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1
De, Santis Ruggero. "Curve spline generalizzate di interpolazione locale". Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2015. http://amslaurea.unibo.it/9016/.
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Questa tesi presenta un metodo generale per la costruzione di curve spline generalizzate di interpolazione locale. Costruiremo quest'ultime miscelando polinomi interpolanti generalizzati a blending function generalizzate. Verrano inoltre verificate sperimentalmente alcune delle proprietà di queste curve.
2
Baki, Isa. "Yield Curve Estimation By Spline-based Models". Master's thesis, METU, 2006. http://etd.lib.metu.edu.tr/upload/12608050/index.pdf.
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This thesis uses Spline-based model, which was developed by McCulloch, and parsimonious model, which was developed by Nelson-Siegel, to estimate the yield curves of zero-coupon bonds in Turkey. In this thesis, we construct the data by using Turkish secondary government zero-coupon bond data, which contain the data from January 2005 to June 2005. After that, relative performances of models are compared using in-sample goodness of fit. As a result, we see that performance of McCulloch model in fitting yield is better than that of Nelson-Siegel model.
3
Randrianarivony, Maharavo, i Guido Brunnett. "Parallel implementation of curve reconstruction from noisy samples". Universitätsbibliothek Chemnitz, 2006. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200600519.
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This paper is concerned with approximating noisy
samples by non-uniform rational B-spline curves
with special emphasis on free knots. We show how to
set up the problem such that nonlinear optimization
methods can be applied efficiently. This involves
the introduction of penalizing terms in order to
avoid undesired knot positions. We report on our
implementation of the nonlinear optimization and we
show a way to implement the program in parallel.
Parallel performance results are described. Our
experiments show that our program has a linear
speedup and an efficiency value close to unity.
Runtime results on a parallel computer are
displayed.
4
Antonelli, Michele. "New strategies for curve and arbitrary-topology surface constructions for design". Doctoral thesis, Università degli studi di Padova, 2015. http://hdl.handle.net/11577/3423911.
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This dissertation presents some novel constructions for curves and surfaces with arbitrary topology in the context of geometric modeling.
In particular, it deals mainly with three intimately connected topics that are of interest in both theoretical and applied research: subdivision surfaces, non-uniform local interpolation (in both univariate and bivariate cases), and spaces of generalized splines.
Specifically, we describe a strategy for the integration of subdivision surfaces in computer-aided design systems and provide examples to show the effectiveness of its implementation.
Moreover, we present a construction of locally supported, non-uniform, piecewise polynomial univariate interpolants of minimum degree with respect to other prescribed design parameters (such as support width, order of continuity and order of approximation).
Still in the setting of non-uniform local interpolation, but in the case of surfaces, we devise a novel parameterization strategy that, together with a suitable patching technique, allows us to define composite surfaces that interpolate given arbitrary-topology meshes or curve networks and satisfy both requirements of regularity and aesthetic shape quality usually needed in the CAD modeling framework.
Finally, in the context of generalized splines, we propose an approach for the construction of the optimal normalized totally positive (B-spline) basis, acknowledged as the best basis of representation for design purposes, as well as a numerical procedure for checking the existence of such a basis in a given generalized spline space.
All the constructions presented here have been devised keeping in mind also the importance of application and implementation, and of the related requirements that numerical procedures must satisfy, in particular in the CAD context.Questa tesi presenta alcune nuove costruzioni per curve e superfici a topologia arbitraria nel contesto della modellazione geometrica. In particolare, riguarda principalmente tre argomenti strettamente collegati tra loro che sono di interesse sia nella ricerca teorica sia in quella applicata: le superfici di suddivisione, l'interpolazione locale non-uniforme (nei casi univariato e bivariato), e gli spazi di spline generalizzate. Nello specifico, descriviamo una strategia per l'integrazione di superfici di suddivisione in sistemi di progettazione assistita dal calcolatore e forniamo degli esempi per mostrare l'efficacia della sua implementazione. Inoltre, presentiamo un metodo per la costruzione di interpolanti univariati polinomiali a tratti, non-uniformi, a supporto locale e che hanno grado minimo rispetto agli altri parametri di progettazione prescritti (come l'ampiezza del supporto, l'ordine di continuità e l'ordine di approssimazione). Sempre nel contesto dell'interpolazione locale non-uniforme, ma nel caso di superfici, introduciamo una nuova strategia di parametrizzazione che, insieme a una opportuna tecnica di patching, ci permette di definire superfici composite che interpolano mesh o network di curve a topologia arbitraria e che soddisfano i requisiti di regolarità e di qualità estetica di forma solitamente richiesti nell'ambito della modellazione CAD. Infine, nel contesto delle spline generalizzate, proponiamo un approccio per la costruzione della base (B-spline) ottimale, normalizzata, totalmente positiva, riconosciuta come la miglior base di rappresentazione ai fini della progettazione. In aggiunta, forniamo una procedura numerica per controllare l'esistenza di una tale base in un dato spazio di spline generalizzate. Tutte le costruzioni qui presentate sono state ideate tenendo in considerazione anche l'importanza delle applicazioni e dell'implementazione, e dei relativi requisiti che le procedure numeriche devono soddisfare, in particolare nel contesto CAD.
5
Popiel, Tomasz. "Geometrically-defined curves in Riemannian manifolds". University of Western Australia. School of Mathematics and Statistics, 2007. http://theses.library.uwa.edu.au/adt-WU2007.0119.
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[Truncated abstract] This thesis is concerned with geometrically-defined curves that can be used for interpolation in Riemannian or, more generally, semi-Riemannian manifolds. As in much of the existing literature on such curves, emphasis is placed on manifolds which are important in computer graphics and engineering applications, namely the unit 3-sphere S3 and the closely related rotation group SO(3), as well as other Lie groups and spheres of arbitrary dimension. All geometrically-defined curves investigated in the thesis are either higher order variational curves, namely critical points of cost functionals depending on (covariant) derivatives of order greater than 1, or defined by geometrical algorithms, namely generalisations to manifolds of algorithms from the field of computer aided geometric design. Such curves are needed, especially in the aforementioned applications, since interpolation methods based on applying techniques of classical approximation theory in coordinate charts often produce unnatural interpolants. However, mathematical properties of higher order variational curves and curves defined by geometrical algorithms are in need of substantial further investigation: higher order variational curves are solutions of complicated nonlinear differential equations whose properties are not well-understood; it is usually unclear how to impose endpoint derivative conditions on, or smoothly piece together, curves defined by geometrical algorithms. This thesis addresses these difficulties for several classes of curves. ... The geometrical algorithms investigated in this thesis are generalisations of the de Casteljau and Cox-de Boor algorithms, which define, respectively, polynomial B'ezier and piecewise-polynomial B-spline curves by dividing, in certain ratios and for a finite number of iterations, piecewise-linear control polygons corresponding to finite sequences of control points. We show how the control points of curves produced by the generalised de Casteljau algorithm in an (almost) arbitrary connected finite-dimensional Riemannian manifold M should be chosen in order to impose desired endpoint velocities and (covariant) accelerations and, thereby, piece the curves together in a C2 fashion. A special case of the latter construction simplifies when M is a symmetric space. For the generalised Cox-de Boor algorithm, we analyse in detail the failure of a fundamental property of B-spline curves, namely C2 continuity at (certain) knots, to carry over to M.
6
Qu, Ruibin. "Recursive subdivision algorithms for curve and surface design". Thesis, Brunel University, 1990. http://bura.brunel.ac.uk/handle/2438/5447.
