between a deformable body and a rigid obstacle, the master rigid surface can be described by smooth parameterizations typically used in CAD models. However, in the general case of contact between deformable bodies, the spatial discretization of both bodies with low order finite elements yields a piecewise bilinear representation of the master surface. This is the central source of problems in solving contact problems involving large sliding, since it leads to the discontinuity of the surface normal vector field. Thus, a surface smoothing procedure based on the Nagata patch interpolation is proposed to describe the master contact surfaces, which led to the development of the Node-to-Nagata contact element. The accuracy of the surface smoothing method using Nagata patches is evaluated by means of simple geometries. The nodal normal vectors required for the Nagata interpolation are evaluated from the CAD geometry in case of rigid master surfaces, while in case of deformable bodies they are approximated using the weighted average of the normal vectors of the neighbouring facets. The residual vectors and tangent matrices of the contact elements are derived coherently with the surface smoothing approach, allowing to obtain quadratic convergence rate in the generalized Newton method used for solving the nonlinear system of equations. The developed surface smoothing method and corresponding contact elements are validated through standard numerical examples with known analytical or semi-analytical solutions. More advanced frictional contact problems are studied, covering the contact of a deformable body with rigid obstacles and the contact between deformable bodies, including self-contact phenomena. The smoothing of the master surface improves the robustness of the computational methods and reduces strongly the non-physical oscillations in the contact force introduced by the traditional faceted description of the contact surface. The presented results are compared with numerical solutions obtained by other authors and experimental results, demonstrating the accuracy and performance of the implemented algorithms for highly nonlinear problems.Todos os movimentos no mundo envolvem contato e atrito, desde andar até conduzir um carro. A mecânica do contacto tem aplicação em muitos problemas de engenharia, incluindo a ligação de elementos estruturais com parafusos, projeto de engrenagens e rolamentos, estampagem ou forjamento, contato entre os pneus e a estrada, colisão de estruturas, bem como o desenvolvimento de próteses em engenharia biomédica. Devido à natureza não-linear e não-suave da mecânica do contato (área de contato desconhecida a priori), tais problemas são atualmente resolvidos usando o método dos elementos finitos no domínio da mecânica do contato computacional. No entanto, a maioria dos programas comerciais de elementos finitos atualmente disponíveis não é totalmente capaz de resolver problemas de contato com atrito, exigindo métodos numéricos mais eficientes e robustos. Portanto, o principal objetivo deste estudo é o desenvolvimento de algoritmos e métodos numéricos para aplicar na simulação numérica de problemas de contato com atrito entre corpos envolvendo grandes deformações. Os desenvolvimentos apresentados são implementados no programa de elementos finitos DD3IMP. A formulação quasi-estática de problemas de contato com atrito entre corpos deformáveis envolvendo grandes deformações é primeiramente apresentada no âmbito da mecânica dos meios contínuos, seguindo o método clássico usado em mecânica dos sólidos. A descrição cinemática dos corpos deformáveis é apresentada adotando uma formulação Lagrangeana reatualizada. O comportamento mecânico dos corpos é descrito por uma lei constitutiva elastoplástica em conjunto com uma lei de plasticidade associada, permitindo modelar uma grande variedade de problemas de contacto envolvidos em aplicações industriais. O contacto com atrito entre os corpos é definido por duas condições: o princípio da impenetrabilidade e a lei de atrito de Coulomb, ambas impostas na interface de contato. O método do Lagrangeano aumentado é aplicado na resolução do problema de minimização com restrições resultantes das condições de contato e atrito, produzindo uma formulação mista envolvendo deslocamentos e forças de contato. A discretização espacial dos corpos é realizada com elementos finitos sólidos isoparamétricos, enquanto a discretização da interface de contacto é realizado utilizando a técnica Node-to-Segment, impedindo os nós slave de penetrar na superfície master. A parte geométrica do elemento de contacto, definida por um nó slave e o segmento master mais próximo, é criada pelo algoritmo de deteção de contacto com base na seleção do ponto mais próximo na superfície master, obtido pela projeção normal do nó slave. No caso particular de contato entre um corpo deformável e um obstáculo rígido, a superfície rígida master pode ser descrita por parametrizações normalmente utilizadas em modelos CAD. No entanto, no caso geral de contato entre corpos deformáveis, a discretização espacial dos corpos com elementos finitos lineares origina uma representação da superfície master por facetas. Esta é a principal fonte de problemas na resolução de problemas de contato envolvendo grandes escorregamentos, uma vez que a distribuição dos vetor normais à superfície é descontínua. Assim, é proposto um método de suavização para descrever as superfícies de contacto master baseado na interpolação Nagata, que conduziu ao desenvolvimento do elemento de contacto Node-to-Nagata. A precisão do método de suavização das superfícies é avaliada através de geometrias simples. Os vetores normais nodais necessários para a interpolação Nagata são avaliados a partir da geometria CAD no caso de superfícies rígidas, enquanto no caso de corpos deformáveis são aproximados utilizando a média ponderada dos vetores normais das facetas vizinhas. Tanto os vetores de segundo membro como as matrizes residuais tangentes dos elementos de contacto são obtidas de forma coerente com o método de suavização da superfície, permitindo obter convergência quadrática no método de Newton generalizado, o qual é utilizado para resolver o sistema de equações não lineares. O método de suavização das superfícies e os elementos de contacto desenvolvidos são validados através de exemplos com soluções analíticas ou semi-analíticas conhecidas. Também são estudados outros problemas de contato mais complexos, incluindo o contato de um corpo deformável com obstáculos rígidos e o contato entre corpos deformáveis, contemplando fenómenos de auto-contato. A suavização da superfície master melhora a robustez dos métodos computacionais e reduz fortemente as oscilações na força de contato, associadas à descrição facetada da superfície de contato. Os resultados são comparados com soluções numéricas de outros autores e com resultados experimentais, demonstrando a precisão e o desempenho dos algoritmos implementados para problemas fortemente não-lineares.Fundação para a Ciência e Tecnologia - SFRH/BD/69140/201

