Video Data Compression by Progressive Iterative Approximation

In the present paper, the B-spline curve is used for reducing the entropy of video data. We consider the color or luminance variations of a spatial position in a series of frames as input data points in Euclidean space R or R3. The progressive and iterative approximation (PIA) method is a direct and intuitive way of generating curve series of high and higher fitting accuracy. The video data points are approximated using progressive and iterative approximation for least square (LSPIA) fitting. The Lossless video data compression is done through storing the B-spline curve control points (CPs) and the difference between fitted and original video data. The proposed method is applied to two classes of synthetically produced and naturally recorded video sequences and makes a reduction in the entropy of both. However, this reduction is higher for syntactically created than those naturally produced. The comparative analysis of experiments on a variety of video sequences suggests that the entropy of output video data is much less than that of input video data

Non-Uniform Rational B-Splines and Rational Bezier Triangles for Isogeometric Analysis of Structural Applications

Isogeometric Analysis (IGA) is a major advancement in computational analysis that bridges the gap between a computer-aided design (CAD) model, which is typically constructed using Non-Uniform Rational B-splines (NURBS), and a computational model that traditionally uses Lagrange polynomials to represent the geometry and solution variables. In IGA, the same shape functions that are used in CAD are employed for analysis. The direct manipulation of CAD data eliminates approximation errors that emanate from the process of converting the geometry from CAD to Finite Element Analysis (FEA). As a result, IGA allows the exact geometry to be represented at the coarsest level and maintained throughout the analysis process. While IGA was initially introduced to streamline the design and analysis process, this dissertation shows that IGA can also provide improved computational results for complex and highly nonlinear problems in structural mechanics. This dissertation addresses various problems in structural mechanics in the context of IGA, with the use of NURBS and rational Bézier triangles for the description of the parametric and physical spaces. The approaches considered here show that a number of important properties (e.g., high-order smoothness, geometric exactness, reduced number of degrees of freedom, and increased flexibility in discretization) can be achieved, leading to improved numerical solutions. Specifically, using B-splines and a layer-based discretization, a distributed plasticity isogeometric frame model is formulated to capture the spread of plasticity in large-deformation frames. The modeling approach includes an adaptive analysis where the structure of interest is initially modeled with coarse mesh and knots are inserted based on the yielding information at the quadrature points. It is demonstrated that improvement on efficiency and convergence rates is attained. With NURBS, an isogeometric rotation-free multi-layered plate formulation is developed based on a layerwise deformation theory. The derivation assumes a separate displacement field expansion within each layer, and considers transverse displacement component as C0-continuous at dissimilar material interfaces, which is enforced via knot repetition. The separate integration of the in-plane and through-thickness directions allows to capture the complete 3D stresses in a 2D setting. The proposed method is used to predict the behavior of advanced materials such as laminated composites, and the results show advantages in efficiency and accuracy. To increase the flexibility in discretizing complex geometries, rational Bézier triangles for domain triangulation is studied. They are further coupled with a Delaunay-based feature-preserving discretization algorithm for static bending and free vibration analysis of Kirchhoff plates. Lagrange multipliers are employed to explicitly impose high-order continuity constraints and the augmented system is solved iteratively without increasing the matrix size. The resulting discretization is geometrically exact, admits small geometric features, and constitutes C1-continuity. The feature-preserving rational Bézier triangles are further applied to smeared damage modeling of quasi-brittle materials. Due to the ability of Lagrange multipliers to raise global continuity to any desired order, the implicit fourth- and sixth-order gradient damage models are analyzed. The inclusion of higher-order terms in the nonlocal Taylor expansion improves solution accuracy. A local refinement algorithm that resolves marked regions with high resolution while keeping the resulting mesh conforming and well-conditioned is also utilized to improve efficiency. The outcome is a unified modeling framework where the feature-preserving discretization is able to capture the damage initiation and early-stage propagation, and the local refinement technique can then be applied to adaptively refine the mesh in the direction of damage propagation.PHDCivil EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/147668/1/ningliu_1.pd

