Relevant bibliographies by topics / B-Spline Curve

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  1. Journal articles
  2. Dissertations / Theses
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  4. Book chapters
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Academic literature on the topic 'B-Spline Curve'

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Published: 6 September 2023

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Journal articles on the topic "B-Spline Curve"

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DUBE, MRIDULA, and REENU SHARMA. "PIECEWISE QUARTIC TRIGONOMETRIC POLYNOMIAL B-SPLINE CURVES WITH TWO SHAPE PARAMETERS." International Journal of Image and Graphics 12, no. 04 (October 2012): 1250028. http://dx.doi.org/10.1142/s0219467812500283.

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Analogous to the quartic B-splines curve, a piecewise quartic trigonometric polynomial B-spline curve with two shape parameters is presented in this paper. Each curve segment is generated by three consecutive control points. The given curve posses many properties of the B-spline curve. These curves are closer to the control polygon than the different other curves considered in this paper, for different values of shape parameters for each curve. With the increase of the value of shape parameters, the curve approach to the control polygon. For nonuniform and uniform knot vector the given curves have C0, G3; C1, G3; C1, G7; and C3 continuity for different choice of shape parameters. A quartic trigonometric Bézier curves are also introduced as a special case of the given trigonometric spline curves. A comparison of quartic trigonometric polynomial curve is made with different other curves. In the last, quartic trigonometric spline surfaces with two shape parameters are constructed. They have most properties of the corresponding curves.
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Dube, Mridula, and Reenu Sharma. "Cubic TP B-Spline Curves with a Shape Parameter." International Journal of Engineering Research in Africa 11 (October 2013): 59–72. http://dx.doi.org/10.4028/www.scientific.net/jera.11.59.

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In this paper a new kind of splines, called cubic trigonometric polynomial B-spline (cubic TP B-spline) curves with a shape parameter, are constructed over the space spanned by As each piece of the curve is generated by three consecutive control points, they posses many properties of the quadratic B-spline curves. These trigonometric curves with a non-uniform knot vector are C1 and G2 continuous. They are C2 continuous when choosing special shape parameter for non-uniform knot vector. These curves are closer to the control polygon than the quadratic B-spline curves when choosing special shape parameters. With the increase of the shape parameter, the trigonometric spline curves approximate to the control polygon. The given curves posses many properties of the quadratic B-spline curves. The generation of tensor product surfaces by these new splines is straightforward.
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Tirandaz, H., A. Nasrabadi, and J. Haddadnia. "Curve Matching and Character Recognition by Using B-Spline Curves." International Journal of Engineering and Technology 3, no. 2 (2011): 183–86. http://dx.doi.org/10.7763/ijet.2011.v3.221.

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Liu, Xu Min, Wei Xiang Xu, Jing Xu, and Yong Guan. "G1/C1 Matching of Spline Curves." Applied Mechanics and Materials 20-23 (January 2010): 202–8. http://dx.doi.org/10.4028/www.scientific.net/amm.20-23.202.

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The research is mainly made on the G1/C1 matching condition of spline curves. On the basis of the analysis on the basic function of T-B spline curves and the features of curve endpoints, we proposed the n+1 order T-B spline basic function and the solving method. The G1/C1 matching condition of C-B spline curves and T-B spline curves is put forward in this paper. On this condition, when matching C-B spline curves and T-B spline curves, the controlling vertexes can be added to make C-B spline curve tangent with the first and last edge by the first and last vertex of controlling polygon. Application instances were put up in this paper which illustrated that the G1/C1 matching between T-B spline curve and C-B spline curve using the feature of T-B spline curve which can represents semiellipse arc (semicircle arc) precisely can solve the problem that C-B spline curve cannot represents semiellipse arc (semicircle arc) precisely.
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Sukri, Nursyazni Binti Mohamad, Puteri Ainna Husna Binti Megat Mohd, Siti Musliha Binti Nor-Al-Din, and Noor Khairiah Binti Razali. "Irregular Symmetrical Object Designed By Using Lambda Miu B-Spline Degree Four." Journal of Physics: Conference Series 2084, no. 1 (November 1, 2021): 012018. http://dx.doi.org/10.1088/1742-6596/2084/1/012018.

