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Lorenczyk, Jiří. "Matematický popis trajektorie pohybu vozidla." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2020. http://www.nusl.cz/ntk/nusl-445453.
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The goal of this thesis is to nd types of curves which would allow for the construction of a path that could be traversed by a vehicle. It seems that a minimal constraint for such a path is the continuity of curve's curvature. This leads to a closer look at the three types of curves: Clothoids, which are able to smoothly connect straights with arcs of a constant curvature, interpolation quintic splines, which are C2 smooth in the interpolation nodes and -splines, these belong to the family of quintic polynomial curves too, however, they are characterised by the vector of parameters which modies the shape of the curve. The thesis is accompanied by an application allowing for manual construction of the path composed of spline curves.
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Hladíková, Hana. "Metody konstrukce výnosové křivky státních dluhopisů na českém dluhopisovém trhu." Doctoral thesis, Vysoká škola ekonomická v Praze, 2008. http://www.nusl.cz/ntk/nusl-71673.
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The zero coupon yield curve is one of the most fundamental tools in finance and is essential in the pricing of various fixed-income securities. Zero coupon rates are not observable in the market for a range of maturities. Therefore, an estimation methodology is required to derive the zero coupon yield curves from observable data. If we deal with approximations of empirical data to create yield curves it is necessary to choose suitable mathematical functions. We discuss the following methods: the methods based on cubic spline functions, methods employing linear combination of the Fourier or exponential basis functions and the parametric model of Nelson and Siegel. The current mathematical apparatus employed for this kind of approximation is outlined. In order to find parameters of the models we employ the least squares minimization of computed and observed prices. The theoretical background is applied to an estimation of the zero-coupon yield curves derived from the Czech coupon bond market. Application of proper smoothing functions and weights of bonds is crucial if we want to select a method which performs best according to given criteria. The best performance is obtained for Bspline models with smoothing.
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Pereira, Larissa Rocha. "Ajuste de curva B-spline fechada com peso." Universidade Federal de Uberlândia, 2014. https://repositorio.ufu.br/handle/123456789/14947.
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Coordenação de Aperfeiçoamento de Pessoal de Nível SuperiorThe aim of this work is to develop a method of curve fitting using closed B-spline closed for application on reconstruction of cross-sections of objects. For this study specifically where the sections are closed curves, it has been implemented a method to close the curve B-spline curve, in such way that the curve is smooth on the closing point. The developed method is based on least squares approximation with weights, which defines that the curve should be as close as possible to the real curve. The weights in this case are responsible for the tightness of the approximation to each data points, whose points represent the coordinate of the object section that will be rebuild. Moreover, adjustments and impositions on the curve have been proposed so that it has a better result and represent more accurately the desired cross section. Particular characteristics of the curve were used to help enforce and define the settings. For the analysis, B-spline curves using the developed method, were obtained showing good results.
O objetivo desse trabalho é desenvolver um método de ajuste de curvas B-spline fechada para a aplicação na reconstrução de seções transversais de um objeto. Por especificamente nesse trabalho as seções serem seções fechadas, foi implementado um método para o fechamento da curva B-spline, de modo que a mesma possuía suavidade no seu fechamento. O método desenvolvido e utilizado foi baseado na aproximação por mínimos quadrados com pesos, que define que a curva obtida deva ser mais próxima possível da curva real. Os pesos nesse caso são responsáveis pela aproximação ou afastamento da curva em relação aos pontos dados, pontos esses que melhor representam as coordenadas da seção do objeto que se deseja reconstruir. Além disso, foram desenvolvidos ajustes e imposições na curva para que ela tivesse um melhor resultado e representasse de forma mais fiel a seção transversal desejada. Para a imposição e definição dos ajustes foram utilizadas características particulares da curva. Para a análise, curvas B-spline utilizando o método desenvolvido, foram traçadas e foram constatados os resultados desejados.
Mestre em Engenharia Mecânica
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Elsaesser, Bernhard. "Approximation mit rationalen B-Spline Kurven und Flaechen. Approximation with rational B-spline curves and surfaces." Phd thesis, Shaker, 1998. https://tuprints.ulb.tu-darmstadt.de/1126/1/elsaesser.pdf.
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Dag, Idris. "Studies of B-spline finite elements." Thesis, Bangor University, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.358041.
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Rojas, Roberto. "Geometric trimming of B-spline surfaces." Thesis, Virginia Tech, 1994. http://hdl.handle.net/10919/40634.
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Elsässer, Bernhard [Verfasser]. "Approximation mit rationalen B-Spline Kurven und Flaechen. Approximation with rational B-spline curves and surfaces / Bernhard Elsaesser." Darmstadt : Universitäts- und Landesbibliothek Darmstadt, 2008. http://d-nb.info/1104177943/34.
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Aggarwal, Aditya Mohan. "B-Spline Boundary Element Method for Ships." ScholarWorks@UNO, 2008. http://scholarworks.uno.edu/td/853.
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The development of a three dimensional B-Spline based method, which is suitable for the steady-state potential flow analysis of free surface piercing bodies in hydrodynamics, is presented. The method requires the B-Spline or Non Uniform Rational B-Spline (NURBS) representation of the body as an input. In order to solve for the unknown potential, the source surface, both for the body as well as the free surface, is represented by NURBS surfaces. The method does not require the body surface to be discritized into flat panels. Therefore, instead of a mere panel approximation, the exact body geometry is utilized for the computation. The technique does not use a free surface Green's function, which already satisfies the linear free surface boundary conditions, but uses a separate source patch for the free surface. By eliminating the use of a free surface Green's function, the method can be extended to considering non-linear free surface conditions, thus providing the possibility for wave resistance calculations. The method is first applied to the double body flow problem around a sphere and a Wigley hull. Some comparisons are made with exact solutions to validate the accuracy of the method. Results of linear free surface conditions are then presented.
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Junger, Jean-Claude. "Modélisation et réalisation d'une prothèse de genou." Vandoeuvre-les-Nancy, INPL, 1993. http://www.theses.fr/1993INPL052N.
