Relevant bibliographies by topics / Bezier splines

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Bezier splines'

Author: Grafiati
Published: 5 June 2025
Last updated: 24 June 2025

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Journal articles on the topic "Bezier splines"

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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 (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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Shubhashree Bebarta, Shubhashree Bebarta, Bibhakar Kodamasingh Bibhakar Kodamasingh, and Ranjan Kumar Jati Ranjan Kumar Jati. "A Short Survey on B-spline and Bezier Methods." International Journal of Engineering and Science Invention 14, no. 5 (2025): 15–20. https://doi.org/10.35629/6734-14051520.

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Two effective techniques for approximating data in all areas of engineering problems are the B-spline and Bezier methods. They can be used for data interpolation with a few tweaks and enhancements. Although there are various methods for formulating B-splines in the literature, the B-spline equation is defined by a set of independent functions. The number of pairs of data or control points is equal to the number of coefficients in the B-spline equation. The B-spline method's benefit is that most set functions decrease at specific control points. The governing parametric equations can be drawn to produce Bezier curves. Bernstein polynomials are the parametric equations. A Bezier curve passes through the end points but not all of the data points. It is typically used in approximation methods. The Bezier curve can be used for interpolation since it can be made to pass through every control point by taking into account a few complimentary points between the original locations. This procedure produces curves that are smoother and less sinuous. These two approaches handle a number of challenges for comparing the interpolation qualities. The findings demonstrate the strength and resilience of both approaches for interpolating a highly irregular data set. In terms of accuracy, smoothness, and less computations, the Bezier model outperforms B-splines
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Balkir, S., M. Yanilmaz, and M. Plonus. "Numerical integration using Bezier splines." IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 13, no. 6 (1994): 737–45. http://dx.doi.org/10.1109/43.285248.

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Panchuk, K. L., and E. V. Lyubchinov. "Cyclographic images of Bezier Splines." Journal of Physics: Conference Series 1441 (January 2020): 012071. http://dx.doi.org/10.1088/1742-6596/1441/1/012071.

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Sharma, Arvind Kumar, and Amrita Puri. "Rational b-spline adaptive filter for active noise control of machinary noises." INTER-NOISE and NOISE-CON Congress and Conference Proceedings 268, no. 6 (2023): 2084–95. http://dx.doi.org/10.3397/in_2023_0307.

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Spline adaptive filter has a different architecture than linear-in-parameter nonlinear filters like Volterra filter. There are various kinds of splines like Bezier spline, B-spline and rational B-spline. Rational B spline has weights associated with control points and hence, provides more flexibility than B-spline to create a curve. This paper presents development of rational b-spline adaptive filter for active noise control. Updating equations to update control points and weights of control points are derived. A simulation study is presented to study performance of proposed rational B-spline adaptive filter to reduce machinary noises. Performance of proposed rational B-spline filter are compared with B-spline filter and Bezier filter for active noise control of experimentally recorded noises of band-saw, CNC machine and compressor
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Zaharov, A., and Y. Zakharova. "Content of the “Geometric Modeling” Course for the “Mathematics and Computer Science” Training Program." Geometry & Graphics 9, no. 4 (2022): 35–45. http://dx.doi.org/10.12737/2308-4898-2022-9-4-35-45.

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In this paper has been considered the main content and distinctive features of the “Geometric Modeling” training course for the “Mathematics and Computer Science” training program 02.03.01 (“Mathematical and Computer Modeling” specialization).
 The goal of the “Geometric Modeling” course study is the assimilation of mathematical methods for construction of geometric objects with complex curved shapes, and techniques for their computer visualization by using polygons of curves and surfaces. Methods for construction of structures’ curved shapes using spline representations, as well as techniques for construction of surfaces and volumetric geometries using motion operations and basic logical operations on geometric objects are considered. The spline representations include linear and bilinear splines, Hermite cubic splines and Hermite surfaces, natural cubic and bicubic interpolation splines, Bezier curves and surfaces, rational Bezier splines, B-splines and B-spline surfaces, NURBS-curves and NURBS-surfaces, transfinite interpolation methods, and splines of surfaces with triangular form. Logical operations for intersection of two spline curves, and intersection of two parametric surfaces are considered. The principles of scientific visualization and computer animation are considered in this course as well.
 Some examples for visualization of initial data and results of curves and surfaces construction in two- and three-dimensional spaces through the software shell developed by authors and used by students while doing tests have been demonstrated. The software shell has a web interface with the WebGL library graphic support. Tasks for four practical studies in a computer classroom, as well as several variations of homework are represented.
 The problems occurring in preparation materials for some course sections are discussed, as well as the practical importance of acquired knowledge for the further progress of students.
 The paper may be interesting for teachers of “Geometric Modeling” and “Computer Graphics” courses aimed to students with a specialization in mathematics and information, as well as to those who independently develop software interfaces for algorithms of geometric modeling.
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Yukhimets, Dmitry. "Neuron Net for Forming Optimal Smooth Trajectories Based on Bezier Splines." Applied Mechanics and Materials 865 (June 2017): 442–49. http://dx.doi.org/10.4028/www.scientific.net/amm.865.442.