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In this thesis, the author studies recursIve subdivision algorithms for curves and surfaces. Several subdivision algorithms are constructed and investigated. Some graphic examples are also presented. Inspired by the Chaikin's algorithm and the Catmull-Clark's algorithm, some non-uniform schemes, the non-uniform corner cutting scheme and the recursive subdivision algorithm for non-uniform B-spline curves, are constructed and analysed. The adapted parametrization is introduced to analyse these non-uniform algorithms. In order to solve the surface interpolation problem, the Dyn-Gregory-Levin's 4-point interpolatory scheme is generalized to surfaces and the 10-point interpolatory subdivision scheme for surfaces is formulated. The so-called Butterfly Scheme, which was firstly introduced by Dyn, Gregory Levin in 1988, is just a special case of the scheme. By studying the Cross-Differences of Directional Divided Differences, a matrix approach for analysing uniform subdivision algorithms for surfaces is established and the convergence of the 10-point scheme over both uniform and non-uniform triangular networks is studied. Another algorithm, the subdivision algorithm for uniform bi-quartic B-spline surfaces over arbitrary topology is introduced and investigated. This algorithm is a generalization of Doo-Sabin's and Catmull-Clark's algorithms. It produces uniform Bi-quartic B-spline patches over uniform data. By studying the local subdivision matrix, which is a circulant, the tangent plane and curvature properties of the limit surfaces at the so-called Extraordinary Points are studied in detail.
7
González, Cindy. "Les courbes algébriques trigonométriques à hodographe pythagorien pour résoudre des problèmes d'interpolation deux et trois-dimensionnels et leur utilisation pour visualiser les informations dentaires dans des volumes tomographiques 3D". Thesis, Valenciennes, 2018. http://www.theses.fr/2018VALE0001/document.
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Les problèmes d'interpolation ont été largement étudiés dans la Conception Géométrique Assistée par Ordinateur. Ces problèmes consistent en la construction de courbes et de surfaces qui passent exactement par un ensemble de données. Dans ce cadre, l'objectif principal de cette thèse est de présenter des méthodes d'interpolation de données 2D et 3D au moyen de courbes Algébriques Trigonométriques à Hodographe Pythagorien (ATPH). Celles-ci sont utilisables pour la conception de modèles géométriques dans de nombreuses applications. En particulier, nous nous intéressons à la modélisation géométrique d'objets odontologiques. À cette fin, nous utilisons les courbes spatiales ATPH pour la construction de surfaces développables dans des volumes odontologiques. Initialement, nous considérons la construction de courbes planes ATPH avec continuité C² qui interpolent une séquence ordonnée de points. Nous employons deux méthodes pour résoudre ce problème et trouver la « bonne » solution. Nous étendons les courbes ATPH planes à l'espace tridimensionnel. Cette caractérisation 3D est utilisée pour résoudre le problème d'interpolation Hermite de premier ordre. Nous utilisons ces splines ATPH spatiales C¹ continues pour guider des facettes développables, qui sont déployées à l'intérieur de volumes tomodensitométriques odontologiques, afin de visualiser des informations d'intérêt pour le professionnel de santé. Cette information peut être utile dans l'évaluation clinique, diagnostic et/ou plan de traitementInterpolation problems have been widely studied in Computer Aided Geometric Design (CAGD). They consist in the construction of curves and surfaces that pass exactly through a given data set, such as point clouds, tangents, curvatures, lines/planes, etc. In general, these curves and surfaces are represented in a parametrized form. This representation is independent of the coordinate system, it adapts itself well to geometric transformations and the differential geometric properties of curves and surfaces are invariant under reparametrization. In this context, the main goal of this thesis is to present 2D and 3D data interpolation schemes by means of Algebraic-Trigonometric Pythagorean-Hodograph (ATPH) curves. The latter are parametric curves defined in a mixed algebraic-trigonometric space, whose hodograph satisfies a Pythagorean condition. This representation allows to analytically calculate the curve's arc-length as well as the rational-trigonometric parametrization of the offsets curves. These properties are usable for the design of geometric models in many applications including manufacturing, architectural design, shipbuilding, computer graphics, and many more. In particular, we are interested in the geometric modeling of odontological objects. To this end, we use the spatial ATPH curves for the construction of developable patches within 3D odontological volumes. This may be a useful tool for extracting information of interest along dental structures. We give an overview of how some similar interpolating problems have been addressed by the scientific community. Then in chapter 2, we consider the construction of planar C2 ATPH spline curves that interpolate an ordered sequence of points. This problem has many solutions, its number depends on the number of interpolating points. Therefore, we employ two methods to find them. Firstly, we calculate all solutions by a homotopy method. However, it is empirically observed that only one solution does not have any self-intersections. Hence, the Newton-Raphson iteration method is used to directly compute this \good" solution. Note that C2 ATPH spline curves depend on several free parameters, which allow to obtain a diversity of interpolants. Thanks to these shape parameters, the ATPH curves prove to be more exible and versatile than their polynomial counterpart, the well known Pythagorean-Hodograph (PH) quintic curves and polynomial curves in general. These parameters are optimally chosen through a minimization process of fairness measures. We design ATPH curves that closely agree with well-known trigonometric curves by adjusting the shape parameters. We extend the planar ATPH curves to the case of spatial ATPH curves in chapter 3. This characterization is given in terms of quaternions, because this allows to properly analyze their properties and simplify the calculations. We employ the spatial ATPH curves to solve the first-order Hermite interpolation problem. The obtained ATPH interpolants depend on three free angular values. As in the planar case, we optimally choose these parameters by the minimization of integral shape measures. This process is also used to calculate the C1 interpolating ATPH curves that closely approximate well-known 3D parametric curves. To illustrate this performance, we present the process for some kind of helices. In chapter 4 we then use these C1 ATPH splines for guiding developable surface patches, which are deployed within odontological computed tomography (CT) volumes, in order to visualize information of interest for the medical professional. Particularly, we construct piecewise conical surfaces along smooth ATPH curves to display information related to the anatomical structure of human jawbones. This information may be useful in clinical assessment, diagnosis and/or treatment plan. Finally, the obtained results are analyzed and conclusions are drawn in chapter 5
8
Ramaswami, Hemant. "A Novel Method for Accurate Evaluation of Size for Cylindrical Components". University of Cincinnati / OhioLINK, 2010. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1267548284.
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Ondroušková, Jana. "Modelování NURBS křivek a ploch v projektivním prostoru". Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2009. http://www.nusl.cz/ntk/nusl-228872.
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In the first part I discuss ancestors of NURBS curves and surfaces, rather Ferguson, Beziere, Coons and B-spline curves and surfaces and furthermore B-spline functions. In the second part I devote to NURBS curves and surfaces, their description as a linear combination of B-spline functions in the projective space. I specify conical arcs more detailed, their submit in the projective space and NURBS surfasec given as tensor product of NURBS curves. Last part is devote to describtion programs for modeling conicals and NURBS surface.
10
Škvarenina, Ľubomír. "Interpolace signálů pomocí NURBS křivek". Master's thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2014. http://www.nusl.cz/ntk/nusl-220618.
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Diploma thesis deals with image interpolation. The aim of this work is to study theoretically and then describe the nature of the various methods of image interpolation and some of them implemented in the program MATLAB. The introductory part of this work theoretically closer to important terms that are closely related to this topic of digital image processing sufficient to understand the principle. In the following of the thesis will be discussed all of today's commonly used method of image interpolation. Will hear all about the method of image interpolation using nearest neightbor interpolation and image help of polynimals such as (bi)linear, (bi)quadratic and (bi)kubic method. Then work theoretically analyzes the theory of individual species curves and splines. More specifically, coming to their most frequently used variants of B-spline curves and ther generalizations called NURBS, with addressing the problem of interpolating these curves. The final chapter consists of the results achieved in the program MATLAB.
11
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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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.
13
Xu, Bo. "Multiresolution editing for B-spline curves and surfaces". [Ames, Iowa : Iowa State University], 2008.
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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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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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Malina, Jakub. "Vytvoření interaktivních pomůcek z oblasti 2D počítačové grafiky". Master's thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2013. http://www.nusl.cz/ntk/nusl-219924.