Augmented interaction for custom-fit products by means of interaction devices at low costs

This Ph.D thesis refers to a research project that aims at developing an innovative platform to design lower limb prosthesis (both for below and above knee amputation) centered on the virtual model of the amputee and based on a computer-aided and knowledge-guided approach. The attention has been put on the modeling tool of the socket, which is the most critical component of the whole prosthesis. The main aim has been to redesign and develop a new prosthetic CAD tool, named SMA2 (Socket Modelling Assistant2) exploiting a low-cost IT technologies (e.g. hand/finger tracking devices) and making the user’s interaction as much as possible natural and similar to the hand-made manipulation. The research activities have been carried out in six phases as described in the following. First, limits and criticalities of the already available modeling tool (namely SMA) have been identified. To this end, the first version of SMA has been tested with Ortopedia Panini and the orthopedic research group of Salford University in Manchester with real case studies. Main criticalities were related to: (i) automatic reconstruction of the residuum geometric model starting from medical images, (ii) performance of virtual modeling tools to generate the socket shape, and (iii) interaction mainly based on traditional devices (e.g., mouse and keyboard). The second phase lead to the software reengineering of SMA according to the limits identified in the first phase. The software architecture has been re-designed adopting an object-oriented paradigm and its modularity permits to remove or add new features in a very simple way. The new modeling system, i.e. SMA2, has been totally implemented using open source Software Development Kit-SDK (e.g., Visualization ToolKit VTK, OpenCASCADE and Qt SDK) and based on low cost technology. It includes: • A new module to automatically reconstruct the 3D model of the residual limb from MRI images. In addition, a new procedure based on low-cost technology, such as Microsoft Kinect V2 sensor, has been identified to acquire the 3D external shape of the residuum. • An open source software library, named SimplyNURBS, for NURBS modeling and specifically used for the automatic reconstruction of the residuum 3D model from medical images. Even if, SimplyNURBS has been conceived for the prosthetic domain, it can be used to develop NURBS-based modeling tools for a range of applicative domains from health-care to clothing design. • A module for mesh editing to emulate the hand-made operations carried out by orthopedic technicians during traditional socket manufacturing process. In addition several virtual widgets have been implemented to make available virtual tools similar to the real ones used by the prosthetist, such as tape measure and pencil. • A Natural User Interface (NUI) to allow the interaction with the residuum and socket models using hand-tracking and haptic devices. • A module to generate the geometric models for additive manufacturing of the socket. The third phase concerned the study and design of augmented interaction with particular attention to the Natural User Interface (NUI) for the use of hand-tracking and haptic devices into SMA2. The NUI is based on the use of the Leap Motion device. A set of gestures, mainly iconic and suitable for the considered domain, has been identified taking into account ergonomic issues (e.g., arm posture) and ease of use. The modularity of SMA2 permits us to easily generate the software interface for each device for augmented interaction. To this end, a software module, named Tracking plug-in, has been developed to automatically generate the source code of software interfaces for managing the interaction with low cost hand-tracking devices (e.g., Leap Motion and Intel Gesture Camera) and replicate/emulate manual operations usually performed to design custom-fit products, such medical devices and garments. Regarding haptic rendering, two different devices have been considered, the Falcon Novint, and a haptic mouse developed in-house. In the fourth phase, additive manufacturing technologies have been investigated, in particular FDM one. 3D printing has been exploited in order to permit the creation of trial sockets in laboratory to evaluate the potentiality of SMA2. Furthermore, research activities have been done to study new ways to design the socket. An innovative way to build the socket has been developed based on multi-material 3D printing. Taking advantage of flexible material and multi-material print possibility, new 3D printers permit to create object with soft and hard parts. In this phase, issues about infill, materials and comfort have been faced and solved considering different compositions of materials to re-design the socket shape. In the fifth phase the implemented solution, integrated within the whole prosthesis design platform, has been tested with a transfemoral amputee. Following activities have been performed: • 3D acquisition of the residuum using MRI and commercial 3D scanning systems (low cost and professional). • Creation of the residual limb and socket geometry. • Multi-material 3D printing of the socket using FDM technology. • Gait analysis of the amputee wearing the socket using a markerless motion capture system. • Acquisition of contact pressure between residual limb and a trial socket by means of Teskan’s F-Socket System. Acquired data have been combined inside an ad-hoc developed application, which permits to simultaneously visualize pressure data on the 3D model of the residual lower limb and the animation of gait analysis. Results and feedback have been possible thanks to this application that permits to find correlation between several phases of the gait cycle and the pressure data at the same time. Reached results have been considered very interested and several tests have been planned in order to try the system in orthopedic laboratories in real cases. The reached results have been very useful to evaluate the quality of SMA2 as a future instruments that can be exploited for orthopedic technicians in order to create real socket for patients. The solution has the potentiality to begin a potential commercial product, which will be able to substitute the classic procedure for socket design. The sixth phase concerned the evolution of SMA2 as a Mixed Reality environment, named Virtual Orthopedic LABoratory (VOLAB). The proposed solution is based on low cost devices and open source libraries (e.g., OpenCL and VTK). In particular, the hardware architecture consists of three Microsoft Kinect v2 for human body tracking, the head mounted display Oculus Rift SDK 2 for 3D environment rendering, and the Leap Motion device for hand/fingers tracking. The software development has been based on the modular structure of SMA2 and dedicated modules have been developed to guarantee the communication among the devices. At present, two preliminary tests have been carried out: the first to verify real-time performance of the virtual environment and the second one to verify the augmented interaction with hands using SMA2 modeling tools. Achieved results are very promising but, highlighted some limitations of this first version of VOLAB and improvements are necessary. For example, the quality of the 3D real world reconstruction, especially as far as concern the residual limb, could be improved by using two HD-RGB cameras together the Oculus Rift. To conclude, the obtained results have been evaluated very interested and encouraging from the technical staff of orthopedic laboratory. SMA2 will made possible an important change of the process to design the socket of lower limb prosthesis, from a traditional hand-made manufacturing process to a totally virtual knowledge-guided process. The proposed solutions and results reached so far can be exploited in other industrial sectors where the final product heavily depends on the human body morphology. In fact, preliminary software development has been done to create a virtual environment for clothing design by starting from the basic modules exploited in SMA2