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La complexité du mouvement des os de l'articulation du genou requiert une étude anatomique pour construire une prothèse de genou. Une bonne prothèse repose sur des surfaces permettant tous les mouvements du genou. Le nouveau type de prothèse présenté ici, est le résultat de cette approche scientifique. Dans un premier temps, nous mesurons les surfaces des condyles et de la trochlée d'une population significative d'os humains en utilisant une machine triaxiale. Puis, nous déterminons une surface moyenne servant de base à la réalisation de notre prothèse. Ensuite, en utilisant les techniques des fonctions b-splines, nous étudions les paramètres permettant de reconstruire la surface des condyles tout en respectant la cinématique ligamentaire et la transmission des contraintes. Notre prothèse respecte la position de la rotule sur les condyles et la trochlée et présente une forme proche de la forme anatomique. En relation avec cette étude, nous avons développé de nouveaux types de tiges intramédullaires ainsi que la technique de pose associée
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Tazeroualti, Mohammed. "Modélisation de surfaces à l'aide de fonctions splines : conception d'un verre progressif." Grenoble 1, 1993. http://tel.archives-ouvertes.fr/tel-00343495.
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Ce travail se décompose en trois parties distinctes. Dans la première partie, on introduit un algorithme du type Gauss-Seidel pour la minimisation de fonctionnelles symétriques semi-définies positives. La convergence de cet algorithme est démontrée. En application, on donne deux méthodes de lissage de surfaces. Ces méthodes sont basées sur l'idée de ramener un probleme de lissage a deux dimensions a la resolution d'une suite de problèmes a une dimension faciles a résoudre. Pour cela on utilise l'opération d'inf-convolution spline. Dans la deuxième partie, on introduit une nouvelle methode pour la conception d'un verre progressif. Ce verre est représente par une surface suffisamment régulière, a laquelle on impose des conditions sur ses courbures principales dans certaines zones (zone de vision de loin et zone de vision de pres), et des conditions sur ses directions principales de courbure dans d'autres zones (zone nasale et zone temporale). La surface est écrite sous forme de produit tensoriel de b-splines de degré quatre. Pour la calculer, on est amené a minimiser un opérateur non quadratique. Cette minimisation est alors effectuée par un procédé itératif dont on a teste numériquement la convergence rapide
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Andriamaro, Miangaly Gaelle. "Vector refinable splines and subdivision." Thesis, Stellenbosch : Stellenbosch University, 2008. http://hdl.handle.net/10019.1/1747.
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Thesis (MSc (Mathematics))--Stellenbosch University, 2008.In this thesis we study a standard example of refinable functions, that is, functions which can be reproduced by the integer shifts of their own dilations. Using the cardinal B-spline as an introductory example, we prove some of its properties, thereby building a basis for a later extension to the vector setting. Defining a subdivision scheme associated to the B-spline refinement mask, we then present the proof of a well-known convergence result. Subdivision is a powerful tool used in computer-aided geometric design (CAGD) for the generation of curves and surfaces. The basic step of a subdivision algorithm consists of starting with a given set of points, called the initial control points, and creating new points as a linear combination of the previous ones, thereby generating new control points. Under certain conditions, repeated applications of this procedure yields a continuous limit curve. One important goal of this thesis is to study a particular extension of scalar subdivision to matrix subdivision ...
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WANG, DONGHUI. "Modelisation de surfaces b-splines s'appuyant sur des courbes de bezier ou b-splines." Paris, ENSAM, 1990. http://www.theses.fr/1989ENAM0009.
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Ce travail concerne l'elaboration d'une methode de modelisation des surfaces b-splines en s'appuyant sur des courbes de bezier ou b-splines predefinies. Il a ete realise successivement chez renault automation et matra datavision, sur le systeme unisurf integre a euclid-is de matra datavision. Le probleme pose est de savoir comment on peut modeliser une surface polynomiale (surface de bezier ou b-spline) sous les contraintes suivantes: la surface obtenue doit respecter l'esthetique et la regularite des sections donnees par l'utilisateur; la methode proposee doit etre simple a utiliser et facile a controler; la surface doit respecter une precision voulue. Pour essayer de la resoudre, nous proposons une methode generale en utilisant le mecanisme de la modelisation des surfaces proposee par les methodes de coons et de gordon, ainsi que la representation mathematique b-spline et ses diverses techniques. L'etude et la realisation de notre probleme peuvent etre examinees selon les aspects suivants: etude de la transformation entre la representation de bezier et la representation b-spline, et elaboration de l'algorithme wm; analyse du mecanisme de la modelisation des surfaces; etablissement d'un type de modelisation des surfaces general
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Aggarwal, Bhavya. "B-spline finite elements for plane elasticity problems." Texas A&M University, 2006. http://hdl.handle.net/1969.1/4849.
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The finite element method since its development in the 1950âÂÂs has been used
extensively in solving complex problems involving partial differential equations. The
conventional finite element methods use piecewise Lagrange interpolation functions for
approximating displacements. The aim of this research is to explore finite element
analysis using B-spline interpolation. B-splines are piecewise defined polynomial curves
which provide higher continuity of derivatives than piecewise Lagrange interpolation
functions. This work focuses on the implementation and comparison of the B-spline
finite elements in contrast with the conventional finite elements. This thesis observes
that the use of B-spline interpolation functions can reduce the computational cost
significantly. It is an efficient technique and can be conveniently implemented into the
existing finite element programs.
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Ingram, Christopher. "A Geometric B-Spline Over the Triangular Domain." Thesis, University of Waterloo, 2003. http://hdl.handle.net/10012/1039.
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For modelling curves, B-splines [3] are among the most versatile control schemes. However, scaling this technique to surface patches has proven to be a non-trivial endeavor. While a suitable scheme exists for rectangular patches in the form of tensor product B-splines, techniques involving the triangular domain are much less spectacular.
The current cutting edge in triangular B-splines [2] is the DMS-spline. While the resulting surfaces possess high degrees of continuity, the control scheme is awkward and the evaluation is computationally expensive. A more fundamental problem is the construction bears little resemblance to the construction used for the B-Spline. This deficiency leads to the central idea of the thesis; what happens if the simple blending functions found at the heart of the B-Spline construction are used over higher dimension domains?
