A Robust Approach to Find the Control Points for Wide Variety of 3rd Order Bzier Curves

This paper represents a new approach that can recover the control points for wide variety of 3rd order BE9;zier curves. In this regards, the two stage approximation learning algorithm is adopted with some modifications. At 1st stage our key feature is segmentation of the curve which can determine intermediate points of the wide variety of curves. In this respect, an efficient recursive algorithm is used to find out the height of the curve (h) with less iteration. The proposed approach introduced horizontal segmentation rather than vertical segmentation. Different height (H), where the 2nd and 3rd control point are assumed, and also the step-size (2202;), at which the control points are moved toward the actual direction, are used to find out the exact location of the control points. Experimental results demonstrate that our proposing method can recover control points for wide variety of curves with minimum error level and less iteration. Wide variety of curve shapes are used to test the proposing approach and results are presented to prove its effectivenes

Interactive real-time three-dimensional visualisation of virtual textiles

Virtual textile databases provide a cost-efficient alternative to the use of existing hardcover sample catalogues. By taking advantage of the high performance features offered by the latest generation of programmable graphics accelerator boards, it is possible to combine photometric stereo methods with 3D visualisation methods to implement a virtual textile database. In this thesis, we investigate and combine rotation invariant texture retrieval with interactive visualisation techniques. We use a 3D surface representation that is a generic data representation that allows us to combine real-time interactive 3D visualisation methods with present day texture retrieval methods. We begin by investigating the most suitable data format for the 3D surface representation and identify relief-mapping combined with Bézier surfaces as the most suitable 3D surface representations for our needs, and go on to describe how these representation can be combined for real-time rendering. We then investigate ten different methods of implementing rotation invariant texture retrieval using feature vectors. These results show that first order statistics in the form of histogram data are very effective for discriminating colour albedo information, while rotation invariant gradient maps are effective for distinguishing between different types of micro-geometry using either first or second order statistics.Engineering and physical Sciences Research (EPSRC

Métodos de reconstrucción en dominio temporal para tomografía por transmisión de ultrasonidos

Tesis inédita de la Universidad Complutense de Madrid, Facultad de Ciencias Físicas, Departamento de Física Atómica, Molecular y Nuclear, leída el 06-06-2017Breast cancer (BC) is the leading cause of cancer-related death for women in Europe, and the second one after lung cancer in the US [World Cancer Report, 2008]. Early detection is very important for the survival rate of BC, because the smaller the local extension of the neoplasia, the better the output of the surgical treatments employed. Besides, early detection increases the possibility of preserving the breast and decreases the probability of needing more invasive treatments [Secretaría de Salud, 2007, Alteri et al., 2011]. Mammography is currently the standard procedure employed for breast screening programs around the world. Nevertheless, its efficiency has been questioned lately because: (i) it generates many abnormal findings not related to cancer, (ii) it requires irradiating the patient and (iii) it has low specificity with dense breasts [Santen and Mansel, 2005]. Consequently, complementary techniques to mammography are being proposed to improve the detection and characterization of BC. Among these techniques, is the Ultrasound Computed Tomography (USCT), in reflection mode (which provides qualitative maps with the concentration of scatterers in the tissue), and transmission mode (which provides quantitative maps of the sound speed (SS) and the acoustic attenuation (AA) of the tissues). The images provided by the transmission modality have been proposed for BC detection as they can improve the detectability of malignancies in the breast [Mast, 2000, Duric et al., 2009]...El cáncer de mama (CM) es el cáncer más mortal entre las mujeres europeas, y el segundo más común en Estados Unidos [World Cancer Report, 2008]. La detección temprana es un factor que condiciona en gran medida la tasa de supervivencia a esta enfermedad, ya que a menor tamaño de la neoplasia detectada, mejores resultados pueden esperarse para los tratamientos quirúrgicos que se realicen. Además, la detección temprana aumenta la posibilidad de conservar la mama después de la cirugía y disminuye la necesidad de emplear otros tratamientos más invasivos[Secretaría de Salud, 2007, Alteri et al., 2011]. La mamografía es actualmente el procedimiento estándar que se emplea para el cribado del CM. Sin embargo, en los últimas años su eficiencia está siendo muy cuestionada por varios factores: (i) alta tasa de falsos positivos, (ii) requiere la irradiación del paciente y (iii) baja especificidad en mamas densas 2. Debido a lo anterior, para mejorar la detección y caracterización del CM se han propuesto varias técnicas complementarias. Entre ellas está la tomografía ultrasónica (TU), que es una técnica en desarrollo que presenta dos modalidades principales: la reflexión (proporciona mapas cualitativos de la concentración de dispersores en el tejido) y la transmisión (proporciona mapas cuantitativos de la velocidad y atenuación del sonido en el tejido). Los mapas del modo transmisión han sido propuestos como una eficiente alternativa, libre de radiación, para la detección del CM, ya que proporcionan alto contraste y especificidad [Mast, 2000, Duric et al., 2009]...Depto. de Estructura de la Materia, Física Térmica y ElectrónicaFac. de Ciencias FísicasTRUEunpu