Deformation Tracking in Depth and Color Video: An Analysis by Synthesis Approach

The tracking of deforming objects and the reconstruction of deformation in image sequences is one of the current research areas in computer vision. In contrast to rigid scenes, which can be analyzed and reconstructed very well, general deformations come with an infinite number of sub-movements and ways to parametrize them, which makes it very difficult to formulate discrete tracking goals. In contrast to the classic reconstructions based on color data alone, the combination of depth and color video provides tracking algorithms with a data foundation with less room for ambiguities, but also requires new algorithmic approaches to handle different entities and to exploit the available data. This thesis discusses an Analysis by Synthesis (AbS) scheme as an approach to the deformation tracking problem, a method that differs in many key aspects from common reconstruction schemes. It is demonstrated that AbS based deformation reconstruction can reconstruct complex deformations, deal with occlusions and self-occlusions, and can also be used for real-time tracking

Digital Alchemy: Matter and Metamorphosis in Contemporary Digital Animation and Interface Design

The recent proliferation of special effects in Hollywood film has ushered in an era of digital transformation. Among scholars, digital technology is hailed as a revolutionary moment in the history of communication and representation. Nevertheless, media scholars and cultural historians have difficulty finding a language adequate to theorizing digital artifacts because they are not just texts to be deciphered. Rather, digital media artifacts also invite critiques about the status of reality because they resurrect ancient problems of embodiment and transcendence.In contrast to scholarly approaches to digital technology, computer engineers, interface designers, and special effects producers have invented a robust set of terms and phrases to describe the practice of digital animation. In order to address this disconnect between producers of new media and scholars of new media, I argue that the process of digital animation borrows extensively from a set of preexisting terms describing materiality that were prominent for centuries prior to the scientific revolution. Specifically, digital animators and interface designers make use of the ancient science, art, and technological craft of alchemy. Both alchemy and digital animation share several fundamental elements: both boast the power of being able to transform one material, substance, or thing into a different material, substance, or thing. Both seek to transcend the body and materiality but in the process, find that this elusive goal (realism and gold) is forever receding onto the horizon.The introduction begins with a literature review of the field of digital media studies. It identifies a gap in the field concerning disparate arguments about new media technology. On the one hand, scholars argue that new technologies like cyberspace and digital technology enable radical new forms of engagement with media on individual, social, and economic levels. At the same time that media scholars assert that our current epoch is marked by a historical rupture, many other researchers claim that new media are increasingly characterized by ancient metaphysical problems like embodiment and transcendence. In subsequent chapters I investigate this disparity