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Abstract In Computer Aided Geometry Design (CAGD), B-splines curves are piecewise polynomial parametric curves that play an important role. CAGD involves the interpolation and approximation curves and surfaces. CAGD has been widely used which brings good impact of computers to industries in manufacturing. There are many improved methods in the B-spline curve such as extended cubic B-spline, trigonometric B-spline, quasi trigonometric B-spline, and λμ-B-spline. Each of the methods has its behaviour and advantage. In this paper, λμ-B-spline was used to be implemented in generating irregular symmetrical objects. λμ-B-spline has a shape parameter that can change the global shape by manipulating the value of the shape parameter. The bottle has been chosen as an irregular symmetrical object. The 2-dimensional symmetrical curves of Bottle design were formed by using λμ-B-spline degree 4. The curves designed are dependent on the shape parameter which can be adjusted. Then, the curves generated were revolved using the Sweep Surface method to form 3-dimensional objects. Every object has its volume and this research focused on the numerical method which was Simpson’s 3/8 to compute the volume. The volumes obtained were compared to the actual volume to determine the best shape parameter used. The results show that the λμ-B-spline curve with a shape parameter of 1 is the best shape parameter in designing symmetrical irregular objects with the desired volume.
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TSIANOS, KONSTANTINOS I., and RON GOLDMAN. "BEZIER AND B-SPLINE CURVES WITH KNOTS IN THE COMPLEX PLANE." Fractals 19, no. 01 (March 2011): 67–86. http://dx.doi.org/10.1142/s0218348x11005221.

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We extend some well known algorithms for planar Bezier and B-spline curves, including the de Casteljau subdivision algorithm for Bezier curves and several standard knot insertion procedures (Boehm's algorithm, the Oslo algorithm, and Schaefer's algorithm) for B-splines, from the real numbers to the complex domain. We then show how to apply these polynomial and piecewise polynomial algorithms in a complex variable to generate many well known fractal shapes such as the Sierpinski gasket, the Koch curve, and the C-curve. Thus these fractals also have Bezier and B-spline representations, albeit in the complex domain. These representations allow us to change the shape of a fractal in a natural manner by adjusting their complex Bezier and B-spline control points. We also construct natural parameterizations for these fractal shapes from their Bezier and B-spline representations.
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Zhao, Yuming, Zhongke Wu, Xingce Wang, and Xinyue Liu. "G2 Blending Ball B-Spline Curve by B-Spline." Proceedings of the ACM on Computer Graphics and Interactive Techniques 6, no. 1 (May 12, 2023): 1–16. http://dx.doi.org/10.1145/3585504.

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Blending two Ball B-Spline Curves(BBSC) is an important tool in modeling tubular objects. In this paper, we propose a new BBSC blending method. Our method has the following three main contributions: First, we use BBSC instead of ball Bézier to model the blending part to expand the solution space and make the resultant BBSC have better fairness. Second, we consider both the skeleton line and radius of BBSC, which makes the skeleton line and radius consistent. Thirdly, we propose a two-step optimization process to solve the problem of excessive amount of parameters brought by expanding the solution space, so that our method satisfies the real-time.
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Rahayu, Putri Indi, and Pardomuan Robinson Sihombing. "PENERAPAN REGRESI NONPARAMETRIK KERNEL DAN SPLINE DALAM MEMODELKAN RETURN ON ASSET (ROA) BANK SYARIAH DI INDONESIA." JURNAL MATEMATIKA MURNI DAN TERAPAN EPSILON 14, no. 2 (March 2, 2021): 115. http://dx.doi.org/10.20527/epsilon.v14i2.2968.