Changing representation of curves and surfaces: exact and approximate methods

Το κύριο αντικείμενο μελέτης στην παρούσα διατριβή είναι η αλλαγή αναπαράστασης γεωμετρικών αντικειμένων από παραμετρική σε αλγεβρική (ή πεπλεγμένη) μορφή. Υπολογίζουμε την αλγεβρική εξίσωση παρεμβάλλοντας τους άγνωστους συντελεστές του πολυωνύμου δεδομένου ενός υπερσυνόλου των μονωνύμων του. Το τελευταίο υπολογίζεται απο το Newton πολύτοπο της αλγεβρικής εξίσωσης που υπολογίζεται από μια πρόσφατη μέθοδο πρόβλεψης του συνόλου στήριξης της εξίσωσης. H μέθοδος πρόβλεψης του συνόλου στήριξης βασίζεται στην αραιή (ή τορική) απαλοιφή: το πολύτοπο υπολογίζεται από το Newton πολύτοπο της αραιής απαλοίφουσας αν θεωρίσουμε την παραμετροποίηση ως πολυωνυμικό σύστημα. Στα μονώνυμα που αντιστοιχούν στα ακέραια σημεία του Newton πολυτόπου δίνονται τιμές ώστε να σχηματίσουν έναν αριθμητικό πίνακα. Ο πυρήνα του πίνακα αυτού, διάστασης 1 σε ιδανική περίπτωση, περιέχει τους συντελεστές των μονωνύμων στην αλγεβρική εξίσωση. Υπολογίζουμε τον πυρήνα του πίνακα είτε συμβολικά είτε αριθμητικά εφαρμόζοντας την μέθοδο του singular value decomposition (SVD). Προτείνουμε τεχνικές για να διαχειριστούμε την περίπτωση ενός πολυδιάστατου πυρήνα το οποίο εμφανίζεται όταν το προβλεπόμενο σύνολο στήριξης είναι ένα υπερσύνολο του πραγματικού. Αυτό δίνει έναν αποτελεσματικό ευαίσθητο-εξόδου αλγόριθμο υπολογισμού της αλγεβρικής εξίσωσης. Συγκρίνουμε διαφορετικές προσεγγίσεις κατασκευής του πίνακα μέσω των λογισμικών Maple και SAGE. Στα πειράματά μας χρησιμοποιήθηκαν ρητές καμπύλες και επιφάνειες καθώς και NURBS. Η μέθοδός μας μπορεί να εφαρμοστεί σε πολυώνυμα ή ρητές παραμετροποιήσεις επίπεδων καμπυλών ή (υπερ)επιφανειών οποιασδήποτε διάστασης συμπεριλαμβανομένων και των περιπτώσεων με παραμετροποίηση σεσημεία βάσης που εγείρουν σημαντικά ζητήματα για άλλες μεθόδους αλγεβρικοποίησης. Η μέθοδος έχει τον εξής περιορισμό: τα γεωμετρικά αντικείμενα πρέπει να αναπαριστώνται από βάσεις μονωνύμων που στην περίπτωση τριγωνομετρικών παραμετροποιήσεων θα πρέπει να μπορούν να μετασχηματιστούν σε ρητές συναρτήσεις. Επιπλέον η τεχνική που προτείνουμε μπορεί να εφαρμοστεί σε μη γεωμετρικά προβλήματα όπως ο υπολογισμόςτης διακρίνουσας ενός πολυωνύμου με πολλές μεταβλητές ή της απαλοίφουσας ενός συστήματος πολυωνύμων με πολλές μεταβλητές.The main object of study in our dissertation is the representation change of the geometric objects from the parametric form to implicit. We compute the implicit equation interpolating the unknown coefficients of the implicit polynomial given a superset of its monomials. The latter is derived from the Newton polytope of the implicit equation obtained by the recently developed method for support prediction. The support prediction method we use relies on sparse (or toric) elimination: the implicit polytope is obtained from the Newton polytope of the sparse resultant of the system in parametrization, represented as polynomials. The monomials that correspond to the lattice points of the Newton polytope are suitably evaluated to build a numeric matrix, ideally of corank 1. Its kernel contains their coefficients in the implicit equation. We compute kernel of the matrix either symbolically, or numerically, applying singular value decomposition (SVD). We propose techniques for handling the case of the multidimensional kernel space, caused by the predicted support being a superset of the actual. This yields an efficient, output-sensitive algorithm for computing the implicit equation. We compare different approaches for constructing the matrix in Maple and SAGE software. In our experiments we have used classical algebraic curves and surfaces as well as NURBS. Our method can be applied to polynomial or rational parametrizations of planar curves or (hyper)surfaces of any dimension including cases of parameterizations with base points which raise important issues for other implicitization methods. The method has its limits: geometric objects have to be presented using monomial basis; in the case of trigonometric parametrizations they have to be convertible to rational functions. Moreover, the proposed technique can be applied for nongeometric problems such as the computation of the discriminant of a multivariate polynomial or the resultant of a system of multivariate polynomials