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In this master’s thesis we focus on the basic properties of computer curves and their practical applicability. We explain how the curve can be understood in general, what are polynomial curves and their composing possibilities. Then we focus on the description of Bezier curves, especially the Bezier cubic. We discuss in more detail some of fundamental algorithms that are used for modelling these curves on computers and then we will show their practical interpretation. Then we explain non uniform rational B-spline curves and De Boor algorithm. In the end we discuss topic rasterization of segment, thick line, circle and ellipse. The aim of master’s thesis is the creation of the set of interactive applets, simulating some of the methods and algorithm we discussed in theoretical part. This applets will help facilitate understanding and will make the teaching more effective.
17
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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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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Gdhami, Asma. "Méthodes isogéométriques pour les équations aux dérivées partielles hyperboliques". Thesis, Université Côte d'Azur (ComUE), 2018. http://www.theses.fr/2018AZUR4210/document.
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L’Analyse isogéométrique (AIG) est une méthode innovante de résolution numérique des équations différentielles, proposée à l’origine par Thomas Hughes, Austin Cottrell et Yuri Bazilevs en 2005. Cette technique de discrétisation est une généralisation de l’analyse par éléments finis classiques (AEF), conçue pour intégrer la conception assistée par ordinateur (CAO), afin de combler l’écart entre la description géométrique et l’analyse des problèmes d’ingénierie. Ceci est réalisé en utilisant des B-splines ou des B-splines rationnelles non uniformes (NURBS), pour la description des géométries ainsi que pour la représentation de champs de solutions inconnus.L’objet de cette thèse est d’étudier la méthode isogéométrique dans le contexte des problèmes hyperboliques en utilisant les fonctions B-splines comme fonctions de base. Nous proposons également une méthode combinant l’AIG avec la méthode de Galerkin discontinue (GD) pour résoudre les problèmes hyperboliques. Plus précisément, la méthodologie de GD est adoptée à travers les interfaces de patches, tandis que l’AIG traditionnelle est utilisée dans chaque patch. Notre méthode tire parti de la méthode de l’AIG et la méthode de GD.Les résultats numériques sont présentés jusqu’à l’ordre polynomial p= 4 à la fois pour une méthode deGalerkin continue et discontinue. Ces résultats numériques sont comparés pour un ensemble de problèmes de complexité croissante en 1D et 2DIsogeometric Analysis (IGA) is a modern strategy for numerical solution of partial differential equations, originally proposed by Thomas Hughes, Austin Cottrell and Yuri Bazilevs in 2005. This discretization technique is a generalization of classical finite element analysis (FEA), designed to integrate Computer Aided Design (CAD) and FEA, to close the gap between the geometrical description and the analysis of engineering problems. This is achieved by using B-splines or non-uniform rational B-splines (NURBS), for the description of geometries as well as for the representation of unknown solution fields.The purpose of this thesis is to study isogeometric methods in the context of hyperbolic problems usingB-splines as basis functions. We also propose a method that combines IGA with the discontinuous Galerkin(DG)method for solving hyperbolic problems. More precisely, DG methodology is adopted across the patchinterfaces, while the traditional IGA is employed within each patch. The proposed method takes advantageof both IGA and the DG method.Numerical results are presented up to polynomial order p= 4 both for a continuous and discontinuousGalerkin method. These numerical results are compared for a range of problems of increasing complexity,in 1D and 2D
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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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Santos, Tyssia Nogueira Maciel dos. "AvaliaÃÃo genÃtica da curva de lactaÃÃo de cabras saanen utilizando modelos de regressÃo aleatÃria". Universidade Federal do CearÃ, 2014. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=13819.
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CoordenaÃÃo de AperfeÃoamento de Pessoal de NÃvel SuperiorO objetivo deste estudo foi realizar uma avaliaÃÃo genÃtico-quantitativa da curva de lactaÃÃo atà 305 dias de cabras da raÃa Saanen, avaliando distintos modelos de regressÃo aleatÃria para o melhor ajuste das trajetÃrias fixa e aleatÃrias desta curva, e assim estimar as covariÃncias e parÃmetros genÃticos associados a este perÃodo. Foram utilizados 11.018 controles leiteiros de 950 lactaÃÃes de cabras pertencentes a rebanhos associados ao Programa de Melhoramento GenÃtico de Caprinos Leiteiros (CaprageneÂ). Os efeitos fixos utilizados nas anÃlises foram de grupo de contemporÃneos, sexo das crias, tipo de ordenha e manejo. Foram avaliados 18 modelos, com diferentes ordens, para verificar o melhor ajuste simultÃneo das regressÃes para as trajetÃrias fixa e aleatÃrias (efeitos genÃticos aditivos diretos, de ambiente permanente e residual). Para ajuste da regressÃo fixa, foram utilizados os polinÃmios ordinÃrios e os polinÃmios ortogonais de Legendre, de segunda ordem. Para as regressÃes aleatÃrias, foram utilizados os polinÃmios ordinÃrios, os polinÃmios ortogonais de Legendre e as funÃÃes b-spline, variando da segunda a quarta ordem. O modelo com os polinÃmios ortogonais de Legendre de segunda ordem para a parte fixa e as funÃÃes b-spline de quarta ordem para a parte aleatÃria foi o mais adequado para o ajuste dos dados analisados. Na trajetÃria fixa, este modelo estimou o pico de lactaÃÃo entre 52-61 dias, com valor mÃdio de 2,378 kg de leite/dia. A curva iniciou-se com uma produÃÃo mÃdia de 2,298 kg/dia, encerrando aos 305 dias com uma produÃÃo mÃdia de 0,758 kg/dia. As estimativas de herdabilidade variaram de 0,294  0,135 a 0,794  0,075. Maior variabilidade genÃtica foi estimada para os controles leiteiros intermediÃrios na trajetÃria da curva de lactaÃÃo, entre 79 e 180 dias, com maiores estimativas de herdabilidade. As correlaÃÃes genÃticas entre os controles variaram entre 0,551  0,125 e 0,998  0,001, como maiores valores para produÃÃes de leite em dias prÃximos e subsequentes, e tornando-se menores à medida que os controles se distanciavam. A variabilidade genÃtica estimada indica que à possÃvel modificar por seleÃÃo a curva de lactaÃÃo das cabras Saanen da populaÃÃo estudada. Esta seleÃÃo deve ser realizada entre 79 e 180 dias de lactaÃÃo, perÃodo posterior ao pico de lactaÃÃo, entretanto onde se observaram as maiores herdabilidades. A seleÃÃo neste ponto permitirà alteraÃÃes na curva como um todo, em funÃÃo das respostas genÃticas correlacionadas.
The aim of this study was to perform a genetic-quantitative evaluation of the lactation curve up to 305 days of Saanen goats, fitting different random regression models to the best fit on the fixed and random trajectories of this curve and thus estimate the (co) variances and genetic parameters associated to this period. 11,018test-day milk yieldof 950 goats belonging to herds supported by the Dairy Goats Breeding Program (CaprageneÂ) were used. The fixed effects used in the analysis were contemporary group, sex of offspring, type of milking and management. 18 models with different orderswere evaluated, to verify the simultaneous best fit of the regressions for the fixed and random trajectories (direct additive genetic, permanent environmental and residual effects). Ordinary orthogonal polynomials and Legendre polynomials, of second order were used to fit the fixed regression. Ordinary polynomials, orthogonal Legendre polynomials and B-spline functions, ranging from second to fourth order, were used for fit the random regressions. The model with orthogonal Legendre polynomials of second order to the fixed part and the b-spline function of fourth order for the random part was the most suitable for the fitting of the data analyzed. In fixed path, this model estimated peak lactation between 52-61 days, with an average of 2.378 kg of milk / day. The curve began with an average yield of 2.298 kg / day, ending 305 days with an average yield of 0.758 kg / day. Heritability estimates ranged from 0.294 Â 0.135 to 0.794 Â 0.075. Greater genetic variability was estimated for the intermediate test-day yields in the trajectory of the lactation curve, between 79 and 180 days, with higher heritability estimates. Genetic correlations among the test-day yields ranged from 0.551 Â 0.125 and 0.998 Â 0.001, with higher values between milk yield in the next and subsequent days, and becoming smaller as the distanceamong the test-day yield increase. The estimated genetic variability indicates that it is possible to modify the lactation curve of Saanen goats of the study population. The selection should be performed between 79 and 180 days of lactation, after the peak of lactation, however where the greatest heritabilities were observed period. The selection on this point will change the curve as a whole on the basis of correlated genetic responses.