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In this paper, the problem of planning smooth trajectories of mechatronic objects on the basis of Bezier splines of the third order with a minimal curvature is solved. Using such trajectories provides the maximal speed of movement for mechatronic objects. The neuron net, which approximates the function of the optimal selection of spline parameters is proposed to solve this problem. The advantage of the proposed approach is its lack of computational complexity, which allows its use in most on-board computers in real time.
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Lee, Sangil, Chris M. Glaze, Eric T. Bradlow, and Joseph W. Kable. "Flexible Utility Function Approximation via Cubic Bezier Splines." Psychometrika 85, no. 3 (2020): 716–37. http://dx.doi.org/10.1007/s11336-020-09723-4.

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Abstract In intertemporal and risky choice decisions, parametric utility models are widely used for predicting choice and measuring individuals’ impulsivity and risk aversion. However, parametric utility models cannot describe data deviating from their assumed functional form. We propose a novel method using cubic Bezier splines (CBS) to flexibly model smooth and monotonic utility functions that can be fit to any dataset. CBS shows higher descriptive and predictive accuracy over extant parametric models and can identify common yet novel patterns of behavior that are inconsistent with extant parametric models. Furthermore, CBS provides measures of impulsivity and risk aversion that do not depend on parametric model assumptions.
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Ganchuk, S. N., O. V. Krivosheev, S. V. Mavrin, and S. A. Ryzhov. "APPROXIMATION OF CONJUGATION OF BEZIER CURVES WITH PRESERVATION OF SMOOTHNESS ORDER AND ADDITIONAL RESTRICTIONS." Bulletin of South Ural State University series "Construction Engineering and Architecture" 24, no. 1 (2024): 59–69. http://dx.doi.org/10.14529/build240108.

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Bezier curves are a mandatory component of the geometric core of modern computer-aided design (CAD). The article proposes a mathematical approach that makes it possible to approximate the conjugation (connection) of Bezier curves of arbitrary degree, so that at the conjugation point the conditions of smoothness (continuity) are satisfied up to the order of an equal degree of the given Bezier curves. This approach helps to represent conjugate curves of a single Bezier curve with the degree equal to the degrees of the given curves. Additional restrictions can be imposed on the conjugate curves and the approximating curve in the form of a complete coincidence with one of the given curves, or the passage of the approximating curve through a given point and the equality of the derivatives to the given values at this point. To solve these problems, we introduced two difference metrics between the given curves and the approximating curve, and formulated optimization problems with constraints in the form of equalities. We applied the method of Lagrange multipliers which solves the corresponding system of linear algebraic equations. To represent Bezier curves, it is proposed to use the basic functions of B-splines, which allows you to use the software functions included in the geometric core of modern CAD systems. This greatly simplifies the derivation of all degree derivatives for curves and, without significant changes in the future, will make it possible to extend the results to conjugation problems of B-splines. The paper provides examples of approximations using various metrics and their limitations.
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Gackstatter, Dipl Inf Christina, Dipl Ing Bernd Dornieden, and Dipl Inf Gernot Rüb. "Road Course Prediction Using Radar Objects and “Bezier-Splines”." IFAC Proceedings Volumes 43, no. 7 (2010): 668–73. http://dx.doi.org/10.3182/20100712-3-de-2013.00126.

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Dissertations / Theses on the topic "Bezier splines"

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WANG, DONGHUI. "Modelisation de surfaces b-splines s'appuyant sur des courbes de bezier ou b-splines." Paris, ENSAM, 1990. http://www.theses.fr/1989ENAM0009.