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Sharia Bank Return On Assets (ROA) modeling in Indonesia in 2018 aims to analyze the relationship pattern of Retturn On Assets (ROA) with interest rates. The analysis that is often used for modeling is regression analysis. Regression analysis is divided into two, namely parametric and nonparametric. The most commonly used nonparametric regression methods are kernel and spline regression. In this study, the nonparametric regression used was kernel regression with the Nadaraya-Watson (NWE) estimator and Local Polynomial (LPE) estimator, while the spline regression was smoothing spline and B-splines. The fitting curve results show that the best model is the B-splines regression model with a degree of 3 and the number of knots 5. This is because the B-splines regression model has a smooth curve and more closely follows the distribution of data compared to other regression curves. The B-splines regression model has a determination coefficient of R ^ 2 of 74.92%,%, meaning that the amount of variation in the ROA variable described by the B-splines regression model is 74.92%, while the remaining 25.8% is explained by other variables not included in the model.
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Cheng, Fuhua, Xuefu Wang, and B. A. Barsky. "Quadratic B-spline curve interpolation." Computers & Mathematics with Applications 41, no. 1-2 (January 2001): 39–50. http://dx.doi.org/10.1016/s0898-1221(01)85004-5.

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Lord, Marilyn. "Curve and Surface Representation by Iterative B-Spline Fit to a Data Point Set." Engineering in Medicine 16, no. 1 (January 1987): 29–35. http://dx.doi.org/10.1243/emed_jour_1987_016_008_02.

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The method of B-splines provides a very powerful way of representing curves and curved surfaces. The definition is ideally suited to applications in Computer Aided Design (CAD) where the designer is required to remodel the surface by reference to interactive graphics. This particular facility can be advantageous in CAD of body support surfaces, such as design of sockets of limb prostheses, shoe insoles, and custom seating. The B-spline surface is defined by a polygon of control points which in general do not lie on the surface, but which form a convex hull enclosing the surface. Each control point can be adjusted to remodel the surface locally. The resultant curves are well behaved. However, in these biomedical applications the original surface prior to modification is usually defined by a limited set of point measurements from the body segment in question. Thus there is a need initially to define a B-spline surface which interpolates this set of data points. In this paper, a computer-iterative method of fitting a B-spline surface to a given set of data points is outlined, and the technique is demonstrated for a curve. Extension to a surface is conceptually straightforward.
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Dissertations / Theses on the topic "B-Spline Curve"

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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.
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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.
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Randrianarivony, Maharavo, and 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.
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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.
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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.
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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.
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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 traitement
Interpolation 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
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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.
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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.
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Books on the topic "B-Spline Curve"

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Su, Pu-chʻing. Computational geometry--curve and surface modeling. Boston: Academic Press, 1989.

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1928-, Boehm Wolfgang, and Paluszny Marco 1950-, eds. Bézier and B-spline techniques. Berlin: Springer, 2002.

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Goldman, Ronald N., and Tom Lyche, eds. Knot Insertion and Deletion Algorithms for B-Spline Curves and Surfaces. Philadelphia, PA: Society for Industrial and Applied Mathematics, 1992. http://dx.doi.org/10.1137/1.9781611971583.

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1947-, Goldman Ron, Lyche Tom, and Society for Industrial and Applied Mathematics., eds. Knot insertion and deletion algorithms for B-spline curves and surfaces. Philadelphia: Society for Industrial and Applied Mathematics, 1993.

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Bu-Qing, Su, and Liu Ding-Yuan. Computational Geometry: Curve and Surface Modeling. Academic Pr, 1989.

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Bu-Qing, Su, and Liu Ding-Yuan. Computational Geometry: Curve and Surface Modeling. Academic Pr, 1989.

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Achieving high data reduction with integral cubic B-splines. Moffett Field, Calif: National Aeronautics and Space Administration, Ames Research Center, 1993.