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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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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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Santos, Tyssia Nogueira Maciel dos. "Avaliação genética da curva de lactação de cabras saanen utilizando modelos de regressão aleatória". reponame:Repositório Institucional da UFC, 2014. http://www.repositorio.ufc.br/handle/riufc/19004.
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SANTOS, Tyssia Nogueira Maciel dos. Avaliação genética da curva de lactação de cabras saanen utilizando modelos de regressão aleatória. 2014. 51 f. : Dissertação (Mestrado) - Universidade Federal do Ceará, Centro de Ciências, Departamento de Zootecnia, Programa de Pós-Graduação em Zootecnia. Fortaleza-CE, 2014.Submitted by Eric Santiago (erichhcl@gmail.com) on 2016-08-09T13:21:33Z No. of bitstreams: 1 2014_dis_tnmsantos.pdf: 879224 bytes, checksum: 96fe44313df6f0e17fee9e748d618407 (MD5)
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The aim of this study was to perform a genetic-quantitative evaluation of the lactation curve up to 305 days of Saanen goats, fitting different random regression models to the best fit on the fixed and random trajectories of this curve and thus estimate the (co) variances and genetic parameters associated to this period. 11,018test-day milk yieldof 950 goats belonging to herds supported by the Dairy Goats Breeding Program (Capragene®) were used. The fixed effects used in the analysis were contemporary group, sex of offspring, type of milking and management. 18 models with different orderswere evaluated, to verify the simultaneous best fit of the regressions for the fixed and random trajectories (direct additive genetic, permanent environmental and residual effects). Ordinary orthogonal polynomials and Legendre polynomials, of second order were used to fit the fixed regression. Ordinary polynomials, orthogonal Legendre polynomials and B-spline functions, ranging from second to fourth order, were used for fit the random regressions. The model with orthogonal Legendre polynomials of second order to the fixed part and the b-spline function of fourth order for the random part was the most suitable for the fitting of the data analyzed. In fixed path, this model estimated peak lactation between 52-61 days, with an average of 2.378 kg of milk / day. The curve began with an average yield of 2.298 kg / day, ending 305 days with an average yield of 0.758 kg / day. Heritability estimates ranged from 0.294 ± 0.135 to 0.794 ± 0.075. Greater genetic variability was estimated for the intermediate test-day yields in the trajectory of the lactation curve, between 79 and 180 days, with higher heritability estimates. Genetic correlations among the test-day yields ranged from 0.551 ± 0.125 and 0.998 ± 0.001, with higher values between milk yield in the next and subsequent days, and becoming smaller as the distanceamong the test-day yield increase. The estimated genetic variability indicates that it is possible to modify the lactation curve of Saanen goats of the study population. The selection should be performed between 79 and 180 days of lactation, after the peak of lactation, however where the greatest heritabilities were observed period. The selection on this point will change the curve as a whole on the basis of correlated genetic responses.
O objetivo deste estudo foi realizar uma avaliação genético-quantitativa da curva de lactação até 305 dias de cabras da raça Saanen, avaliando distintos modelos de regressão aleatória para o melhor ajuste das trajetórias fixa e aleatórias desta curva, e assim estimar as covariâncias e parâmetros genéticos associados a este período. Foram utilizados 11.018 controles leiteiros de 950 lactações de cabras pertencentes a rebanhos associados ao Programa de Melhoramento Genético de Caprinos Leiteiros (Capragene®). Os efeitos fixos utilizados nas análises foram de grupo de contemporâneos, sexo das crias, tipo de ordenha e manejo. Foram avaliados 18 modelos, com diferentes ordens, para verificar o melhor ajuste simultâneo das regressões para as trajetórias fixa e aleatórias (efeitos genéticos aditivos diretos, de ambiente permanente e residual). Para ajuste da regressão fixa, foram utilizados os polinômios ordinários e os polinômios ortogonais de Legendre, de segunda ordem. Para as regressões aleatórias, foram utilizados os polinômios ordinários, os polinômios ortogonais de Legendre e as funções b-spline, variando da segunda a quarta ordem. O modelo com os polinômios ortogonais de Legendre de segunda ordem para a parte fixa e as funções b-spline de quarta ordem para a parte aleatória foi o mais adequado para o ajuste dos dados analisados. Na trajetória fixa, este modelo estimou o pico de lactação entre 52-61 dias, com valor médio de 2,378 kg de leite/dia. A curva iniciou-se com uma produção média de 2,298 kg/dia, encerrando aos 305 dias com uma produção média de 0,758 kg/dia. As estimativas de herdabilidade variaram de 0,294 ± 0,135 a 0,794 ± 0,075. Maior variabilidade genética foi estimada para os controles leiteiros intermediários na trajetória da curva de lactação, entre 79 e 180 dias, com maiores estimativas de herdabilidade. As correlações genéticas entre os controles variaram entre 0,551 ± 0,125 e 0,998 ± 0,001, como maiores valores para produções de leite em dias próximos e subsequentes, e tornando-se menores à medida que os controles se distanciavam. A variabilidade genética estimada indica que é possível modificar por seleção a curva de lactação das cabras Saanen da população estudada. Esta seleção deve ser realizada entre 79 e 180 dias de lactação, período posterior ao pico de lactação, entretanto onde se observaram as maiores herdabilidades. A seleção neste ponto permitirá alterações na curva como um todo, em função das respostas genéticas correlacionadas.
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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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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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Barbarini, Luiz Henrique Maiorino. "Síntese de cascos de embarcações através de métodos de otimização aplicados a curvas B-Spline". Universidade de São Paulo, 2007. http://www.teses.usp.br/teses/disponiveis/3/3152/tde-08052007-171701/.