In this thesis I develop a geometric generalization of B-Spline curves over the triangular domain. This construction mimics the control point blending that occurs with uniform B-Splines. The construction preserves the simple control scheme and evaluation of B-Splines, without the immense computational requirements of DMS-splines. The result is a new patch control scheme, the G-Patch, possessing C0 continuity between adjacent patches.
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Lampis, Alberto. "Sul Calcolo di B-Spline Tchebycheffiane Multi-Order." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2021. http://amslaurea.unibo.it/23217/.
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Viene descritto un nuovo algoritmo numericamente stabile per il calcolo di B-spline Tchebycheffiane multi-order, basato sull'espressione delle matrici relative alla procedura di knot insertion in termini dei coefficienti di Greville generalizzati dello spazio in analisi.
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Armstrong, Curtis A. "Vectorization of Raster Images Using B-Spline Surfaces." Diss., CLICK HERE for online access, 2006. http://contentdm.lib.byu.edu/ETD/image/etd1513.pdf.
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Wong, Chee Kiang. "Intersection of B-spline surfaces by elimination method." Thesis, This resource online, 1990. http://scholar.lib.vt.edu/theses/available/etd-03032009-040559/.
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Haq, Shaiq A. "Filament winding machine control using B-spline interpolation." Thesis, University of Nottingham, 1994. http://eprints.nottingham.ac.uk/14216/.
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Filament winding is a process for the placement of reinforcement fibres on to a rotating surface in a specified geometric pattern. A conventional straight line interpolation controller is not very appropriate for filament winding because the fibre pay-out-eye is at some distance away from the mandrel surface and its movement from one point to another may disturb the position of previously laid fibre on the mandrel. Filament winding demands a controller which can produce fast and smooth carriage movements, and have a path-anticipation capability so that while moving around curves the effect of pay-out-eye movement on previous fibre positions is minimised. This problem can be overcome by using an interpolation technique which determines the pay-out-eye path by considering more than two data points, and whose profile is continuous in nature up to its second derivative. In this project an IDM PC based filament winding controller, using B-spline interpolation technique, is developed. To test the performance of the controller a 3-axis CNC filament winding machine was designed and manufactured. For optimum performance, emphasis was given to the low inertia of the machine carriage, while at the same time maintaining the system's structural stiffness. To reduce the machine carriage weight, the DC servomotors were installed on the machine's frame, instead of the carriage, and a timing belt arrangement was used for power transmission. The controller's electronic hardware was assembled using servo amplifiers, DAC cards, and a purpose built optical encoder interface card. The controller software was developed using TURBO C++ as the main programming language, whereas the hardware interface routines were written in Assembly Language. Problems of winding path deviation as a result of B-spline approximation were tackled using knowledge based programming techniques. The results showed a considerable improvement in winding speed and less fibre slippage in the case of non-geodesic winding patterns, resulting in higher accuracy of fibre placement on the mandrel.
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Loop, Charles Teorell. "Generalized B-spline surfaces of arbitrary topological type /." Thesis, Connect to this title online; UW restricted, 1992. http://hdl.handle.net/1773/6888.
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Xu, Bo. "Multiresolution editing for B-spline curves and surfaces." [Ames, Iowa : Iowa State University], 2008.
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Jain, Aashish. "Error Visualization in Comparison of B-Spline Surfaces." Thesis, Virginia Tech, 1999. http://hdl.handle.net/10919/35319.
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Geometric trimming of surfaces results in a new mathematical description of the matching surface. This matching surface is required to closely resemble the remaining portion of the original surface. Typically, the approximation error in such cases is measured with a view to minimize it. The data associated with the error between two matching surfaces is large and needs to be filtered into meaningful information.This research looks at suitable norms for achieving this data reduction or abstraction with a view to provide quantitative feedback about the approximation error. Also, the differences between geometric shapes are easily discerned by the human eye but are difficult to characterize or describe. Error visualization tools have been developed to provide effective visual inputs that the designer can interpret into meaningful information.Master of Science
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Mößner, Bernhard. "B-splines als Finite Elemente /." Aachen : Shaker, 2006. http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&doc_number=015210875&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA.
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Nguyen, Tan Khoi. "Surfaces polyédriques et surfaces paramétriques : une reconstruction par approximation via les surfaces de subdivision." Thesis, Aix-Marseille 2, 2010. http://www.theses.fr/2010AIX22055/document.
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La Conception Assistée par Ordinateur (C.A.O) qui permet de concevoir des objets physiques à partir de modèles mathématiques est utilisée dans de nombreux secteurs de l’industrie.On constate actuellement une volonté généralisée de tirer parti de deux approches jusqu’à présent plutôt antagonistes : la modélisation géométrique continue qui crée des objets continus représentant par la modélisation à partir de surfaces B-splines ou NURBS) et la modélisation géométrique discrète qui qu’il s’agisse de maillages ou de surfaces de subdivision.Cette dualité d’approche a de nombreuses applications industrielles potentielles et présente donc un intérêt scientifique important. Les surfaces polyédriques et en particulier les surfaces de subdivision offrent intrinsèquement la discrétisation, sont d’une manipulation très simple, mais elles ne remplacent pas les surfaces B-splines ou NURBS. Les travaux présentés dans la thèse et qui ont abouti au passage réciproque d’une surface paramétrique à une surface polyédrique. Nous nous intéressons plus particulière aux surfaces de subdivision considérant comme une liaison entre la surface polyédriquee et la surface paramétrique parce qu’après quelques étapes de subdivision, le polyèdre caractéristique converge à une surface paramétrique correspondant. Nous y proposons des schémas de la subdivision inverse permettent de récréer les surface polyédrique grossier de subdivision précédent. Nous avons donc développé deux méthodes pour la reconstruction d’une courbe/surface paramétrique en utilisant le schéma de subdivision inverse uniforme et le schéma de subdivision inverse non-uniforme. Pour améliorer les résultats de reconstruction par la subdivision inverse, nous associons à ces méthodes une possibilité d’ajustement d’approximation qui permet de diminuer grandement l’erreur de reconstruction. Les résultats obtenus ont été comparés à une méthode bien connu de reconstruction sens au sens des moindres carrés. Nos méthodes sont très prometteuses en termes d’approximation et de compressionComputer Aided Geometric Design (CAGD) which allows us to design the physical objects from mathematical models is used in many sectors of industry. It is currently a general wish to take advantage of the two these approaches rather than the antagonists : The goal that the continuous geometric model creates the continuous objects represented by the modelof the surfaces B-splines or NURBS) and the discreet geometric model made by eitherthe meshes or the subdivision surfaces. This duality of the approach has many potential industrial applications and therefore submits interesting significant science. The polyhedral surfaces and the subdivision surfaces in particular which offer the intrinsically discretization,are a very simple manipulation, but they do not replace the surfaces B-splines or NURBS.The works presented in this thesis aim to the reciprocal passage from a parametric surfaceto a polyhedral surface. We are more specialy interested to subdivisions surfaces considering as a liaison between the polyhedral surface and the parametric surface, because after a few steps of subdivision, the polyhedron characteristic converges to a parametric surface corresponding.We have proposed the schemas of the inverse subdivision allowing recreating the polyhedral surface coarse of subdivision precedent. We thus presented two methods for there construction of a parametric curve/surface : one for using the schema of uniform inverse subdivision and the other for non-uniform inverse subdivision. To improve the results of reconstruction by the inverse subdivision methods, we associate these methods with the process of adjustment the approximation which allows reducing the error of reconstruction.The results obtained have been compared with a well-known least squares method. Our methods are very promising in terms of approximation and compression
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Nafziger, John S. "Reverse parameterization of B-spline surfaces for data transfer." Thesis, This resource online, 1993. http://scholar.lib.vt.edu/theses/available/etd-06302009-040414/.