Advanced Techniques for Design and Manufacturing in Marine Engineering

Modern engineering design processes are driven by the extensive use of numerical simulations; naval architecture and ocean engineering are no exception. Computational power has been improved over the last few decades; therefore, the integration of different tools such as CAD, FEM, CFD, and CAM has enabled complex modeling and manufacturing problems to be solved in a more feasible way. Classical naval design methodology can take advantage of this integration, giving rise to more robust designs in terms of shape, structural and hydrodynamic performances, and the manufacturing process.This Special Issue invites researchers and engineers from both academia and the industry to publish the latest progress in design and manufacturing techniques in marine engineering and to debate the current issues and future perspectives in this research area. Suitable topics for this issue include, but are not limited to, the following:CAD-based approaches for designing the hull and appendages of sailing and engine-powered boats and comparisons with traditional techniques;Finite element method applications to predict the structural performance of the whole boat or of a portion of it, with particular attention to the modeling of the material used;Embedded measurement systems for structural health monitoring;Determination of hydrodynamic efficiency using experimental, numerical, or semi-empiric methods for displacement and planning hulls;Topology optimization techniques to overcome traditional scantling criteria based on international standards;Applications of additive manufacturing to derive innovative shapes for internal reinforcements or sandwich hull structures

Modelling and Animation using Partial Differential Equations. Geometric modelling and computer animation of virtual characters using elliptic partial differential equations.

This work addresses various applications pertaining to the design, modelling and animation of parametric surfaces using elliptic Partial Differential Equations (PDE) which are produced via the PDE method. Compared with traditional surface generation techniques, the PDE method is an effective technique that can represent complex three-dimensional (3D) geometries in terms of a relatively small set of parameters. A PDE-based surface can be produced from a set of pre-configured curves that are used as the boundary conditions to solve a number of PDE. An important advantage of using this method is that most of the information required to define a surface is contained at its boundary. Thus, complex surfaces can be computed using only a small set of design parameters. In order to exploit the advantages of this methodology various applications were developed that vary from the interactive design of aircraft configurations to the animation of facial expressions in a computer-human interaction system that utilizes an artificial intelligence (AI) bot for real time conversation. Additional applications of generating cyclic motions for PDE based human character integrated in a Computer-Aided Design (CAD) package as well as developing techniques to describe a given mesh geometry by a set of boundary conditions, required to evaluate the PDE method, are presented. Each methodology presents a novel approach for interacting with parametric surfaces obtained by the PDE method. This is due to the several advantages this surface generation technique has to offer. Additionally, each application developed in this thesis focuses on a specific target that delivers efficiently various operations in the design, modelling and animation of such surfaces.The project files will not be available online

Geometric modelling and shape optimisation of pharmaceutical tablets. Geometric modelling and shape optimisation of pharmaceutical tablets using partial differential equations.

