Subdivision Surface based One-Piece Representation

Subdivision surfaces are capable of modeling and representing complex shapes of arbi-trary topology. However, methods on how to build the control mesh of a complex surfaceare not studied much. Currently, most meshes of complicated objects come from trian-gulation and simplification of raster scanned data points, like the Stanford 3D ScanningRepository. This approach is costly and leads to very dense meshes.Subdivision surface based one-piece representation means to represent the final objectin a design process with only one subdivision surface, no matter how complicated theobject\u27s topology or shape. Hence the number of parts in the final representation isalways one.In this dissertation we present necessary mathematical theories and geometric algo-rithms to support subdivision surface based one-piece representation. First, an explicitparametrization method is presented for exact evaluation of Catmull-Clark subdivisionsurfaces. Based on it, two approaches are proposed for constructing the one-piece rep-resentation of a given object with arbitrary topology. One approach is to construct theone-piece representation by using the interpolation technique. Interpolation is a naturalway to build models, but the fairness of the interpolating surface is a big concern inprevious methods. With similarity based interpolation technique, we can obtain bet-ter modeling results with less undesired artifacts and undulations. Another approachis through performing Boolean operations. Up to this point, accurate Boolean oper-ations over subdivision surfaces are not approached yet in the literature. We presenta robust and error controllable Boolean operation method which results in a one-piecerepresentation. Because one-piece representations resulting from the above two methodsare usually dense, error controllable simplification of one-piece representations is needed.Two methods are presented for this purpose: adaptive tessellation and multiresolutionanalysis. Both methods can significantly reduce the complexity of a one-piece represen-tation and while having accurate error estimation.A system that performs subdivision surface based one-piece representation was im-plemented and a lot of examples have been tested. All the examples show that our ap-proaches can obtain very good subdivision based one-piece representation results. Eventhough our methods are based on Catmull-Clark subdivision scheme, we believe they canbe adapted to other subdivision schemes as well with small modifications

3D RECONSTRUCTION USING MULTI-VIEW IMAGING SYSTEM

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

Continuous Medial Models in Two-Sample Statistics of Shape

In questions of statistical shape analysis, the foremost is how such shapes should be represented. The number of parameters required for a given accuracy and the types of deformation they can express directly influence the quality and type of statistical inferences one can make. One example is a medial model, which represents a solid object using a skeleton of a lower dimension and naturally expresses intuitive changes such as "bending", "twisting", and "thickening". In this dissertation I develop a new three-dimensional medial model that allows continuous interpolation of the medial surface and provides a map back and forth between the boundary and its medial axis. It is the first such model to support branching, allowing the representation of a much wider class of objects than previously possible using continuous medial methods. A measure defined on the medial surface then allows one to write integrals over the boundary and the object interior in medial coordinates, enabling the expression of important object properties in an object-relative coordinate system. I show how these properties can be used to optimize correspondence during model construction. This improved correspondence reduces variability due to how the model is parameterized which could potentially mask a true shape change effect. Finally, I develop a method for performing global and local hypothesis testing between two groups of shapes. This method is capable of handling the nonlinear spaces the shapes live in and is well defined even in the high-dimension, low-sample size case. It naturally reduces to several well-known statistical tests in the linear and univariate cases

Arbitrary topology meshes in geometric design and vector graphics

Meshes are a powerful means to represent objects and shapes both in 2D and 3D, but the techniques based on meshes can only be used in certain regular settings and restrict their usage. Meshes with an arbitrary topology have many interesting applications in geometric design and (vector) graphics, and can give designers more freedom in designing complex objects. In the first part of the thesis we look at how these meshes can be used in computer aided design to represent objects that consist of multiple regular meshes that are constructed together. Then we extend the B-spline surface technique from the regular setting to work on extraordinary regions in meshes so that multisided B-spline patches are created. In addition, we show how to render multisided objects efficiently, through using the GPU and tessellation. In the second part of the thesis we look at how the gradient mesh vector graphics primitives can be combined with procedural noise functions to create expressive but sparsely defined vector graphic images. We also look at how the gradient mesh can be extended to arbitrary topology variants. Here, we compare existing work with two new formulations of a polygonal gradient mesh. Finally we show how we can turn any image into a vector graphics image in an efficient manner. This vectorisation process automatically extracts important image features and constructs a mesh around it. This automatic pipeline is very efficient and even facilitates interactive image vectorisation

Blending techniques in Curve and Surface constructions

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Conceptual free-form styling in virtual environments

This dissertation introduces the tools for designing complete models from scratch directly in a head-tracked, table-like virtual work environment. The models consist of free-form surfaces, and are constructed by drawing a network of curves directly in space. This is accomplished by using a tracked pen-like input device. Interactive deformation tools for curves and surfaces are proposed and are based on variational methods. By aligning the model with the left hand, editing is made possible with the right hand, corresponding to a natural distribution of tasks using both hands. Furthermore, in the emerging field of 3D interaction in virtual environments, particularly with regard to system control, this work uses novel methods to integrate system control tasks, such as selecting tools, and workflow of shape design. The aim of this work is to propose more suitable user interfaces to computersupported conceptual shape design applications. This would be beneficial since it is a field that lacks adequate support from standard desktop systems.Diese Dissertation beschreibtWerkzeuge zum Entwurf kompletter virtueller Modelle von Grund auf. Dies geschieht direkt in einer tischartigen, virtuellen Arbeitsumge-bung mit Hilfe von Tracking der Hände und der Kopfposition. Die Modelle sind aus Freiformlächen aufgebaut und werden als Netz von Kurven mit Hilfe eines getrack-ten, stiftartigen Eingabegerätes direkt im Raum gezeichnet. Es werden interaktive Deformationswerkzeuge für Kurven und Flächen vorgestellt, die auf Methoden des Variational Modeling basieren. Durch das Ausrichten des Modells mit der linken Hand wird das Editieren mit der rechten Hand erleichtert. Dies entspricht einer natürlichen Aufteilung von Aufgaben auf beide Hände. Zusätzlich stellt diese Arbeit neue Techniken für die 3D-Interaktion in virtuellen Umgebungen, insbesondere im Bereich Anwendungskontrolle, vor, die die Aufgabe der Werkzeugauswahl in den Arbeitsablauf der Formgestaltung integrieren. Das Ziel dieser Arbeit ist es, besser geeignete Schnittstellen für den computer-unterstützten, konzeptionellen Formentwurf zur Verfügung zu stellen; ein Gebiet, für das Standard-Desktop-Systeme wenig geeignete Unterstützung bieten