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Jones, Robert W. "Intersection and filleting of non-uniform B-spline surfaces." Thesis, Virginia Tech, 1991. http://hdl.handle.net/10919/42189.
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Preliminary aircraft design codes requIre a more complete and integrated geometry
definition than that used by conceptual design codes. This thesis documents the design
and creation of an interactive CAD system which converts the geometry descriptions
commonly used in conceptual aircraft design codes to descriptions that meet the
requirements of preliminary design systems. In particular, the conversion of ACSYNT
Hermite surface data of aircraft models to the non-uniform hi-cubic B-Spline surface
representation is addressed. The topics discussed in this thesis include the design and
development of an interactive graphics user interface, the design and coding of an
intersection method for non-uniform hi-cubic B-Spline surfaces utilizing subdivision
techniques and the development of a one-dimensional filleting algorithm for blending
surfaces along iso-parametric curves.
Master of Science
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Jayaram, Uma. "Extracting dimensional geometric parameters from B-spline surface models." Diss., Virginia Tech, 1991. http://hdl.handle.net/10919/37877.
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In an integrated design environment, the common thread between the different design stages is usually the geometric model of the part. However, the requirements for the geometric definition of the design is usually different for each stage. The transformation of data between these different stages is essential for the success of the integrated design environment. For example, conceptual design systems usually deal with geometric dimensional parameters (e.g. length, radius, etc.) whereas preliminary design systems frequently require the geometry definition to be in the form of surface models.
This dissertation presents the necessity and scope of creating and implementing methodologies to obtain dimensional geometric parameters from the surface description of an object. Since the study of geometric modeling and parametric surfaces is a new field, few classical methods are applicable. Methods and algorithms for the extraction of various geometry parameters are created. A few methods to pre-process and manipulate these surfaces before the parameter extraction methods can be applied are outlined.
One of the most important applications of parameter extraction is in the field of aircraft design. There are two important aspects of geometry data conversion in the design cycle. The first is the conversion from conceptual CAD models to CFD compatible models. The second is the conversion from surface representations of CFD models to obtain component parameters (e.g. wing span, fuselage fineness ratio, moments of inertia, etc.). The methods created in this dissertation are used to extract geometric parameters of importance in aircraft design. This enables the design cycle to be complete and promotes integrated design.
These methods have been implemented in the aircraft design software, ACSYNT. Examples of the conversion of data from B-spline surface models to dimensional geometric parameters using these methods are included.
The emphasis of this dissertation is on non-uniform B-spline surfaces. Methods for obtaining geometric parameters from aircraft models described by characteristic points are also considered briefly.Ph. D.
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Kaya, Hikmet Emre. "A comparative study between the cubic spline and b-spline interpolation methods in free energy calculations." Master's thesis, Faculty of Science, 2020. http://hdl.handle.net/11427/32228.
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Numerical methods are essential in computational science, as analytic calculations for large datasets are impractical. Using numerical methods, one can approximate the problem to solve it with basic arithmetic operations. Interpolation is a commonly-used method, inter alia, constructing the value of new data points within an interval of known data points. Furthermore, polynomial interpolation with a sufficiently high degree can make the data set differentiable. One consequence of using high-degree polynomials is the oscillatory behaviour towards the endpoints, also known as Runge's Phenomenon. Spline interpolation overcomes this obstacle by connecting the data points in a piecewise fashion. However, its complex formulation requires nested iterations in higher dimensions, which is time-consuming. In addition, the calculations have to be repeated for computing each partial derivative at the data point, leading to further slowdown. The B-spline interpolation is an alternative representation of the cubic spline method, where a spline interpolation at a point could be expressed as the linear combination of piecewise basis functions. It was proposed that implementing this new formulation can accelerate many scientific computing operations involving interpolation. Nevertheless, there is a lack of detailed comparison to back up this hypothesis, especially when it comes to computing the partial derivatives. Among many scientific research fields, free energy calculations particularly stand out for their use of interpolation methods. Numerical interpolation was implemented in free energy methods for many purposes, from calculating intermediate energy states to deriving forces from free energy surfaces. The results of these calculations can provide insight into reaction mechanisms and their thermodynamic properties. The free energy methods include biased flat histogram methods, which are especially promising due to their ability to accurately construct free energy profiles at the rarely-visited regions of reaction spaces. Free Energies from Adaptive Reaction Coordinates (FEARCF) that was developed by Professor Kevin J. Naidoo has many advantages over the other flat histogram methods. iii Because of its treatment of the atoms in reactions, FEARCF makes it easier to apply interpolation methods. It implements cubic spline interpolation to derive biasing forces from the free energy surface, driving the reaction towards regions with higher energy. A major drawback of the method is the slowdown experienced in higher dimensions due to the complicated nature of the cubic spline routine. If the routine is replaced by a more straightforward B-spline interpolation, sampling and generating free energy surfaces can be accelerated. The dissertation aims to perform a comparative study between the cubic spline interpolation and B-spline interpolation methods. At first, data sets of analytic functions were used instead of numerical data to compare the accuracy and compute the percentage errors of both methods by taking the functions themselves as reference. These functions were used to evaluate the performances of the two methods at the endpoints, inflections points and regions with a steep gradient. Both interpolation methods generated identically approximated values with a percentage error below the threshold of 1%, although they both performed poorly at the endpoints and the points of inflection. Increasing the number of interpolation knots reduced the errors, however, it caused overfitting in the other regions. Although significant speed-up was not observed in the univariate interpolation, cubic spline suffered from a drastic slowdown in higher dimensions with up to 103 in 3D and 105 in 4D interpolations. The same results applied to the classical molecular dynamics simulations with FEARCF with a speed-up of up to 103 when B-spline interpolation was implemented. To conclude, the B-spline interpolation method can enhance the efficiency of the free energy calculations where cubic spline interpolation has been the currently-used method.