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Este trabalho apresenta uma ferramenta flexível e eficiente para o campo de projeto e desenho preliminar de cascos de embarcações. O estado da arte de projeto de cascos de embarcações consiste em um processo iterativo onde, primeiramente, definem-se parâmetros geométricos, de estabilidade, e hidrodinâmicos. Em seguida, o casco é modelado através de curvas paramétricas. submetido a uma análise de desempenho, e, após isso, é feita a tomada de decisão para otimizar os parâmetros iniciais. O ciclo se repete até que se atinja o resultado desejado. O que será apresentado cumpre com a parte de modelagem paramétrica, e é capaz de gerar de forma automática e otimizada curvas que compõem o projeto de uma embarcação de recreio. A ferramenta recebe parâmetros de alto nível, como razões adimensionais, coeficientes de forma e restrições, e desenha tridimensionalmente um casco intrinsecamente suave, de forma que todos os parâmetros especificados sejam atendidos. Uma metodologia de projeto de cascos de veleiros é utilizada em conjunto com curvas B-Splines, submetidas a um algoritmo de otimização, em cuja função objetivo se empregam critérios de suavidade (\"fairness criteria\"). O problema de otimização de curvas B-Splines é não linear, pela própria formulação da função objetivo e suas restrições. Para tal, utiliza-se um método de Programação Quadrática Seqüencial. Para a otimização dos parâmetros principais do casco, utiliza-se uma metodologia de baixo custo, baseada na técnica de Superfície de Resposta, que otimiza uma função de mérito, no caso, a resistência residual, variando-se dois parâmetros do casco. A interface com softwares CAD é desenvolvida com o objetivo de se realizar outras análises, como de curvatura da superfície, além do projeto do restante da embarcação. Neste também pode ser gerado o bloco sólido para integração com softwares de CAM para a usinagem e fabricação do mesmo.This article presents a flexible and efficient tool to the field of ship project and preliminary design by using an approach of parametric modeling of hull forms. The state of the art of design of hulls consists in an iterative process where, first, geometric, stability and hydrodynamic parameters are defined. After that, the hull is modeled through parametric curves, simulated in a performance analysis software, and, after that, it is taken the decision to optimize the initial parameters. The cycle repeats until it reaches the desired result. This work deals with the part of parametric modeling, and is capable to generate, in an automatic way, optimized curves that compose the design of the hull of a yacht. The tool receives high level parameters, such as non-dimensional ratios, coefficients and restrictions, and draws a three-dimensional hull, intrinsically fair, fulfilling all the specified parameters. A methodology for the design of sail-boats is presented together with B-Splines curves, submitted to an optimization algorithm, using fairness criteria as the objective function. The optimization problem of B-Splines curves is not linear, because of its mathematical formulation, the objective function and constraints adopted. Therefore, a method of Sequential Quadratic Programming is used. For the optimization of the main parameters of the hull, a cost-effective methodology, based on the Surface Response Method, is proposed, optimizing a merit criterion, such as, the residuary resistance, changing two parameters of the hull. The interface with CAD software is implemented in order to allow other analyses, such as surface curvature, and the design of the other parts of the boat. The drawing also can be transformed into a solid model, and integrated with a CAM software to be ready for itsmanufacturing.
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Veciana, Joaquim M. (Joaquim Maria). "Reducció de vibracions residuals en moviments transitoris. Definició de lleis de moviment per mitjà de corbes B-spline". Doctoral thesis, Universitat de Girona, 2007. http://hdl.handle.net/10803/7768.
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Molts sistemes mecànics existents tenen un comportament vibratori funcionalment perceptible, que es posa de manifest enfront d'excitacions transitòries. Normalment, les vibracions generades segueixen presents després del transitori (vibracions residuals), i poden provocar efectes negatius en la funció de disseny del mecanisme.El mètode que es proposa en aquesta tesi té com a objectiu principal la síntesi de lleis de moviment per reduir les vibracions residuals. Addicionalment, els senyals generats permeten complir dues condicions definides per l'usuari (anomenats requeriments funcionals). El mètode es fonamenta en la relació existent entre el contingut freqüencial d'un senyal transitori, i la vibració residual generada, segons sigui l'esmorteïment del sistema. Basat en aquesta relació, i aprofitant les propietats de la transformada de Fourier, es proposa la generació de lleis de moviment per convolució temporal de polsos. Aquestes resulten formades per trams concatenats de polinomis algebraics, cosa que facilita la seva implementació en entorns numèrics per mitjà de corbes B-spline.
Many mechanical systems have a vibratory behavior, functionally noticeable, which can be raised when transient excitations happen. Usually, such generated vibrations remain in the system after this transient (residual vibrations), and may imply negative effects in the mechanism's intended function.
The method proposed in this thesis has as main objective, the synthesis of excitation signals for mechanical systems in order to reduce residual vibrations. In addition, generated signals are able to achieve two conditions defined by the user related to function of the mechanism (called functional requirements). This method is based on the relationship between the frequency contents of the transient signal and the residual vibration generated, depending on the system damping. From this relation, and taking advantage of the Fourier transform properties, motion laws are generated through the pulses' time convolution. Resultant laws are made up of algebraic polynomial pieces linked together, which makes them very suitable for implementation with numerical calculus through B-spline curves.
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Lins, Sidney de Oliveira. "Otimiza??o de forma aplicando B-splines sob crit?rio integral de tens?es". Universidade Federal do Rio Grande do Norte, 2009. http://repositorio.ufrn.br:8080/jspui/handle/123456789/15574.
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Previous issue date: 2009-02-09Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior
This work proposes a computational methodology to solve problems of optimization in structural design. The application develops, implements and integrates methods for structural analysis, geometric modeling, design sensitivity analysis and optimization. So, the optimum design problem is particularized for plane stress case, with the objective to minimize the structural mass subject to a stress criterion. Notice that, these constraints must be evaluated at a series of discrete points, whose distribution should be dense enough in order to minimize the chance of any significant constraint violation between specified points. Therefore, the local stress constraints are transformed into a global stress measure reducing the computational cost in deriving the optimal shape design. The problem is approximated by Finite Element Method using Lagrangian triangular elements with six nodes, and use a automatic mesh generation with a mesh quality criterion of geometric element. The geometric modeling, i.e., the contour is defined by parametric curves of type B-splines, these curves hold suitable characteristics to implement the Shape Optimization Method, that uses the key points like design variables to determine the solution of minimum problem. A reliable tool for design sensitivity analysis is a prerequisite for performing interactive structural design, synthesis and optimization. General expressions for design sensitivity analysis are derived with respect to key points of B-splines. The method of design sensitivity analysis used is the adjoin approach and the analytical method. The formulation of the optimization problem applies the Augmented Lagrangian Method, which convert an optimization problem constrained problem in an unconstrained. The solution of the Augmented Lagrangian function is achieved by determining the analysis of sensitivity. Therefore, the optimization problem reduces to the solution of a sequence of problems with lateral limits constraints, which is solved by the Memoryless Quasi-Newton Method It is demonstrated by several examples that this new approach of analytical design sensitivity analysis of integrated shape design optimization with a global stress criterion purpose is computationally efficient
Neste trabalho prop?e-se uma metodologia computacional para resolver problemas de Otimiza??o de Forma para projeto estrutural. A aplica??o ? particularizada para problemas bidimensionais em estado plano de tens?es, de modo a minimizar a massa atendendo um crit?rio de tens?o. Para atender ao crit?rio param?trico de tens?es ? proposto um crit?rio global de tens?o de von Mises, dessa maneira, amplia-se o crit?rio local de tens?es sobre o dom?nio, visando ? obten??o de programas mais seguros. O problema ? aproximado pelo M?todo dos Elementos Finitos utilizando elementos triangulares da base Lagrangiana padr?o com seis n?s, tendo uma estrat?gia de gera??o autom?tica de malhas baseada em um crit?rio geom?trico do elemento. O modelo geom?trico do contorno material ? definido por curvas param?tricas B-splines. Estas curvas possuem caracter?sticas vantajosas para implementa??o do processo de otimiza??o de forma, que se utiliza dos pontos-chave para determinar o m?nimo do problema. A formula??o do problema de otimiza??o faz uso do M?todo Lagrangiano Aumentado, que transforma o problema de otimiza??o com restri??o, em problema irrestrito. A solu??o da fun??o Lagrangiana Aumentada ? alcan?ada pela determina??o da an?lise das sensibilidades anal?ticas em rela??o aos pontos-chave da curva B-spline. Como conseq??ncia, o problema de otimiza??o reduz-se ? solu??o de uma seq??ncia de problemas de limites laterais do tipo caixa, o qual ? resolvido por um m?todo de proje??o de segunda ordem que usa o m?todo de Quase-Newton projetado sem mem?ria. S?o demonstrados v?rios exemplos para o M?todo de Otimiza??o de Forma integrado a An?lise da Sensibilidade Anal?tica sob o crit?rio global de tens?o de von Mises
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Špiřík, Jan. "Modul pro generování "atomů" pro přeparametrizovanou reprezentaci signálu". Master's thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2010. http://www.nusl.cz/ntk/nusl-218234.