A novel parallel algorithm for surface editing and its FPGA implementation

A thesis submitted to the University of Bedfordshire in partial fulfilment of the requirements for the degree of Doctor of PhilosophySurface modelling and editing is one of important subjects in computer graphics. Decades of research in computer graphics has been carried out on both low-level, hardware-related algorithms and high-level, abstract software. Success of computer graphics has been seen in many application areas, such as multimedia, visualisation, virtual reality and the Internet. However, the hardware realisation of OpenGL architecture based on FPGA (field programmable gate array) is beyond the scope of most of computer graphics researches. It is an uncultivated research area where the OpenGL pipeline, from hardware through the whole embedded system (ES) up to applications, is implemented in an FPGA chip. This research proposes a hybrid approach to investigating both software and hardware methods. It aims at bridging the gap between methods of software and hardware, and enhancing the overall performance for computer graphics. It consists of four parts, the construction of an FPGA-based ES, Mesa-OpenGL implementation for FPGA-based ESs, parallel processing, and a novel algorithm for surface modelling and editing. The FPGA-based ES is built up. In addition to the Nios II soft processor and DDR SDRAM memory, it consists of the LCD display device, frame buffers, video pipeline, and algorithm-specified module to support the graphics processing. Since there is no implementation of OpenGL ES available for FPGA-based ESs, a specific OpenGL implementation based on Mesa is carried out. Because of the limited FPGA resources, the implementation adopts the fixed-point arithmetic, which can offer faster computing and lower storage than the floating point arithmetic, and the accuracy satisfying the needs of 3D rendering. Moreover, the implementation includes Bézier-spline curve and surface algorithms to support surface modelling and editing. The pipelined parallelism and co-processors are used to accelerate graphics processing in this research. These two parallelism methods extend the traditional computation parallelism in fine-grained parallel tasks in the FPGA-base ESs. The novel algorithm for surface modelling and editing, called Progressive and Mixing Algorithm (PAMA), is proposed and implemented on FPGA-based ES’s. Compared with two main surface editing methods, subdivision and deformation, the PAMA can eliminate the large storage requirement and computing cost of intermediated processes. With four independent shape parameters, the PAMA can be used to model and edit freely the shape of an open or closed surface that keeps globally the zero-order geometric continuity. The PAMA can be applied independently not only FPGA-based ESs but also other platforms. With the parallel processing, small size, and low costs of computing, storage and power, the FPGA-based ES provides an effective hybrid solution to surface modelling and editing

A generic shape descriptor using Bezier curves

Bezier curves are robust tool for a wide array of applications ranging from computer-aided design to calligraphic character, outlining and object shape description. In terms of the control point generation process, existing shape descriptor techniques that employ Bezier curves do not distinguish between regions where an object's shape changes rapidly and those where the change is more gradual or flat. This can lead to an erroneous shape description, particularly where there are significantly sharp changes in shape, such as at sharp corners. This paper presents a novel shape description algorithm called a generic shape descriptor using Bezier curves (SDBC), which defines a new strategy for Bezier control point generation by integrating domain specific information about the shape of an object in a particular region. The strategy also includes an improved dynamic fixed length coding scheme for control points. The SDBC framework has been rigorously tested upon a number of arbitrary shapes, and both quantitative and qualitative analyses have confirmed its superior performance in comparison with existing algorithms

Parametric design and optimization of arched trusses under vertical and horizontal multi-load cases

This dissertation faces the problem of the optimum design of steel truss arches subject to multiple load cases. Arches are one of the most ancient shape-resistant structures, widely used in both civil engineering and architecture. For instance, arches can be considered as purely compressed structures, provided that their “line of thrust” coincides with the centre line of the arch. The “line of thrust” is the locus of the points of application of the thrusts (internal forces or stress resultants) that must be contained within the cross-section of the arch in such a way that the arch transfers loads to the foundations through axial compressive stresses only. As a matter of fact, the more the “line of thrust” differs from the centre line of the arch, the larger the unfavourable bending moments that arise in the arch. This is the reason why it is fundamental to pay close attention to the choice of the shape for an arch in order to minimize (or avoid when it is possible) unfavourable bending effects. Several analytical, graphical and physical methods are provided to find the optimal shape of a monolithic (single rib) arch subjected to a certain load case (i.e. the “funicular curve” for that load). However, if multiple load cases must be considered, it is not possible to find a proper optimal shape for an arch with single rib. In this case, the choice of truss arches with at least two chords becomes indispensable. Indeed, it has been demonstrated that structural optimization of in-plane truss arches with two chords subjected to a single load case leads to optimal solutions in which upper and lower chords tend to coincide with each other and with the “funicular curve” (i.e. the “line of thrust”) for that load. In light of the above, simultaneous shape and size optimization of steel truss arches with two arched chords linked each other through a bracing system (with variable Pratt-type pattern) has been performed for multiple load cases and different structural boundary conditions. Truss arches are effectively used in arch bridges, especially when the arch span exceeds 200 meters (five out of the six steel arch bridges with a span over 500 m are truss arch bridges). For this purpose, a hybrid optimization routine integrating a parametric definition of the design problem, a metaheuristic optimization algorithm and a code for Finite Element Analysis (FEA) has been developed through a MATLAB program. The proposed optimization method allows to simultaneously optimize a larger set of design variables, notwithstanding their large number and various nature (topology, shape and size, as well as continuous and discrete variables, have been concurrently considered). Third-degree Rational Bézier Curves have been chosen to optimize the shape of the arch chords because they can represent a wide family of curves (including conic curves), depending on a small number of parameters. In so doing, in-plane truss arches with different span lengths and structural boundary conditions have been optimized for multiple load cases, only considering vertical loads (acting on the same plane as the arch), since in-plane arches are not suited to withstand out-of-plane loads. On the other hand, spatial arched trusses with two arched chords lying on different planes have been optimally designed for multiple loadings acting in different directions. In particular, a steel arched truss with a lower arched chord variably inclined in the 3D-space and a horizontal upper arched chord linked each other through a bracing system has been designed and optimized for three vertical load cases and a horizontal seismic action parallel to the upper chord plane. Thus, analysing the obtained results, useful suggestions for steel truss arch design have been deduced and presented in this dissertation