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Silva, Luiz Marcelo Chiesse da. "Geração de b-splines via FPGA." Universidade de São Paulo, 2012. http://www.teses.usp.br/teses/disponiveis/18/18152/tde-10102012-084652/.
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As b-splines são utilizadas em sistemas CAD/CAM/CAE para representar e definir curvas e superfícies complexas, sendo adotada pelos principais padrões da computação gráfica devido a características como representação matemática de forma compacta, flexibilidade e transformações afins. Em sistemas de aquisição de dados 3D e sistemas CAM-CNC integrados, a utilização da b-spline na transferência de informações geométricas e na reconstrução da superfície de objetos resulta em um significativo incremento na eficiência do processo, geralmente implementado em sistemas embarcados. Nestes sistemas embarcados, integrados no auxílio a máquinas de manufatura, a utilização de FPGAs é incipiente, sem circuitos para b-splines disponibilizados em lógica reconfigurável de circuito aberto (open core), razão pela qual este projeto propõe o desenvolvimento de um circuito de geração b-spline aberto, em um sistema embarcado FPGA, utilizando algoritmos adaptados para os circuitos, elaborados em linguagem Verilog HDL, padronizada para a síntese de circuitos em lógica reconfigurável. Os circuitos foram desenvolvidos, utilizando-se um barramento de dados padronizado em circuito aberto, nas seguintes implementações para processamento paralelo das b-splines: o BFEA, o método baseado em funções base fixas, ambos projetados para circuitos integrados, e o fast Cox-de Boor, desenvolvido para FPGAs. Foram comparados o tempo de execução e o consumo de recursos disponíveis no FPGA utilizado, entre cada implementação. Os resultados evidenciaram que os circuitos de funções base fixas apresentaram o processamento mais rápido para a geração de b-splines em um FPGA, com um tempo de execução em média 20% menor em relação às outras implementações. Os circuitos BFEA apresentaram a menor utilização de elementos lógicos, em média 50% menor em relação aos outros circuitos implementados. O circuito fast Cox-de Boor apresentou a melhor escalabilidade, devido à modularidade da implementação, com tempos de execução similares aos circuitos de funções base fixas.The b-splines are used in CAD/CAM/CAE systems to represent and define complex curves and surfaces, being adopted by the main computer graphics standards due to features like compact mathematic representation, flexibility and affine transformations. In 3D acquisition systems and integrated CAM-CNC systems, the use of the b-spline in the geometric information data transfer and in the object surface reconstruction results in a increase in the process efficiency, generally implemented in embedded systems. In these embedded systems, integrated in the aid to manufacturing machines, the use of FPGAs is incipient, without available b-splines open core circuits in reconfigurable logic, the reason why this project propose the development of a b-spline generation open core circuit, in a FPGA embedded system, using adaptated algorithms for the circuits, made in Verilog HDL language, standardized for the circuit synthesis in reconfigurable logic. The circuits were developed, using an open core standardized data bus, in the following implementations of b-spline parallel processing: the BFEA, fixed basis functions based method, both designed for integrated circuits, and the fast Cox-de Boor, developed for FPGAs. The execution time and available resource consumption in the FPGA were compared, between each implementation. The results show that the fixed basis functions circuits presented the fastest processing for the b-splines generation in a FPGA, with a 20% mean execution time reduction in relation to the other implementations. The BFEA circuits presented the lowest logic elements use, in mean 50% fewer in relation to the other implemented circuits. The fast Cox-De Boor circuit presented the best scalability, due to the implementation modularity, with execution times similar to the fixed basis functions circuits.
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Ferreira, de Oliveira Eric. "Reconstrução Tomográfica com superfícies B-splines." Universidade Federal de Pernambuco, 2011. https://repositorio.ufpe.br/handle/123456789/9445.
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Previous issue date: 2011Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
Vários estudos têm indicado que, das várias classes de algoritmos de reconstrução aplicáveis para dados limitados, os baseados na técnica de reconstrução algébrica são mais flexíveis e precisos. Infelizmente, estas técnicas, geralmente, sofrem de ruídos ocasionados por processos de correção durante a reconstrução e também por inconsistências nos dados adquiridos pelos tomógrafos. O pós - processamento da imagem reconstruída com a aplicação de filtros pode ser feito para atenuar a presença de ruídos, mas geralmente atenuam também as descontinuidades presentes em bordas que distinguem objetos ou falhas. O presente trabalho propõe a redução de ruídos assegurando a continuidade (das derivadas) da superfície antes da reconstrução, representando cada incógnita por uma combinação linear de pontos de controle e suas bases B-splines. São aplicadas três bases Bsplines: B1 , B2 e B3, assegurando as continuidade C0, C1 e C2, respectivamente. Para validação da técnica, foram utilizadas simulações de modelos propostos na literatura e medidas experimentais por tomografia gama. Os resultados foram comparados com as técnicas algébricas ART, SIRT, MART e SMART, sendo validada satisfatoriamente para todos os phantoms propostos. Todas as bases B-splines aplicadas obtiveram erros menores que as técnicas de correção ART e SIRT, sendo a B3, a de melhor desempenho. Este resultado pode ser explicado pelas restrições de suavidade impostas à superfície reconstruída pelas bases Bsplines e a inclinação das técnicas aditivas a ruídos, principalmente para um número limitado de dados (5 e 10 vistas). A performance das técnicas multiplicativas para essa situação é a melhor, mostrando uma imagem sem artefatos e com pouco ruído. Devido a esse fato, a técnica b-spline não tem bons resultados, apresentando na maioria dos casos, erros maiores. Para todos os testes realizados, as técnicas de representação B-splines superaram os filtros de mesma natureza aplicados no pós-processamento, sugerindo que a técnica seja utilizada no lugar da filtragem pós-processamento
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Corbin, Max. "Surface fitting head scan data sets." Ohio : Ohio University, 1999. http://www.ohiolink.edu/etd/view.cgi?ohiou1175886726.