Conceptual free-form styling in virtual environments

This dissertation introduces the tools for designing complete models from scratch directly in a head-tracked, table-like virtual work environment. The models consist of free-form surfaces, and are constructed by drawing a network of curves directly in space. This is accomplished by using a tracked pen-like input device. Interactive deformation tools for curves and surfaces are proposed and are based on variational methods. By aligning the model with the left hand, editing is made possible with the right hand, corresponding to a natural distribution of tasks using both hands. Furthermore, in the emerging field of 3D interaction in virtual environments, particularly with regard to system control, this work uses novel methods to integrate system control tasks, such as selecting tools, and workflow of shape design. The aim of this work is to propose more suitable user interfaces to computersupported conceptual shape design applications. This would be beneficial since it is a field that lacks adequate support from standard desktop systems.Diese Dissertation beschreibtWerkzeuge zum Entwurf kompletter virtueller Modelle von Grund auf. Dies geschieht direkt in einer tischartigen, virtuellen Arbeitsumge-bung mit Hilfe von Tracking der Hände und der Kopfposition. Die Modelle sind aus Freiformlächen aufgebaut und werden als Netz von Kurven mit Hilfe eines getrack-ten, stiftartigen Eingabegerätes direkt im Raum gezeichnet. Es werden interaktive Deformationswerkzeuge für Kurven und Flächen vorgestellt, die auf Methoden des Variational Modeling basieren. Durch das Ausrichten des Modells mit der linken Hand wird das Editieren mit der rechten Hand erleichtert. Dies entspricht einer natürlichen Aufteilung von Aufgaben auf beide Hände. Zusätzlich stellt diese Arbeit neue Techniken für die 3D-Interaktion in virtuellen Umgebungen, insbesondere im Bereich Anwendungskontrolle, vor, die die Aufgabe der Werkzeugauswahl in den Arbeitsablauf der Formgestaltung integrieren. Das Ziel dieser Arbeit ist es, besser geeignete Schnittstellen für den computer-unterstützten, konzeptionellen Formentwurf zur Verfügung zu stellen; ein Gebiet, für das Standard-Desktop-Systeme wenig geeignete Unterstützung bieten

Towards a High Quality Real-Time Graphics Pipeline

Modern graphics hardware pipelines create photorealistic images with high geometric complexity in real time. The quality is constantly improving and advanced techniques from feature film visual effects, such as high dynamic range images and support for higher-order surface primitives, have recently been adopted. Visual effect techniques have large computational costs and significant memory bandwidth usage. In this thesis, we identify three problem areas and propose new algorithms that increase the performance of a set of computer graphics techniques. Our main focus is on efficient algorithms for the real-time graphics pipeline, but parts of our research are equally applicable to offline rendering. Our first focus is texture compression, which is a technique to reduce the memory bandwidth usage. The core idea is to store images in small compressed blocks which are sent over the memory bus and are decompressed on-the-fly when accessed. We present compression algorithms for two types of texture formats. High dynamic range images capture environment lighting with luminance differences over a wide intensity range. Normal maps store perturbation vectors for local surface normals, and give the illusion of high geometric surface detail. Our compression formats are tailored to these texture types and have compression ratios of 6:1, high visual fidelity, and low-cost decompression logic. Our second focus is tessellation culling. Culling is a commonly used technique in computer graphics for removing work that does not contribute to the final image, such as completely hidden geometry. By discarding rendering primitives from further processing, substantial arithmetic computations and memory bandwidth can be saved. Modern graphics processing units include flexible tessellation stages, where rendering primitives are subdivided for increased geometric detail. Images with highly detailed models can be synthesized, but the incurred cost is significant. We have devised a simple remapping technique that allowsfor better tessellation distribution in screen space. Furthermore, we present programmable tessellation culling, where bounding volumes for displaced geometry are computed and used to conservatively test if a primitive can be discarded before tessellation. We introduce a general tessellation culling framework, and an optimized algorithm for rendering of displaced Bézier patches, which is expected to be a common use case for graphics hardware tessellation. Our third and final focus is forward-looking, and relates to efficient algorithms for stochastic rasterization, a rendering technique where camera effects such as depth of field and motion blur can be faithfully simulated. We extend a graphics pipeline with stochastic rasterization in spatio-temporal space and show that stochastic motion blur can be rendered with rather modest pipeline modifications. Furthermore, backface culling algorithms for motion blur and depth of field rendering are presented, which are directly applicable to stochastic rasterization. Hopefully, our work in this field brings us closer to high quality real-time stochastic rendering