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Ce travail concerne l'elaboration d'une methode de modelisation des surfaces b-splines en s'appuyant sur des courbes de bezier ou b-splines predefinies. Il a ete realise successivement chez renault automation et matra datavision, sur le systeme unisurf integre a euclid-is de matra datavision. Le probleme pose est de savoir comment on peut modeliser une surface polynomiale (surface de bezier ou b-spline) sous les contraintes suivantes: la surface obtenue doit respecter l'esthetique et la regularite des sections donnees par l'utilisateur; la methode proposee doit etre simple a utiliser et facile a controler; la surface doit respecter une precision voulue. Pour essayer de la resoudre, nous proposons une methode generale en utilisant le mecanisme de la modelisation des surfaces proposee par les methodes de coons et de gordon, ainsi que la representation mathematique b-spline et ses diverses techniques. L'etude et la realisation de notre probleme peuvent etre examinees selon les aspects suivants: etude de la transformation entre la representation de bezier et la representation b-spline, et elaboration de l'algorithme wm; analyse du mecanisme de la modelisation des surfaces; etablissement d'un type de modelisation des surfaces general
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Schiavon, Laurent. "Conditions de monotonie de la courbure pour les courbes et splines d'interpolation." Valenciennes, 2002. https://ged.uphf.fr/nuxeo/site/esupversions/ebd449f2-087e-4588-b4a1-bedcc9b86660.

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Pour une courbe, la courbure est une grandeur géométrique déterminante pour sa forme. Dans de nombreuses applications de la CAO (automobile, aéronautique), les courbes que l'on cherche à modéliser doivent être à courbure monotone, dans le but d'obtenir des formes aérodynamiques et esthétiques. Dans ce travail, nous apportons des solutions via les courbes polynomiales cubiques et rationnelles quadratiques (arcs coniques) quisont controlées par un ensemble de points (et de masses dans le cas rationnel)<br>For a curve, the curvature is a deciding geometric feature for its shape. For some applications of CAD (automotive, aeronautics), it is important to maintain monotone curvature along the curve we aim to modelize in order to obtain aerodynamic and aesthetic shapes. In this work, solutions are given via the cubic polynomial curves and the quadratic rational curves (conic segments) which are controlled by a set of points (and weights in the rational case)
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Rocha, Pedro Miguel Vieira Guiomar da. "Sistema de visão para apoio à avaliação da obstrução da orofaringe em crianças." Master's thesis, FCT - UNL, 2009. http://hdl.handle.net/10362/2595.

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Dissertação apresentada na Faculdade de Ciências e Tecnologia da Universidade Nova de Lisboa para a obtenção do grau de Mestre em Engenharia Electrotécnica e de Computadores<br>A amigdalite representa uma infecção das amígdalas palatinas provocada por microrganismos de origem viral ou bacteriana. Ocorre com maior frequência na infância, registando-se um maior índice de incidência em crianças até aos nove anos de idade. Perante a evolução da infecção, poderá registar-se a ocorrência de abcessos periamigdalinos, cuja ausência de adequado tratamento poderá incorrer numa perturbação da estabilidade vital do doente. Nesta dissertação é proposta uma metodologia que visa auxiliar a congregação especialista na avaliação do grau de obstrução da orofaringe. A metodologia proposta recorre à utilização de modelos de contornos activos, tendo em conta o seu relevante contributo na detecção de contornos de objectos. Contudo, problemas relacionados com posições de inicialização e uma deficiente convergência a zonas de elevada concavidade têm limitado a sua aplicabilidade. Deste modo, esta dissertação inclui uma nova abordagem à configuração básica do modelo permitindo uma relevante contribuição para a atenuação de ambas as condicionantes supra mencionadas. A nova arquitectura do respectivo modelo representa uma alteração à usual configuração da energia interna, incorporando também uma renovada formulação da energia externa. As alterações aplicadas à formulação convencional permitem testemunhar a elevada capacidade do modelo apresentado relativamente à sua adaptabilidade a um determinado contorno constituinte do processo de análise. Assim, o modelo apresentado e respectiva metodologia de implementação visam comprovar o seu préstimo na determinação e identificação dos contornos presentes em imagens de motivos relativos à orofaringe humana, onde se exibem contornos de considerável irregularidade, encontrando-se estes inseridos em regiões de fraco contraste. Sob o intuito de demonstrar a validade da idealização efectuada, exibe-se a interface da aplicação desenvolvida, bem como um conjunto de resultados obtidos aquando da experimentação efectuada.
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Berchtold, J. "The Bernstein basis in set-theoretic geometric modelling." Thesis, University of Bath, 2000. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.323604.