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Grove, Olya. "Heterogeneous Modeling of Medical Image Data Using B-Spline Functions." Scholar Commons, 2011. http://scholarcommons.usf.edu/etd/3130.
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Ongoing developments in the field of medical imaging modalities have pushed the frontiers of modern medicine and biomedical engineering, prompting the need for new applications to improve diagnosis, treatment and prevention of diseases.
Biomedical data visualization and modeling rely predominately on manual processing and utilization of voxel and facet based homogeneous models. Biological structures are naturally heterogeneous and in order to accurately design and biomimic biological structures, properties such as chemical composition, size and shape of biological constituents need to be incorporated in the computational biological models.
Our proposed approach involves generating a density point cloud based on the intensity variations in a medical image slice, to capture tissue density variations through point cloud densities. The density point cloud is ordered and approximated with a set of cross-sectional least-squares B-Spline curves, based on which a skinned B-Spline surface is generated. The aim of this method is to capture and accurately represent density variations within the medical image data with a lofted surface function.
The fitted B-Spline surface is sampled at uniformly distributed parameters, and our preliminary results indicate that the bio-CAD model preserves the density variations of the original image based point cloud. The resultant surface can thus be visualized by mapping the density in the parametric domain into color in pixel domain. The B-Spline function produced from each image slice can be used for medical visualization and heterogeneous tissue modeling. The process can be repeated for each slice in the medical dataset to produce heterogeneous B-Spline volumes.
The emphasis of this research is placed on accuracy and shape fidelity needed for medical operations.
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Nandihalli, Sunil S. "A B-spline geometric modeling methodology for free surface simulation." Master's thesis, Mississippi State : Mississippi State University, 2004. http://library.msstate.edu/etd/show.asp?etd=etd-04072004-185017.
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Tjung, Jie Wen. "Projection, design, and representation of curves on B-spline surfaces /." This resource online, 1993. http://scholar.lib.vt.edu/theses/available/etd-03042009-040805/.
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Coe, David H. "Skinning engineering models with non-uniform, hierarchical B-spline surfaces." Thesis, This resource online, 1993. http://scholar.lib.vt.edu/theses/available/etd-09052009-040656/.
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Gloudemans, James R. "Filleting of aircraft components using non-uniform B-spline surfaces." Thesis, Virginia Tech, 1989. http://hdl.handle.net/10919/44637.
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Conceptual and preliminary aircraft design codes have different geometry requirements. Conceptual design codes use component based models, while preliminary design codes require a more complete and integrated geometry. An automatic procedure to convert between the two types of models would prevent geometry inconsistencies and speed up the design process. This thesis describes some of the concepts and algorithms necessary to develop such a procedure. Specifically, the theory and development of C2 continuous fillets between aircraft components is discussed. B-spline surface generation from conceptual geometry data and the relimiting of e surfaces is also presented. Master of Science
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Tjung, Jie Wen. "Projection, design, and representation of curves on B-spline surfaces." Thesis, Virginia Tech, 1992. http://hdl.handle.net/10919/41412.
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Zhang, Xinyu. "Optimal Geometric Trimming of B-spline Surfaces for Aircraft Design." Diss., Virginia Tech, 2005. http://hdl.handle.net/10919/28270.
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B-spline surfaces have been widely used in aircraft design to represent different types of components in a uniform format. Unlike the visual trimming of B-spline surfaces, which hides unwanted portions in rendering, the geometric trimming approach provides a mathematically clean representation. This dissertation focuses on the geometric trimming of fuselage and wing components represented by B-spline surfaces.
To trim two intersecting surfaces requires finding their intersections effectively. Most of the existing algorithms focus on providing intersections suitable for rendering. In this dissertation, an intersection algorithm suitable for geometric trimming of B-spline surfaces is presented. The number of intersection points depends on the number of isoparametric curves selected, and thus is controllable and independent of the error bound of intersection points.
Trimming curves are classified and a new scheme for trimming by a closed trimming curve is provided to improve the accuracy. The surface trimmed by a closed trimming curve is subdivided into four patches and the trimming curve is converted into two open trimming curves. Two surface patches are created by knot insertion, which match the original surface exactly. The other two surface patches are trimmed by the converted open trimming curves. Factors affecting the trimming process are discussed and metrics are provided to measure trimming errors.
Exact trimming is precluded due to the high degree of intersections. The process may lead to significant deviation from the corresponding portion on the original surface. Optimizations are employed to minimize approximation errors and obtain higher accuracy. The hybrid Parallel Tempering and Simulated Annealing optimization method, which is an effective algorithm to overcome the slow convergence waiting dilemma and initial value sensitivity, is applied for the minimization of B-spline surface representation errors. The results confirm that trimming errors are successfully reduced.Ph. D.
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Bindiganavle, Karthik. "An optimal approach to geometric trimming of B-spline surfaces." Thesis, Virginia Tech, 2000. http://hdl.handle.net/10919/31767.