The high strain-rate behaviour of polymers and nanocomposites for lightweight armour applications

The need for efficient, lightweight armour solutions has never been so great as it is today. Increasing numbers of personnel, both military and civilian are being placed in an expanding variety of life-threatening situations, and we must recognise the responsibility to maximise their combat survivability. One way to help protect these people is to provide them with some form of armour. Advanced polymeric materials are finding an increasing range of industrial and defence applications. These materials have the potential to improve the performance of current armour systems, whilst also reducing their cost and weight. Polymers may be reinforced with the addition of nanofillers such as carbon nanotubes or graphene, to produce nanocomposites, an exciting emerging polymer technology. Nanomaterials have been shown to exhibit extraordinary strength, far higher than that of traditional armour materials. Nanocomposites have the possibility of being remarkable materials, with high strength and light weight. The work detailed in this report is an investigation into the mechanical properties of nanocomposites along with some novel blended polymer composites. Two compressive testing techniques have been used to carry out this investigation. The intermediate strain-rate Optical Drop-Weight, and the high strain-rate Split-Hopkinson Pressure Bar. The latter required some significant modifications in order to optimise it for use with low-density polymers. Ultimately, nanocomposites were found to behave virtually indistinguishably from the monolithic polymer matrices. Yield strengths and energy absorption characteristics remained inside the ordinary experimental scatter. Blended composites, in which a long chain length polymer is combined with a chemically similar polymer with a shorter chain length, proved to be more interesting. Yield strengths of these novel materials were increased over that of either constituent material, although energy absorption remained low

IST Austria Thesis

Fabrication of curved shells plays an important role in modern design, industry, and science. Among their remarkable properties are, for example, aesthetics of organic shapes, ability to evenly distribute loads, or efficient flow separation. They find applications across vast length scales ranging from sky-scraper architecture to microscopic devices. But, at the same time, the design of curved shells and their manufacturing process pose a variety of challenges. In this thesis, they are addressed from several perspectives. In particular, this thesis presents approaches based on the transformation of initially flat sheets into the target curved surfaces. This involves problems of interactive design of shells with nontrivial mechanical constraints, inverse design of complex structural materials, and data-driven modeling of delicate and time-dependent physical properties. At the same time, two newly-developed self-morphing mechanisms targeting flat-to-curved transformation are presented. In architecture, doubly curved surfaces can be realized as cold bent glass panelizations. Originally flat glass panels are bent into frames and remain stressed. This is a cost-efficient fabrication approach compared to hot bending, when glass panels are shaped plastically. However such constructions are prone to breaking during bending, and it is highly nontrivial to navigate the design space, keeping the panels fabricable and aesthetically pleasing at the same time. We introduce an interactive design system for cold bent glass façades, while previously even offline optimization for such scenarios has not been sufficiently developed. Our method is based on a deep learning approach providing quick and high precision estimation of glass panel shape and stress while handling the shape multimodality. Fabrication of smaller objects of scales below 1 m, can also greatly benefit from shaping originally flat sheets. In this respect, we designed new self-morphing shell mechanisms transforming from an initial flat state to a doubly curved state with high precision and detail. Our so-called CurveUps demonstrate the encodement of the geometric information into the shell. Furthermore, we explored the frontiers of programmable materials and showed how temporal information can additionally be encoded into a flat shell. This allows prescribing deformation sequences for doubly curved surfaces and, thus, facilitates self-collision avoidance enabling complex shapes and functionalities otherwise impossible. Both of these methods include inverse design tools keeping the user in the design loop

Geometric Piecewise Cubic Bézier Interpolating Polynomial with C2 Continuity

Bézier curve is a parametric polynomial that is applied to produce good piecewise interpolation methods with more advantage over the other piecewise polynomials. It is, therefore, crucial to construct Bézier curves that are smooth and able to increase the accuracy of the solutions. Most of the known strategies for determining internal control points for piecewise Bezier curves achieve only partial smoothness, satisfying the first order of continuity. Some solutions allow you to construct interpolation polynomials with smoothness in width along the approximating curve. However, they are still unable to handle the locations of the inner control points. The partial smoothness and non-controlling locations of inner control points may affect the accuracy of the approximate curve of the dataset. In order to improve the smoothness and accuracy of the previous strategies, а new piecewise cubic Bézier polynomial with second-order of continuity C2 is proposed in this study to estimate missing values. The proposed method employs geometric construction to find the inner control points for each adjacent subinterval of the given dataset. Not only the proposed method preserves stability and smoothness, the error analysis of numerical results also indicates that the resultant interpolating polynomial is more accurate than the ones produced by the existing methods