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Hernández, Abad Francisco 1952. "Superficies adaptables a puntos en el espacio." Doctoral thesis, Universitat Politècnica de Catalunya, 1985. http://hdl.handle.net/10803/6546.

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Es cada día más frecuente la representación de superficies mediante modelos de alambre utilizando ordenador. Una de las dificultades que presentan estos modelos es la obtención de las coordenadas de los puntos de la malla, dificultad que ha sido superada en base a la creación de modelos matemáticos que se adaptan más o menos a la superficie que quieren representar. <br/>En esta tesis se ha diseñado un modelo matemático que difiere esencialmente de los anteriores en que el número de puntos a partir de los cuales se genera la superficie es mucho más reducido; como contrapartida la entrada de dichos puntos debe ser más ordenada, pues tiene en cuenta la forma aproximada de la superficie localmente. Junto a este modelo se desarrollan algunas de las utilidades necesarias para su visualización y también se sugieren algunas de sus aplicaciones.<br/>Se ha optado por considerar la superficie total de la malla formada por la unión de las superficies regladas del cuadrilátero espacial que forman los cuatro puntos de cada cuadrícula.<br/>Cabe destacar las siguientes utilidades:<br/>Obtención de las curvas de nivel de estas superficies y representación en el sistema acotado.<br/>Representación en perspectiva axonométrica y cónica de la malla.<br/>Obtención y representación del perfil generado a través de un recorrido sobre la superficie.<br/>Generación y representación de mallas ficticias.<br>Nowadays it is more frequent the representation of surfaces by means of wire patterns using computer. Obtaining of the mesh points coordinates is one the difficulties derived from these patterns, difficulty that it has been overcome based on the creation of mathematical<br/>patterns that they adapt more or less to the surface that they want to represent.<br/>In this thesis a mathematical patterns has been designed that differs essentially of the previous ones in that the number of points starting from which the surface is generated is much more reduced; as compensation the entrance of this points should be more orderly, because she keeps locally in mind the approximate form of the surface. Next to this pattern some of the necessary utilities are developed for their visualization and some of their applications are also suggested.<br/>It has been opted to consider the total mesh surface formed by the union of the ruled surfaces of the space quadrilateral that they form the four points of each grid.<br/>It is necessary to highlight the following utilities:<br/>The level curves of these surfaces obtaining and representation in the enclosed system.<br/>Obtaining of the level curves of these surfaces and representation in the enclosed system.<br/>The representation of the perpendicular perspective of the mesh.<br/>The representation of the conical perspective of the mesh.<br/>Obtaining and representation of the profile generated through a journey on the surface. The fictitious meshes generation and representation.
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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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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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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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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.
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Arjun, B. S. "Motion Optimistion Of Plunging Airfoil Using Swarm Algorithm." Thesis, 2008. https://etd.iisc.ac.in/handle/2005/708.

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Micro Aerial Vehicles (MAVs) are battery operated, remote controlled miniature flying vehicles. MAVs are required in military missions, traffic management, hostage situation surveillance, sensing, spying, scientific, rescue, police and mapping applications. The essential characteristics required for MAVs are: light weight, maneuverability, ease of launch in variety of conditions, ability to operate in very hostile environments, stealth capabilities and small size. There are three main classes of MAVs : fixed, rotary and flapping wing MAV’s. There are some MAVs which are combinations of these main classes. Each class has its own advantage and disadvantage. Different scenarios may call for different types of MAV. Amongst the various classes, flapping wing class of MAVs offer the required potential for miniaturisation and maneuverability, necessitating the need to understand flapping wing flight. In the case of flapping winged flight, the thrust required for the vehicle flight is obtained due to the flapping of the wing. Hence for efficient flapping flight, optimising the flap motion is necessary. In this thesis work, an algorithm for motion optimisation of plunging airfoils is developed in a parallel framework. An evolutionary optimisation algorithm, PSO (Particle Swarm Optimisation), is coupled with an unsteady flow solver to develop a generic motion optimisation tool for plunging airfoils. All the unsteady flow computations in this work are done with the HIFUN1 code, developed in–house in the Computational Aerodynamics Laboratory, IISc. This code is a cell centered finite volume compressible flow solver. The motion optimisation algorithm involves starting with a population of motion curves from which an optimal curve is evolved. Parametric representation of curves using NURBS is used for efficient handling of the motion paths. In the present case, the motion paths of a plunging NACA 0012 airfoil is optimised to give maximum flight efficiency for both inviscid and laminar cases. Also, the present analysis considers all practically achievable plunge paths, si- nusoidal and non–sinusoidal, with varying plunge amplitudes and slopes. The results show promise, and indicate that the algorithm can be extended to more realistic three dimension motion optimisation studies.
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Books on the topic "Bezier splines"

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Lasser, Dieter. B-spline-Bezier representation of Tau-splines. Naval Postgraduate School, 1988.