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Geometric trimming of a surface involves removal of unwanted portions of the surface and providing a new mathematical description for the trimmed patch. This entails creating a new geometry for the trimmed patch, which closely approximates the corresponding portion on the original patch. The procedure is shown to involve obtaining data points on the B-spline surface that lie within the region specified by the parameter values for the trimming curve and describing a new surface which interpolates this new set of data points. This research looks at optimizing the procedure described above by basing the choice of parameter values for the trimming curve, at points where curvature optima occur over the surface. A visualization tool kit has been developed using OpenGL, as a means to discern the difference between the two surfaces. In order to quantify and aid in minimizing the error (difference) in approximating the original surface with the trimmed patch, an error measurement tool developed in MATLAB has been employed.Master of Science
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Wang, Hongrui. "Error and stability analysis for B-spline finite element methods." Thesis, University of Strathclyde, 2015. http://oleg.lib.strath.ac.uk:80/R/?func=dbin-jump-full&object_id=26570.
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The thesis studies the approximation properties of splines with maximum smoothness. We are interested in the behaviour of the approximation as the degree of the spline increases (so does its smoothness). By studying B-spline interpolation, we obtain error estimates measured in the semi-norm that are explicit in terms of mesh size, degree and smoothness. This new result also gives a higher approximation order than existing estimations. With the results, we investigate the B-spline finite element approximation with k-refinement, which is a strategy of improving the accuracy by increasing the degree and smoothness. The problem is studied in the setting of heat equations and wave equations. We give B-spline FEM schemes for the problems, and obtain error estimates. Moreover, by proving a Markov-type inequality for splines, where an exact constant is derived, we deduce how the stability of the scheme behaves with the k-refinements. We also improve the efficiency of the schemes for problems with periodic boundary conditions by applying the fast Fourier transform. The thesis also focuses on developing algorithms for efficiently evaluating the element system matrices in finite element methods with Berstein-Bâezier splines as shape functions, where the splines are of arbitrary order and defined on quadrilaterals and hexahedrons. The algorithms achieve the optimal complexity by making use of the sum factorial procedure. We test the algorithms in C++ implementation, and the numerical results illustrate that the optimal cost and expected accuracy are achieved.
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Wang, Xijun. "Geometric Trimming and Curvature Continuous Surface Blending for Aircraft Fuselage and Wing Shapes." Thesis, Virginia Tech, 2001. http://hdl.handle.net/10919/31664.
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Most of the work accomplished on surface blending is based on visual trimming. In the process of visual trimming, the unwanted portion of a surface is only hidden but not removed. Geometric trimming provides a complete mathematical description of the wanted portion of the trimming surface, and generates a new mathematical surface or sets of surface patches. The new surface is intended to resemble closely the corresponding portion of the original surface. A robust procedure is developed to geometrically trim the intersecting surfaces and blend the trimmed surface patches into one new surface. This research generates a filleting algorithm for surface blending of an aircraft fuselage shape and a wing shape at a closed trimming intersection curve, and verifies the properties of the newly created surface. In order to distinguish how well the new surface approximates the original, an error comparison tool developed in MATLAB has been employed.Master of Science
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Almeida, Adriano Del Vigna de. "B-Spline : CAEP - algoritmos culturais para a geração de trajetórias B-Spline de robôs móveis / Adriano Del Vigna de Almeida ; orientador, Leandro dos Santos Coelho." reponame:Biblioteca Digital de Teses e Dissertações da PUC_PR, 2005. http://www.biblioteca.pucpr.br/tede/tde_busca/arquivo.php?codArquivo=461.
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Dissertação (mestrado) - Pontifícia Universidade Católica do Paraná, Curitiba, 2005Inclui bibliografia
Pode se dizer que a geração de trajetórias é o mote principal da robótica móvel. Um robô, incapaz de percorrer uma trajetória livre de obstáculo, de forma a atingir um objetivo pré-definido, poderia inclusive deixar de ser chamado de robô móvel. A geração
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Mössner, Bernhard [Verfasser]. "B-Splines als Finite Elemente / Bernhard Mössner." Aachen : Shaker, 2006. http://d-nb.info/1186582669/34.
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Henriksen, Ian Daniel. "Evaluation and Refinement of Generalized B-splines." BYU ScholarsArchive, 2015. https://scholarsarchive.byu.edu/etd/5887.
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In this thesis a method for direct evaluation of Generalized B-splines (GB-splines) via the representation of these curves as piecewise functions is presented. A local structure is introduced that makes the GB-spline curves more amenable to the integration used in constructing bases of higher degree. This basis is used to perform direct computation of piecewise representation of GB-spline bases and curves. Algorithms for refinement using these local structures are also developed.
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Marcaly, Fred W. "Data reduction and knot removal for non-uniform B-spline surfaces." Thesis, Virginia Tech, 1991. http://hdl.handle.net/10919/40638.
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CÉSAR, Vinícius Miranda. "Rastreamento e reconstrução de dutos em ambiente submarino." Universidade Federal de Pernambuco, 2015. https://repositorio.ufpe.br/handle/123456789/16308.
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CNPq
A instalação de dutos flexíveis em ambiente submarino de alta profundidade é realizada recorrentemente pelas indústrias de óleo e gás. Estes dutos transportam fluidos como água, gases e óleo. Durante o minucioso processo de instalação dos dutos flexíveis, é necessário o monitoramento constante de sua geometria a fim de evitar a propagação de esforços e consequentemente danos aos equipamentos envolvidos. Para que este monitoramento seja eficiente, podem ser utilizadas técnicas de reconstrução 3D que usam como entrada as imagens capturadas por um par de câmeras estéreo instaladas nos robôs que acompanham a operação. Esta dissertação de mestrado propõe o desenvolvimento dos algoritmos de rastreamento e reconstrução para dutos flexíveis com o intuito de permitir o monitoramento em tempo real da operação. O algoritmo de rastreamento proposto tem a função de determinar um conjunto de pontos que representam a projeção do eixo medial do duto em cada imagem do par estéreo. Para alcançar esse objetivo, o algoritmo utiliza características da iluminação em ambientes submarinos e de marcações realizadas no duto. A etapa de reconstrução utiliza os pontos rastreados para estimar uma curva B-spline racional não-uniforme (NURBS) sobre um plano tridimensional. Essa aproximação simplifica o processo de reconstrução e permite obter resultados mais precisos. Experimentos realizados em ambiente aquático e aéreo, utilizando uma escala reduzida, permitiram uma análise da acurácia e robustez dos algoritmos propostos. O erro médio alcançado foi menor que meio centímetro em todos os casos analisados. Além disso, concluiu-se que a disposição dos pontos da curva e a posição do plano influenciam na estimativa da reconstrução. Testes com imagens reais da operação foram também realizados e permitiram validar as técnicas propostas neste ambiente. Os resultados obtidos foram robustos em casos de baixa iluminação, ruidosos e com elevada obliquidade. Os métodos propostos são eficientes computacionalmente e permitem a obtenção do resultado a uma taxa superior a 30 quadros por segundo.