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Prautzsch, Hartmut, Marco Paluszny, and Wolfgang Boehm. Bezier and B-Spline Techniques. Springer, 2002.

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Lyche, Tom. Knot Insertion and Deletion Algorithms for B-Spline Curves and Surfaces (Geometric Design Publications). Society for Industrial Mathematics, 1987.

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Book chapters on the topic "B-Spline Curve"

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Kermarrec, Gaël, Vibeke Skytt, and Tor Dokken. "Locally Refined B-Splines." In Optimal Surface Fitting of Point Clouds Using Local Refinement, 13–21. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-16954-0_2.

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AbstractThe univariate minimal support B-spline basis (UMB) has been used in Computer Aided Design (CAD) since the 1970s. Freeform curves use UMB, while sculptured surfaces are represented using a tensor product of two UMBs. The coefficients of a B-spline curve and surface are respectively represented in a vector and a rectangular grid. In CAD-intersection algorithms for UMB represented objects, a divide-and-conquer strategy is often used. Refinement by knot insertion is used to split the objects intersected into objects of the same type with a smaller geometric extent. In many cases the intersection of the resulting sub-objects has simpler topology than the original problem. The sub-objects created are represented using their parents’ UMB format and deleted when the sub-problem is solved. Consequently, no global representations of the locally refined bases are needed. This is contrary to when locally refined splines are used for approximation of large point sets. As soon as a B-spline is locally refined, the regular structure of UMB objects in CAD is no longer valid. In this chapter we discuss how Locally Refined B-splines (LR B-splines) address this challenge and present the properties of LR B-splines.
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Nguyen-Tan, Khoi, and Nguyen Nguyen-Hoang. "Handwriting Recognition Using B-Spline Curve." In Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering, 335–46. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-36642-0_33.

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Park, Hyungjun, and Joo-Haeng Lee. "B-Spline Curve Fitting Using Dominant Points." In Computational Science – ICCS 2006, 362–66. Berlin, Heidelberg: Springer Berlin Heidelberg, 2006. http://dx.doi.org/10.1007/11758525_48.

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Qiu, Jiaqi, and Weiqing Wang. "Verifiable Random Number Based on B-Spline Curve." In Advances in Intelligent Systems and Computing, 25–30. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-62743-0_4.

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Chang, Jincai, Zhao Wang, and Aimin Yang. "Construction of Transition Curve between Nonadjacent Cubic T-B Spline Curves." In Information Computing and Applications, 454–61. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-16167-4_58.

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Tan, Joi San, Ibrahim Venkat, and Bahari Belaton. "An Analytical Curvature B-Spline Algorithm for Effective Curve Modeling." In Advances in Visual Informatics, 283–95. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-25939-0_25.

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Loucera, Carlos, Andrés Iglesias, and Akemi Gálvez. "Lévy Flight-Driven Simulated Annealing for B-spline Curve Fitting." In Nature-Inspired Algorithms and Applied Optimization, 149–69. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-67669-2_7.

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Singh, Prem, and Himanshu Chaudhary. "Shape Optimization of the Flywheel Using the Cubic B Spline Curve." In Lecture Notes in Mechanical Engineering, 805–13. Singapore: Springer Singapore, 2019. http://dx.doi.org/10.1007/978-981-13-6469-3_75.

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Lin, Zizhi, and Yun Ding. "B-Spline Curve Fitting with Normal Constrains in Computer Aided Geometric Designed." In Advances in Intelligent Systems and Computing, 1282–89. Singapore: Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-33-4572-0_184.

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Tongur, Vahit, and Erkan Ülker. "B-Spline Curve Knot Estimation by Using Niched Pareto Genetic Algorithm (NPGA)." In Proceedings in Adaptation, Learning and Optimization, 305–16. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-27000-5_25.