Methods for 3D Geometry Processing in the Cultural Heritage Domain

This thesis presents methods for 3D geometry processing under the aspects of cultural heritage applications. After a short overview over the relevant basics in 3D geometry processing, the present thesis investigates the digital acquisition of 3D models. A particular challenge in this context are on the one hand difficult surface or material properties of the model to be captured. On the other hand, the fully automatic reconstruction of models even with suitable surface properties that can be captured with Laser range scanners is not yet completely solved. This thesis presents two approaches to tackle these challenges. One exploits a thorough capture of the object’s appearance and a coarse reconstruction for a concise and realistic object representation even for objects with problematic surface properties like reflectivity and transparency. The other method concentrates on digitisation via Laser-range scanners and exploits 2D colour images that are typically recorded with the range images for a fully automatic registration technique. After reconstruction, the captured models are often still incomplete, exhibit holes and/or regions of insufficient sampling. In addition to that, holes are often deliberately introduced into a registered model to remove some undesired or defective surface part. In order to produce a visually appealing model, for instance for visualisation purposes, for prototype or replica production, these holes have to be detected and filled. Although completion is a well-established research field in 2D image processing and many approaches do exist for image completion, surface completion in 3D is a fairly new field of research. This thesis presents a hierarchical completion approach that employs and extends successful exemplar-based 2D image processing approaches to 3D and fills in detail-equipped surface patches into missing surface regions. In order to identify and construct suitable surface patches, selfsimilarity and coherence properties of the surface context of the hole are exploited. In addition to the reconstruction and repair, the present thesis also investigates methods for a modification of captured models via interactive modelling. In this context, modelling is regarded as a creative process, for instance for animation purposes. On the other hand, it is also demonstrated how this creative process can be used to introduce human expertise into the otherwise automatic completion process. This way, reconstructions are feasible even of objects where already the data source, the object itself, is incomplete due to corrosion, demolition, or decay.Methoden zur 3D-Geometrieverarbeitung im Kulturerbesektor In dieser Arbeit werden Methoden zur Bearbeitung von digitaler 3D-Geometrie unter besonderer Berücksichtigung des Anwendungsbereichs im Kulturerbesektor vorgestellt. Nach einem kurzen Überblick über die relevanten Grundlagen der dreidimensionalen Geometriebehandlung wird zunächst die digitale Akquise von dreidimensionalen Objekten untersucht. Eine besondere Herausforderung stellen bei der Erfassung einerseits ungünstige Oberflächen- oder Materialeigenschaften der Objekte dar (wie z.B. Reflexivität oder Transparenz), andererseits ist auch die vollautomatische Rekonstruktion von solchen Modellen, die sich verhältnismäßig problemlos mit Laser-Range Scannern erfassen lassen, immer noch nicht vollständig gelöst. Daher bilden zwei neuartige Verfahren, die diesen Herausforderungen begegnen, den Anfang. Auch nach der Registrierung sind die erfassten Datensätze in vielen Fällen