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The aim of this master thesis is generating new "atoms'' for purposes of overcomplete signal representation for toolbox Frames in MATLAB. At first is described the principle of overcomplete systems and so-called frames. In the thesis is introduced the basic distribution of frames and conditions of their constructions. There is described the basic principle of finding the sparse solutions in overcomplete systems too. The main part is dealt with construction single functions for generating "atoms'', such as: Gabor function, B-splines, Bézier curves, Daubechies wavelets, etc. At last there is introduced an example of usage these functions for reconstruction signal in comparison with Fourier and wavelet transforms.
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Estecahandy, Elodie. "Contribution à l'analyse mathématique et à la résolution numérique d'un problème inverse de scattering élasto-acoustique". Phd thesis, Université de Pau et des Pays de l'Adour, 2013. http://tel.archives-ouvertes.fr/tel-00880628.
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La détermination de la forme d'un obstacle élastique immergé dans un milieu fluide à partir de mesures du champ d'onde diffracté est un problème d'un vif intérêt dans de nombreux domaines tels que le sonar, l'exploration géophysique et l'imagerie médicale. A cause de son caractère non-linéaire et mal posé, ce problème inverse de l'obstacle (IOP) est très difficile à résoudre, particulièrement d'un point de vue numérique. De plus, son étude requiert la compréhension de la théorie du problème de diffraction direct (DP) associé, et la maîtrise des méthodes de résolution correspondantes. Le travail accompli ici se rapporte à l'analyse mathématique et numérique du DP élasto-acoustique et de l'IOP. En particulier, nous avons développé un code de simulation numérique performant pour la propagation des ondes associée à ce type de milieux, basé sur une méthode de type DG qui emploie des éléments finis d'ordre supérieur et des éléments courbes à l'interface afin de mieux représenter l'interaction fluide-structure, et nous l'appliquons à la reconstruction d'objets par la mise en oeuvre d'une méthode de Newton régularisée.
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Kao, C. Z., i 高家榮. "Interference-free Curve Fitting with Arcs for B-Spline Curves". Thesis, 1997. http://ndltd.ncl.edu.tw/handle/86308884162677258777.
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碩士國立中興大學
機械工程學系
85
The object of this paper is to develop a efficinet algorithm to approximatea B-Spline curve. The algorithm is applied to construct a smooth curve withG1 continuity and without causing any interference.A B-Spline curve is decomposed into piecewise Bezier curves. Using convexhulls of the Bezier curves to protect the original curve from interferencethe line segments on the same side consist the approximating curve. Basedon the obtained approximating line segments, Biarcs fitting and Circularsingle- arc fitting methods are applied to construct a smooth curve with G1continuity and without causing any interference. If the resulting curve isapplied to generate tool paths for pocketing boundaries with B-Splinecurve, the overcutting problem can be eliminated completely and abruptdirection changes on tool paths can be greatly improved.
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Liu, Pin-hsiu, i 劉品秀. "Curve Design by C2 Cubic B-spline Curve''s Interpolation". Thesis, 2009. http://ndltd.ncl.edu.tw/handle/62783732709493433975.
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碩士國立中正大學
應用數學研究所
97
In there, we persent B-spline curves and C2 cubic B-spline interpolating curves. Next, we do curve design by C2 cubic B-spline interpolating curves to cover irregular shapes.
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陳秀娘. "New Vectorization for Solving B-spline Curve Fitting". Thesis, 1993. http://ndltd.ncl.edu.tw/handle/36894965925908020381.
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碩士國立臺灣科技大學
管理研究所資訊管理學程
81
Curve fitting is important in computer - aided design, graphics, pattern recognition, and picture processing. Using the matrix diagonalization method, this thesis gives a new and fast vectorized algorithm for solving the open B - spline curve fitting. The application of our result to solve the closed B - spline curve fitting is also investigated. Given a set of random points, we demon - strate the good performance of our algorithms on the CRAY X - MP EA / 16se supercomputer. Furthermore, we compare the performance of our algorithms (Fortran codes) with the ones using the subroutine 'folrc' (Assembly codes) in MATH LIBRARY ROUTINES and the ones using the subroutine 'sptsv' (Fortran codes) in LAPACK, respectively.
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Yi-HungKao i 高顗泓. "Lane Departure Warning using Line Hough Transform and B-spline Curve". Thesis, 2014. http://ndltd.ncl.edu.tw/handle/92404271452242590381.
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碩士國立成功大學
資訊工程學系
102
Lane departure warning is one of important parts in intelligent vehicle systems. This paper purpose a technique for lane markings detection and tracking. At first, lane boundaries are detected by line Hough transform. In edge detection, previous step of line Hough transform, we use Otsu’s method as an adaptive-thresholding method for Canny edge detection. To filter undesired detected line, so called noises, by line Hough transform, we employ two approaches, angle of lines and vanishing points, to come to the purpose. After lane markings are detected, we use lane tracking which is lower computation complexity and execution time to make our lane departure warning system real-time. Between detection and tracking, two judgment mechanisms are purposed. One is used to judge that it is going to detection or tracking, the other is used to judge whether lane departure. We collected several video and separate into two databases by cases to do experimenting.
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Chiu, Chih-Chi, i 邱智琦. "Implementation of Patrol Path on B-spline Curve for Wheeled Mobile Robots". Thesis, 2011. http://ndltd.ncl.edu.tw/handle/16396441046573079371.
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碩士中華科技大學
電子工程研究所碩士班
99
The purpose of this paper is to replace the security service personnel with wheeled mobile robot, perform the planned patrol route in advance to reduce the waste of human resources and the potential loss of security negligence. We mainly focus on the B-spline curve navigation mode and manual manipulate mode for the wheeled mobile robot.For B-spline curve navigation mode, Through the GUI platform of host computer, the patrol route of security personnel is planned with B-spline curve. Next, the planned patrol route can be converted into PWM servo machine signal of left and right wheels on host computer. The PWM signal sent to the robot through ZigBee module, so that the patrol route is planned according to B-spline curve design. For manual manipulate mode, a wireless remote control camera (CCD) mounted on the wheeled mobile robot's body structure, to capture the dynamic information environment surrounding the robot. With radio frequency technology, the capture video to send back to the host computer and displayed on the screen window. Remote user can instantly observe the robot dynamics and the surrounding environment, and make the corresponding response. For example, control the robot forward, backward and turn around, or control the robot gripping a bomb. Experimental results show that the proposed B-spline curve navigation mode and manual manipulate mode with ATMega162 embedded microcontroller as the core of the system are applicable, and gives good results.
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Wu, Hsin-I., i 吳新逸. "A Novel Method for G2 Continuity in 3D B-Spline Closed Curve Construction". Thesis, 2004. http://ndltd.ncl.edu.tw/handle/16031818011359015285.
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碩士國立成功大學
機械工程學系碩博士班
92
In the last two decades, the technology of computer-aided design and manufacturing (CAD/CAM) systems has evolved considerably due to the rapid growth in the development of computer hardware. Therefore, the design work changed from styling to CAD. The most complicated subject in CAD would be the design of surface and that is the reason why commercial CAD/CAM software vendors always emphasize the ability for constructing and editing surfaces. In general, a preferable surface is based on well-designed smooth curves. Sometimes a closed curve is needed. For example, when a designer designs the configuration of a cam wheel, closed curves are constructed and the cam wheel surface model passing through all curves is built. If unsmoothness occurs on curves, the surface would lose smoothness as well. In this study, a novel method that constructs smooth closed curves with G2 continuity is proposed. The method of B-spline curve interpolation is applied to construct the closed curve passing through the given points. Since B-splines are parts of graphics exchange standards such as IGES and STEP, so the curves and surfaces can be transmitted to commercial CAD/CAM systems for further engineering activities, e.g., analysis and manufacturing. The proposed algorithm can not only be employed in CAD systems but can also be employed in the reverse-engineering (RE) technique.