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Conference papers on the topic "B-Spline Curve"

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Fatah, Abd, and Rozaimi. "Fuzzy tuning B-spline curve." In INNOVATION AND ANALYTICS CONFERENCE AND EXHIBITION (IACE 2015): Proceedings of the 2nd Innovation and Analytics Conference & Exhibition. AIP Publishing LLC, 2015. http://dx.doi.org/10.1063/1.4937076.

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Laube, Pascal, Matthias O. Franz, and Georg Umlauf. "Deep Learning Parametrization for B-Spline Curve Approximation." In 2018 International Conference on 3D Vision (3DV). IEEE, 2018. http://dx.doi.org/10.1109/3dv.2018.00084.

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Zakaria, Rozaimi, Abd Fatah Wahab, and R. U. Gobithaasan. "Normal type-2 fuzzy interpolating B-spline curve." In PROCEEDINGS OF THE 21ST NATIONAL SYMPOSIUM ON MATHEMATICAL SCIENCES (SKSM21): Germination of Mathematical Sciences Education and Research towards Global Sustainability. AIP Publishing LLC, 2014. http://dx.doi.org/10.1063/1.4887635.

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Zhaohui Huang and Cohen. "Affine-invariant B-spline moments for curve matching." In Proceedings of IEEE Conference on Computer Vision and Pattern Recognition. IEEE Comput. Soc. Press, 1994. http://dx.doi.org/10.1109/cvpr.1994.323871.

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Zhang, Wan-Jun, Shan-Ping Gao, Su-Jia Zhang, and Feng Zhang. "Modification algorithm of Cubic B-spline curve interpolation." In 2016 4th International Conference on Machinery, Materials and Information Technology Applications. Paris, France: Atlantis Press, 2016. http://dx.doi.org/10.2991/icmmita-16.2016.94.

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Wan, Yan, and Suna Yin. "Three-dimensional curve fitting based on cubic B-spline interpolation curve." In 2014 7th International Congress on Image and Signal Processing (CISP). IEEE, 2014. http://dx.doi.org/10.1109/cisp.2014.7003880.

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Chu, Chih-Hsing, and Jang-Ting Chen. "Geometric Design of Uniform Developable B-Spline Surfaces." In ASME 2004 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2004. http://dx.doi.org/10.1115/detc2004-57257.

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This paper studies geometric design of uniform developable B-spline surfaces from two boundary curves. The developability constraints are geometrically derived from the de Boor algorithm and expressed as a set of equations that must be fulfilled by the B-spline control points. These equations help characterize the number of degrees of freedom (DOF’s) for the surface design. For a cubic B-spline surface with a first boundary curve freely chosen, five more DOF’s are available for a second boundary curve when both curves contain four control points. There remain (7-2m) DOF’s for a cubic surface consisting of m consecutive patches with C2 continuity. The results are in accordance with previous findings for equivalent composite Be´zier surfaces. Test examples are illustrated to demonstrate design methods that fully utilize the DOF’s without leading to over-constrained systems in the solution process. Providing a foundation for systematic implementation of a CAGD system for developable B-spline surfaces, this work has substantial improvements over past studies.
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Cheng, Siyuan, Xiangwei Zhang, and Kelun Tang. "Shape Modification of B-Spline Curve with Geometric Constraints." In 2007 International Conference on Computational Intelligence and Security (CIS 2007). IEEE, 2007. http://dx.doi.org/10.1109/cis.2007.43.

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AiLian Leng, HuiXian Yang, WenLong Yue, and Qiufang Dai. "An inverse algorithm of the cubic B-spline curve." In 2010 2nd Conference on Environmental Science and Information Application Technology (ESIAT). IEEE, 2010. http://dx.doi.org/10.1109/esiat.2010.5568896.

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Xumin, Liu, and Xu Weixiang. "Uniform B-Spline Curve and Surface with Shape Parameters." In 2008 International Conference on Computer Science and Software Engineering. IEEE, 2008. http://dx.doi.org/10.1109/csse.2008.354.

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