Pharmaceutical tablets have been the most dominant form for drug delivery and they need to be strong enough to withstand external stresses due to packaging and loading conditions before use. The strength of the produced tablets, which is characterised by their compressibility and compactibility, is usually deter-mined through a physical prototype. This process is sometimes quite expensive and time consuming. Therefore, simulating this process before hand can over-come this problem. A technique for shape modelling of pharmaceutical tablets based on the use of Partial Differential Equations is presented in this thesis. The volume and the sur-face area of the generated parametric tablet in various shapes have been es-timated numerically. This work also presents an extended formulation of the PDE method to a higher dimensional space by increasing the number of pa-rameters responsible for describing the surface in order to generate a solid tab-let. The shape and size of the generated solid tablets can be changed by ex-ploiting the analytic expressions relating the coefficients associated with the PDE method. The solution of the axisymmetric boundary value problem for a finite cylinder subject to a uniform axial load has been utilised in order to model a displace-ment component of a compressed PDE-based representation of a flat-faced round tablet. The simulation results, which are analysed using the Heckel model, show that the developed model is capable of predicting the compressibility of pharmaceutical powders since it fits the experimental data accurately. The opti-mal design of pharmaceutical tablets with particular volume and maximum strength has been obtained using an automatic design optimisation which is performed by combining the PDE method and a standard method for numerical optimisation

Integrated structural analysis using isogeometric finite element methods

The gradual digitization in the architecture, engineering, and construction industry over the past fifty years led to an extremely heterogeneous software environment, which today is embodied by the multitude of different digital tools and proprietary data formats used by the many specialists contributing to the design process in a construction project. Though these projects become increasingly complex, the demands on financial efficiency and the completion within a tight schedule grow at the same time. The digital collaboration of project partners has been identified as one key issue in successfully dealing with these challenges. Yet currently, the numerous software applications and their respective individual views on the design process severely impede that collaboration. An approach to establish a unified basis for the digital collaboration, regardless of the existing software heterogeneity, is a comprehensive digital building model contributed to by all projects partners. This type of data management known as building information modeling (BIM) has many benefits, yet its adoption is associated with many difficulties and thus, proceeds only slowly. One aspect in the field of conflicting requirements on such a digital model is the cooperation of architects and structural engineers. Traditionally, these two disciplines use different abstractions of reality for their models that in consequence lead to incompatible digital representations thereof. The onset of isogeometric analysis (IGA) promised to ease the discrepancy in design and analysis model representations. Yet, that initial focus quickly shifted towards using these methods as a more powerful basis for numerical simulations. Furthermore, the isogeometric representation alone is not capable of solving the model abstraction problem. It is thus the intention of this work to contribute to an improved digital collaboration of architects and engineers by exploring an integrated analysis approach on the basis of an unified digital model and solid geometry expressed by splines. In the course of this work, an analysis framework is developed that utilizes such models to automatically conduct numerical simulations commonly required in construction projects. In essence, this allows to retrieve structural analysis results from BIM models in a fast and simple manner, thereby facilitating rapid design iterations and profound design feedback. The BIM implementation Industry Foundation Classes (IFC) is reviewed with regard to its capabilities of representing the unified model. The current IFC schema strongly supports the use of redundant model data, a major pitfall in digital collaboration. Additionally, it does not allow to describe the geometry by volumetric splines. As the pursued approach builds upon a unique model for both, architectural and structural design, and furthermore requires solid geometry, necessary schema modifications are suggested. Structural entities are modeled by volumetric NURBS patches, each of which constitutes an individual subdomain that, with regard to the analysis, is incompatible with the remaining full model. The resulting consequences for numerical simulation are elaborated in this work. The individual subdomains have to be weakly coupled, for which the mortar method is used. Different approaches to discretize the interface traction fields are implemented and their respective impact on the analysis results is evaluated. All necessary coupling conditions are automatically derived from the related geometry model. The weak coupling procedure leads to a linear system of equations in saddle point form, which, owed to the volumetric modeling, is large in size and, the associated coefficient matrix has, due to the use of higher degree basis functions, a high bandwidth. The peculiarities of the system require adapted solution methods that generally cause higher numerical costs than the standard procedures for symmetric, positive-definite systems do. Different methods to solve the specific system are investigated and an efficient parallel algorithm is finally proposed. When the structural analysis model is derived from the unified model in the BIM data, it does in general initially not meet the requirements on the discretization that are necessary to obtain sufficiently accurate analysis results. The consequently necessary patch refinements must be controlled automatically to allowfor an entirely automatic analysis procedure. For that purpose, an empirical refinement scheme based on the geometrical and possibly mechanical properties of the specific entities is proposed. The level of refinement may be selectively manipulated by the structural engineer in charge. Furthermore, a Zienkiewicz-Zhu type error estimator is adapted for the use with isogeometric analysis results. It is shown that also this estimator can be used to steer an adaptive refinement procedure