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Tu, Li-Jung, i 杜黎蓉. "Determining the Parameters of Rational B-spline Curve by the High Performance Computing". Thesis, 2003. http://ndltd.ncl.edu.tw/handle/41281804086096948725.
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碩士國立成功大學
工程科學系專班
91
Due to the high flexibility, smoothness, and multi-solutions of a numerical curve, which satisfies the engineering requirements, it is a key technology for the curve fitting of the reversal engineering to satisfy the smoothness and continuity properties of engineering requirements. There are orders, knot sequences, and weight sequences, for numerical curves to define the objective functions and which are to be minimized. But it''s a time-consuming process to determine the parameters of a numerical motion curve. The proposed high-performance method, for reducing the execution time, and the sieving method, for increasing the resolution, are used to determine the parameters of Rational B-spline in this thesis. The execution performance (speedup) by using a cluster of 8 PC''s can be raised up to 7.5 times. Experiments on a low-speed high-performance curve and a high-speed vibration-reduction curve for the intermittence motion are applied in automated devices and auto-tool-changer (ATC). The results show that they could decrease 25 % inertia actions and half amplitude of vibrations.
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Lin, Yang-Jie, i 林揚傑. "Non-Uniform Rational B-spline Curve Interpolator Apply to Selective Laser Sintering Electrical Circuits". Thesis, 2016. http://ndltd.ncl.edu.tw/handle/c88nsm.
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碩士國立交通大學
機械工程系所
105
In this thesis, we developed a selective laser sintering (SLS) system with NURBS curve interpolator, and sintering the silver nanoparticles ink on a flexible substrate. Take advantage of laser for reducing thermal damage of substrate, which allow us to use lower laser power to sinter the silver nanoparticles ink. To ensure that sintered silver nanoparticles can be used for conductive line, the experiment are designed for laser power in the range of 100 ~250 mW and the scanning speed in the range of 2~5 mm/s. The best electrical conductivity of the experiment result is used in the following experiment. In order to show if NURBS interpolator can effectively improve the continuity of laser scanning speed, by using a butterfly-shaped of NURBS curve as example to analyze the path of the motion stage. After sintering, traditional method (G01) with purposed method (G06) for the change rate of linewidth in the corner of the path are compared. At last, a planar spiral inductance for application is demonstrated.
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Chia-PinHsu i 許家彬. "Using B-Spline Curve to Build a Conical Spring in the Finite Element Analysis". Thesis, 2013. http://ndltd.ncl.edu.tw/handle/80748206374151655115.
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碩士國立成功大學
機械工程學系碩博士班
101
By using the B-Spline curve, the spring models have been built in this thesis. Since the B-Spline curve has the properties of local control and differential continuity, it is used to create the finite element model in stress analysis. The ANSYS program was used to simulate the barrel-shaped spring due to static load. The force-displacement curve, equivalent stresses and shear stress distribution are shown in the result. In the compression process of barrel-shaped spring, the inner equivalent stress is greater than outer, and the equivalent stresses of the top end and bottom end varied with different spring diameters. Distribution of shear stress is similar to the distribution of equivalent stress. By using the control points to change the geometry of spring, the performance of spring in force-displacement curve with varied parameters can be observed. The results show that the bigger the coil diameter, the greater the spring constant. The condition of contact between circuits should be considered in varied base diameters. The bigger base diameter, the less sliding distance, and the reaction force increased. Changing the spring pitch in the middle part will affect the contact condition that the spring is mostly compressed.
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Lin, Dong-Ying, i 林東瑩. "The Design and Implementation of a Non-Uniform Rational B-Spline Curve and Surface Chip". Thesis, 2000. http://ndltd.ncl.edu.tw/handle/29069599169491932475.
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碩士國立臺灣科技大學
電子工程系
88
B-Splines and Non-Uniform Rational B-Splines (NURBS) have become the essential modeling primitives in computer graphics and geometric modeling applications. In this thesis, we propose a modified NURBS algorithm incorporated with two useful properties, sum up to one and dynamic denominator. This novel algorithm provides less order and fewer division operations than the traditional algorithm reported in the literature. Based on this algorithm, a unified architecture for the computation of various types of B-Spline curves and surfaces is presented. The resultant chip, consisting of approximately 752 K transistors, occupies 3.1 mm by 3.1 mm area in the 0.35-μm SPQM CMOS technology. It operates at 100 MHz with two 16-bit data outputs and consumes only 920mW at a supply voltage of 3.3V. The output data rate is two 16-bit words per cycle, which corresponds to a pair of the coordinate values of a point and its normal on a curve/surface.
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Yeh, Shin-Chiao, i 葉星巧. "Dynamic Animal PET Imaging Using Listmode Data and B-Spline Activity Curve Description : A Pilot Investigation". Thesis, 2009. http://ndltd.ncl.edu.tw/handle/90052152118582741001.
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碩士國立清華大學
生醫工程與環境科學系
97
Dynamic PET imaging based on listmode data acquisition can provide timing information of coincidence events, which permit a flexible way to sort the data into several consecutive time frames. In this work, by using the listmode data combined with B-spline representation of radio-tracer time activity curve (TAC), we proposed a maximum likelihood expectation and maximization (MLEM) to estimate the parameters of TAC curve and restore the continuous TAC curve. Such a continuous TAC curve can provide better temporal resolution for dynamic PET imaging. In this pilot study, we evaluated the performance of the proposed method using clinical animal data acquired from an Inveon microPET scanner. We particularly focused on the FDG metabolic rate functions of heart and brain. Using these two organs as regions of interest (ROIs), the estimated TAC curves can depict the temporal variations of rate changes. In addition, the estimated TAC curves also matched with each other by using different sorting schemes (equal time and equal time). Since the listmode data can incorporate external signal inputs (like gating or respiratory signals), arbitrary temporal segmentation can be achieved as well. In future, we can combine such a generic segmentation into the proposed method and generate high-quality TAC curves corresponding to various physiological changes. The proposed method can be extended to 4D dynamic PET imaging which can make the best use of all collected events. It is optimistically anticipated that the proposed method can provide reliable radiotracer responses and will be useful for applications like drug development, therapy or diagnosis.
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Chuang, Jien-Ching, i 莊健青. "Ｂλ-spline Curves and Surface--B-spline Curves and Surfaces for Interpolation and Local Shape Control". Thesis, 1997. http://ndltd.ncl.edu.tw/handle/80142250601199053546.
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碩士國立臺灣大學
造船工程學系
85
In the field of Computer Aided Geometric Design, there are a lot of method can be used for representation or design of curves. Regarding the generating of free form curves, B-spline curve is one of the often used method. Problems are encountered when applying B-splines for interpolating a curve, because they can not represent some specified local curve shape very well. Bλ- spline curves are constructed by dividing a B-spline curve segment into λsub-segments for improving the drawbacks of the normal B-splines. Bλ-spline curves have excellent local shape control properties. With a set of given data points, it is possible not only to create acurve passing all of them but also to specify some geometrical properties such as slopes or curvature at them. Bλ-spline surface is defined by applying the Bλ-spline curve method extensively for design or representation of surface. Bλ-spline surfaces have also the same advantages as B-spline curves , because unsatisfied surface shapes can be modified easily ; so that they exhibit superior local control capability. Even some complicated surface ,such as ship hulls, can be also represented very exactly.
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Yeh, Shih-Yu, i 葉時有. "Hand-Shape Recognition Based on B-Spline Curves". Thesis, 2008. http://ndltd.ncl.edu.tw/handle/26787024552931776373.