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Dony, Robert. Calcul des parties cachées: Approximation des courbes par la méthode de Bezier et des B-splines. 2nd ed. Masson, 1991.

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

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Book chapters on the topic "Bezier splines"

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Wendel, Katrina, M. Osadebey, and J. Malmivuo. "Coupling Axis-Length Profiles with Bezier Splines in Finite Element Head Models." In IFMBE Proceedings. Springer Berlin Heidelberg, 2008. http://dx.doi.org/10.1007/978-3-540-69367-3_125.

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Barth, W. "Effizientes Ray-Tracing für Bezier- und B-Spline-Flächen." In Beiträge zur Graphischen Datenverarbeitung. Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/978-3-642-86836-8_10.

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"Bezier Curves and Bernstein Approximation." In Geometric Modeling with Splines. A K Peters/CRC Press, 2001. http://dx.doi.org/10.1201/9781439864203-14.

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"Bezier Curves and Bernstein Approximation." In Geometric Modeling with Splines. A K Peters/CRC Press, 2001. http://dx.doi.org/10.1201/9781439864203-14.

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Nowak, Iwona, Andrzej J. Nowak, and Luiz C. Wrobel. "Solution of Inverse Geometry Problems Using Bezier Splines and Sensitivity Coefficients." In Inverse Problems in Engineering Mechanics III. Elsevier, 2002. http://dx.doi.org/10.1016/b978-008043951-8/50013-8.

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"B-Spline Knot-Line Elimination and Bezier Continuity Conditions R. G orm az." In Curves and Surfaces. A K Peters/CRC Press, 1994. http://dx.doi.org/10.1201/9781439863596-25.

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Conference papers on the topic "Bezier splines"

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Tuncer, Ismail, Ozge Pola, and Nilay Uzol. "Genetic Algorithm Based Aerodynamic Shape Optimization Tool for Wind Turbine Blades and Its Implementation to Helicopter Blades." In Vertical Flight Society 70th Annual Forum & Technology Display. The Vertical Flight Society, 2014. http://dx.doi.org/10.4050/f-0070-2014-9692.

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This study presents a methodology first built up for the aerodynamic shape optimization for wind turbine rotors and its modified version for a helicopter rotor in hover. The Genetic Algorithm (GA) coupled with an in-house Blade Element Momentum (BEM) tool is used in the design optimization process. The wind turbine blade optimization studies are performed for maximizing the power production at a given wind speed, rotor speed and rotor diameter, while for the helicopter blade optimization in hover, figure of merit is considered. The airfoil profiles along the span are defined by high order Bezier curves, and the control points of the curves are taken as the design variables. The chord length distribution and the twist distribution are also defined by Bezier splines. The sectional aerodynamic loads needed by the BEM method are obtained by using the potential flow solver with a boundary layer model, XFOIL. The BEM calculations for each individual in the GA population may be computed in parallel using OpenMPI. The BEM tool developed is validated with the available wind turbine and helicopter blade aerodynamic data and then design optimization studies are successfully performed.
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Boykov, Aleksey Aleksandrovich. "Constructive Geometry of some Algebraic Curves Represented by Splines in CAD." In 33rd International Conference on Computer Graphics and Vision. Keldysh Institute of Applied Mathematics, 2023. http://dx.doi.org/10.20948/graphicon-2023-758-770.

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The problem of representing segments of some algebraic curves (curves of the second order and cubic parabolas) is solved using spline curves of CAD systems – Bezier curves and rational splines. Algorithms are being developed for constructing curves, mainly cubic parabolas, according to given conditions in the representation by Bezier curves of 3rd order. The concepts of special pencils of cubic parabolas of the first and second kind are introduced, their properties and application to the construction of cubic parabolas are shown. A way to representing cubic splines in a CAD system is proposed. The representation of arcs of conic curves, as well as arcs of Bezier curves using rational splines is shown. The developed algorithms were used to create a model of the canal surface.
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Diao, Luhong, Sen Zhang, Lei Liu, Hua Li, and Zongkai Lin. "Analysis of conversion matrix between geometrically continuous splines and Bezier representation." In 2010 5th International Conference on Pervasive Computing and Applications (ICPCA 2010). IEEE, 2010. http://dx.doi.org/10.1109/icpca.2010.5871345.