Installing flexible pipes in deep underwater environments is a recurrent task in oil production industry. Such flexible pipes are responsible for transporting fluids such as water, gases and oil. The installation pipe connections is a meticulous process that requires continuous monitoring of the pipe’s geometry in order to prevent excessive tension along the line that may cause costly damages to the end equipment. This master thesis develops a 3D reconstruction method to ensure the success of this critical operation. The model makes use of images captured by a stereo rig mounted on the robots supporting the operation. At the heart of the model is a novel algorithm for tracking and reconstructing flexible pipes in order to allow real time pipe monitoring during the installation operation. Our approach tracks a set of points that represents the pipe’s projected medial axis in each image provided by the stereo rig. This is achieved using the scene’s specifications including the as deep-water environment illumination and marks pre-painted over the used pipes. The reconstruction stage uses the tracked points to estimate a plane non-uniform rational B-spline (NURBS) in 3D space. This approximation simplifies the reconstruction and i8s shown to improve accuracy. Underwater and aerial experiments were performed in a reduced scale scenario to evaluate the proposed method’s accuracy and robustness. In all test cases, the mean of reconstruction error was less than 1 centimeter. Furthermore, we conclude that the points’ distribution along the pipeline and the curve plane position impact the reconstruction’s accuracy. In addition, tests carried out using real operation videos were performed. They allowed us to validate our technical proposal in this harsh environment. The results obtained were robust in almost all the analyzed cases. The proposed methods are computationally efficient and allow obtaining results at a rate of 30 frames per second or higher.
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De, Faria Sergio Manuel Maciel. "Very low bit rate video coding using geometric transform motion compensation." Thesis, University of Essex, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.309768.
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Berchtold, J. "The Bernstein basis in set-theoretic geometric modelling." Thesis, University of Bath, 2000. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.323604.
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Ondřej, Josef. "Expektilová regrese." Master's thesis, 2015. http://www.nusl.cz/ntk/nusl-334683.
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In this thesis we present an alternative to quantiles, which is known as expectiles. At first we define the notion of expectile of a distribution of ran- dom variable and then we show some of its basic properties such as linearity or monotonic behavior of τ-th expectile eτ in τ. Let (Y, X), Y ∈ R, X ∈ Rp be a ran- dom vector. We define conditional expectile of Y given X = x, which we denote eτ (Y |X = x). We introduce model of expectile regression eτ (Y |X = x) = x⊤ βτ , where βτ ∈ Rp and we examine asymptotic behavior of estimate of the regression coefficients βτ and ways how to calculate it. Further we introduce semiparametric expectile regression, which generalizes the previous case and adds restrictions on the estimate of the regression coefficients which enforce desired properties such as smoothness of fitted curves. We illustrate the use of theoretical results on me- chanographic data, which describe dependence of power and force of a jump on age of children and adolescents aged between 6 and 18. Keywords: expectiles, expectile regression, quantiles, penalized B-splines 1
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Tsao, Yu-Ming, and 曹育銘. "Continuity Adjustment of B-spline Surfaces." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/28350937295413573584.
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碩士國立臺灣大學
機械工程學研究所
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With the pursuit of automatic and efficiently industrial development, computer aided design has been played an important role in the industry. In response to the requirements of the work of imitation, reverse engineering is generated. Measuring the shape of products and a series of calculation including segmentation, surface reconstruction and surface adjustment are the steps of the reverse engineering process. Finally, we can reconstruct and analyze the CAD model of products and plan the product’s manufacture procedure. This research focus on continuity adjustment of surfaces in reverse engineering. In order to reach the smoothness of adjacent surfaces, the output of surface reconstruction has been adjusted and modified. This research implements the optimal continuity adjustment of surfaces by using the numerical methods and discussing the basic information of B-spline surfaces which are the main adjust target of the research. The final goal is to export surfaces, that fit G1 and G2 continuity.
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Owens, Brian C. "Implementation of B-splines in a Conventional Finite Element Framework." 2009. http://hdl.handle.net/1969.1/ETD-TAMU-2009-05-469.
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The use of B-spline interpolation functions in the finite element method (FEM)
is not a new subject. B-splines have been utilized in finite elements for many reasons. One reason is the higher continuity of derivatives and smoothness of B-splines.
Another reason is the possibility of reducing the required number of degrees of freedom compared to a conventional finite element analysis. Furthermore, if B-splines
are utilized to represent the geometry of a finite element model, interfacing a finite
element analysis program with existing computer aided design programs (which make
extensive use of B-splines) is possible.
While B-splines have been used in finite element analysis due to the aforementioned goals, it is difficult to find resources that describe the process of implementing
B-splines into an existing finite element framework. Therefore, it is necessary to document this methodology. This implementation should conform to the structure of
conventional finite elements and only require exceptions in methodology where absolutely necessary. One goal is to implement B-spline interpolation functions in a finite
element framework such that it appears very similar to conventional finite elements
and is easily understandable by those with a finite element background.
The use of B-spline functions in finite element analysis has been studied for
advantages and disadvantages. Two-dimensional B-spline and standard FEM have
been compared. This comparison has addressed the accuracy as well as the computational efficiency of B-spline FEM. Results show that for a given number of degrees of freedom, B-spline FEM can produce solutions with lower error than standard FEM.
Furthermore, for a given solution time and total analysis time B-spline FEM will
typically produce solutions with lower error than standard FEM. However, due to a
more coupled system of equations and larger elemental stiffness matrix, B-spline FEM
will take longer per degree of freedom for solution and assembly times than standard
FEM. Three-dimensional B-spline FEM has also been validated by the comparison
of a three-dimensional model with plane-strain boundary conditions to an equivalent
two-dimensional model using plane strain conditions.