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碩士國立暨南國際大學
電機工程學系
96
With an increasing emphasis on security, personal authentication based on biometrics has been receiving extensive attention over the past decade. Among many different biometric technologies, this thesis examines hand-shape technique for personal identification and develops a good performance recognition system based on human hand features. It is implemented and tested on VIP-CCL Lab. Hand image database. The proposed system includes four modules: image acquisition, image pre-processing, feature extraction, and recognition modules. First, the system captures a hand image using digital camera, then uses some image processing algorithms to localize the hand-geometry from the hand image via image pre-processing module. In the feature extraction module, we use 4 B-Spline curves to fit with fingers (except thumb) from a single hand image for a single person. Then we store these control points and curvatures of the B-Spline curves as well as other geometry measurements (the width of fingers) of the hand as the features of that person into the database. Finally, the system applies these features for matching in recognition module. Experimental results show that the system has an encouraging performance on the VIP-CC Lab. Database (including 600 images from 100 classes). The proposed system uses the control points 、the curvatures and the width of fingers to generate the features, we attain the recognition rates up to 95.55%(128bytes)、85.7%(32bytes)and 96.84%(96bytes) (according to equal error rate, EER), respectively. This thesis analyzes the experimented results and verifies the related inferences of the proposed system for providing useful information for further research.
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Menon, Midhun Sreekumar. "Motion Planning of Flexible One-dimensional Object and Hyper-redundant Robots". Thesis, 2016. http://etd.iisc.ac.in/handle/2005/4061.
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This thesis deals with motion planning of flexible one-dimensional objects and hyper-redundant serial robots moving in a plane or in three dimensional space. The flexible one-dimensional object is modeled as a continuous curve and a point on the curve is given a prescribed dis-placement. The key problem studied in the thesis is to obtain the motion of all points on the curve for the prescribed displacement subject to the condition of the length of the curve being preserved. Such motions are motivated by the need to model, analyze and realistically render of motion of hair, ropes and, more recently, flexible endoscopes where the assumption of constant axial length is realistic and reasonable. In this thesis, the discretized form of the flexible one-dimensional object is related to hyper-redundant robots and motion planning for such robots are obtained when the robot moves in free space and in a cluttered environment, avoiding obstacles.
The motion planning of flexible one-dimensional objects is posed as an optimization problem with constraints and calculus of variation is employed to derive general analytical results. The first analytical result is that, for a given motion of a point on the curve and subject to the preservation of the length of the curve, the infinitesimal motion of any other point on the curve is minimized when the velocity vector at that point of the curve is along the tangent to the curve at that point. This leads to the second key result that when one end of a straight line segment is moved along a straight line, the velocity of the distal (far) end is minimized when it is along the straight line segment and the curve traced by the distal end is the well-known tractrix curve whose closed-form analytic expressions can be obtained using hyperbolic functions. If the flexible one-dimensional object is discretized by several piece-wise straight line segments, the magnitude of the velocity vector of the distal end of the segments attenuates as one goes away from the end where the input displacement is provided and if the direction of the input displacement is not changed, all the line segments eventually line up along the direction of the input displacement. It is shown that the attenuating and eventual aligning features lead to realistic and a more natural motion of the discretized segments and results in the establishment of a O(n) algorithm for motion planning. It is shown that the developed algorithm can be used for real-time simulation of the motion of discretized flexible one-dimensional objects and hyper-redundant serial robots.
For realistic simulation and rendering of the motion, the flexible object must be discretized into a large number of straight segments. In the second part of the thesis, the flexible one-dimensional object is represented by a spline and motion planning algorithm is applied to the segments of the underlying control polygon of the spline. Since the number of segments in a control polygon can be significantly less, a significant increase in efficiency in simulation and rendering of the motion is obtained. However, it is known that as the control polygon is moved, the length of the spline curve changes. To overcome this problem, an innovative adaptive algorithm, involving sub-division and merging of the segments of the control polygon, is presented and this restricts the variation in the length of the curve to within a user prescribed tolerance. New analytical results related to the length of the curve and the angle between the adjacent segments of the control polygon are derived for quadratic and cubic splines and, depending on the prescribed tolerance, threshold values of the angle are obtained and used in the algorithm for approximate length preservation.
The last part of the thesis deals with development of a planar hyper-redundant robot and implementation of motion planning algorithm on this robot. The hyper-redundant robot contains 12 links connected by actuated rotary joints which can change the angle between the links in a controlled manner. The links are on the wheels which provide support and allow it to move forward. The leading link also has a DC motor which can rotate the wheels so that it can move forward and pull the trailing links. Using the motion planning algorithm, for a prescribed motion of the leading link, the angle between two successive links are computed. These are given as input to the robot and the path traced by the 12 link robot is observed. It is seen that the motion of the hyper-redundant robot has the expected natural and realistic motion characteristics. It is furthermore demonstrated that the calculus of variation based approach for motion planning can be extended to include obstacle avoidance by adding additional constraints related to the location and size of the obstacles. It is shown that the entire robot optimally avoids the obstacles and moves in a more natural and realistic way.
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Tsai, Chang-Yu, i 蔡昌佑. "CONNECTING OF TWO C^2 CUBIC B-SPLINE CURVES". Thesis, 2010. http://ndltd.ncl.edu.tw/handle/09070942691841201239.
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碩士國立中正大學
應用數學研究所
98
In this thesis, we will introduce the Bezier curve and the B-spline curve, and their derivative. First, we find the condition of connecting of two C^2 cubic Bezier curve, and choose the knot sequence such that the B-spline curve go through them. Second, we find the condition of connecting of two C^2 cubic B-spline curve, and choose the knot sequence such that the new B-spline curve go through them.
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CHEN, CHAO-MING, i 陳超明. "Curved surface design using parametric B-splines". Thesis, 1991. http://ndltd.ncl.edu.tw/handle/68992547031119083729.
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Huang, Fen-Lan, i 黃芬蘭. "A Note on the Knot Sequences of B-spline Curves". Thesis, 2008. http://ndltd.ncl.edu.tw/handle/59320371937135806326.
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碩士國立中正大學
數學所
96
B-spline curves are useful curves in computer aided geometric design (CAGD). It needs some information to construct a B-spline curve such as knots or control points. In this paper, we will discuss about the influence of the knot sequence on B-spline curves.
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Chou, Pi-Ying, i 邱碧英. "A Study on Fitting B-spline Curves to Point Clouds". Thesis, 2007. http://ndltd.ncl.edu.tw/handle/53988026043294334894.
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碩士國立中正大學
應用數學研究所
95
In this paper we consider different objective functions of an approximation curve to fit a given set of points by a B-spline curve. First we give a general algorithm of curve fitting. Second we introduce three methods of different objective functions, PDM, TDM, and SDM. Finally we propose modified SDM methods and practice on the conic sections and point clouds.
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Shen, Yi-Jiun, i 沈宜郡. "Drawing System for Six-axis Robot Manipulator Based on B-Spline Curves". Thesis, 2013. http://ndltd.ncl.edu.tw/handle/04904437376456746042.
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碩士淡江大學
電機工程學系碩士班
101
In this thesis, a drawing system for a six-axis robot manipulator based on the B-Spline curves algorithm is designed and implemented. It can let the users can quickly and effectively design a required smooth curve to fit the desired graph and a six-axis robot manipulator named ABB IRB 120 can really draw this graph. Because the B-Spline curves algorithm just utilize few control points to generate curves and can arbitrarily change the local shape of the curve, the drawing system based on the B-Spline curves algorithm is constructed. First, a software platform used on PC is designed with MATLAB so that the users can add or move control points to let the curves meet the desired graph. When the user determines some satisfied curves based on the B-Spline curves algorithm, the position coordinates of control points can be obtained from the software platform. Then the position information of control points is the input data of the Flex Pendant of the ABB, where the matrix B- Spline curves algorithm is used to let the six-axis robot manipulator to accomplish the curve drawing work and the plotted graph is the same as that designed by the user on the software platform. In comparison with the traditional point-to-point method and the inherent circular movement method of the ABB robot manipulator, the drawing system built in this thesis can indeed quickly and efficiently let the robot manipulator draw the desired graph. Moreover, some coordinate transformation formula are used to let the graph can be plotted on a specified 3D surface.