unvollständig, weisen Löcher oder nicht ausreichend abgetastete Regionen auf. Darüber hinaus werden in vielen Anwendungen auch, z.B. durch Entfernen unerwünschter Oberflächenregionen, Löcher gewollt hinzugefügt. Für eine optisch ansprechende Rekonstruktion, vor allem zu Visualisierungszwecken, im Bildungs- oder Unterhaltungssektor oder zur Prototyp- und Replik-Erzeugung müssen diese Löcher zunächst automatisch detektiert und anschließend geschlossen werden. Obwohl dies im zweidimensionalen Fall der Bildbearbeitung bereits ein gut untersuchtes Forschungsfeld darstellt und vielfältige Ansätze zur automatischen Bildvervollständigung existieren, ist die Lage im dreidimensionalen Fall anders, und die Übertragung von zweidimensionalen Ansätzen in den 3D stellt vielfach eine große Herausforderung dar, die bislang keine zufriedenstellenden Lösungen erlaubt hat. Nichtsdestoweniger wird in dieser Arbeit ein hierarchisches Verfahren vorgestellt, das beispielbasierte Konzepte aus dem 2D aufgreift und Löcher in Oberflächen im 3D unter Ausnutzung von Selbstähnlichkeiten und Kohärenzeigenschaften des Oberflächenkontextes schließt. Um plausible Oberflächen zu erzeugen werden die Löcher dabei nicht nur glatt gefüllt, sondern auch feinere Details aus dem Kontext rekonstruiert. Abschließend untersucht die vorliegende Arbeit noch die Modifikation der vervollständigten Objekte durch Freiformmodellierung. Dies wird dabei zum einen als kreativer Prozess z.B. zu Animationszwecken betrachtet. Zum anderen wird aber auch untersucht, wie dieser kreative Prozess benutzt werden kann, um etwaig vorhandenes Expertenwissen in die ansonsten automatische Vervollständigung mit einfließen zu lassen. Auf diese Weise werden auch Rekonstruktionen ermöglicht von Objekten, bei denen schon die Datenquelle, also das Objekt selbst z.B. durch Korrosion oder mutwillige Zerstörung unvollständig ist

Geometric Surface Processing and Virtual Modeling

In this work we focus on two main topics "Geometric Surface Processing" and "Virtual Modeling". The inspiration and coordination for most of the research work contained in the thesis has been driven by the project New Interactive and Innovative Technologies for CAD (NIIT4CAD), funded by the European Eurostars Programme. NIIT4CAD has the ambitious aim of overcoming the limitations of the traditional approach to surface modeling of current 3D CAD systems by introducing new methodologies and technologies based on subdivision surfaces in a new virtual modeling framework. These innovations will allow designers and engineers to transform quickly and intuitively an idea of shape in a high-quality geometrical model suited for engineering and manufacturing purposes. One of the objective of the thesis is indeed the reconstruction and modeling of surfaces, representing arbitrary topology objects, starting from 3D irregular curve networks acquired through an ad-hoc smart-pen device. The thesis is organized in two main parts: "Geometric Surface Processing" and "Virtual Modeling". During the development of the geometric pipeline in our Virtual Modeling system, we faced many challenges that captured our interest and opened new areas of research and experimentation. In the first part, we present these theories and some applications to Geometric Surface Processing. This allowed us to better formalize and give a broader understanding on some of the techniques used in our latest advancements on virtual modeling and surface reconstruction. The research on both topics led to important results that have been published and presented in articles and conferences of international relevance