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Scheucher, R., and W. Hellinger. "Using Bezier-Splines for Design Optimization of CAMS Regarding Valve Train Dynamics." In ASME 2005 International Mechanical Engineering Congress and Exposition. ASMEDC, 2005. http://dx.doi.org/10.1115/imece2005-79865.

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The aim of this work is the improvement of the cam design for automotive valve trains. A constrained optimization problem is defined, using the control points of the cam profile, which is represented by harmonic splines, as design variables. Additionally to the optimization problem the advantages of the calculation of sensitivity information using direct or adjoint methods are determined. The valve train model is defined by a multi body system containing discontinuities due to the loss of contact between two consecutive components of the valve train. The objective function is to maximize the area below the valve lift, which has a great influence on the gas flow. Constraints for dynamic force, the valve opening and closing phase and the valve lift based on the engine’s thermodynamics considerations are taken into account. Furthermore some constraints for the geometric coordinates of the control points of the cam profile must be imposed.
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Radmanesh, Mohammadreza, Manish Kumar, and Mohammad Sarim. "On the Effect of Different Splines on Way-Point Navigation of Quad-Copters." In ASME 2016 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/dscc2016-9896.

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Unmanned Air Vehicles (UAVs) have become more applicable in several military and civilian domains during the last decade due to their enhanced capabilities. For outdoor environments, one of the most reliable methods for navigation is waypoint following. Usually, the path or trajectory to be followed is decided based on the behavior of the vehicle during path following such as time and energy consumption. However, feasibility of the trajectory is based on the vehicle dynamics and the ability of UAV to follow the path generated based on the way-point setup. Moreover, the paths obtained from minimizing time or energy consumption are often contradictory. This paper investigates two cases where the objective of the path planning based on the Continuous Cubic C1 Bezier Curve (C1CBC) method and 4 other first degree Bezier curves is: i) minimizing the time consumption, and ii) minimizing the energy consumption. At the end, the quad-copters were simulated through the generated path to reveal the effects of the path UAV follows to reach to the goal position.
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Venkataraman, P. "One and Two Dimensional Data Analysis Using Bezier Functions." In ASME 2008 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2008. http://dx.doi.org/10.1115/detc2008-49101.

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Bezier functions, which are Bezier curves constrained to behave like functions, are excellent for representing smooth and continuous function of high degree, over the entire range of the independent variable. They provide excellent solutions to systems of linear, nonlinear, ordinary and partial differential equations. In this paper we examine their usefulness for data approximation as a prelude to their use in solving the inverse problem. Bezier function and B-splines, which are related, have mostly been used in geometrical modeling. There are not many examples of their use in data analysis. In this paper, organized and unorganized data are used to illustrate the effectiveness of Bezier functions for data approximation, reduction, mining, transformation, and prediction. Two criteria are used for the overall data fitting process. A simple incremental strategy identifies the order of the function using the minimum of the sum of the absolute error over all data. For a given order of the function, the least squared error over all data identifies the Bezier function through a non iterative algebraic relation. The entire data can then be represented by the coefficients of the Bezier function. Alternately, the data can also be reduced to a polynomial based on a parameter varying between 0 and 1. The Bezier function is global over all of the data so that all data points, including interpolated data, have the same properties. Three important properties are explicit is using Bezier functions for data analysis. The mean of the original data and the approximate data are the same. Large orders of polynomials can be used without local distortion. The independent and dependent variables can be decoupled by the Bezier representation. The data fitting process can also filter noisy data to recover principal data behavior.
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Schimanski, Sigmund, and Sebastian Runge. "Application of bezier-splines in navigation algorithms by means of the product usage chain." In 2016 IEEE International Conference on Consumer Electronics (ICCE). IEEE, 2016. http://dx.doi.org/10.1109/icce.2016.7430653.

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Zareh, Mehrdad, and Xiaoping Qian. "A New Plate Formulation Based on Triangular Isogeometric Analysis." In ASME 2018 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/detc2018-85577.

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This paper presents application of rational triangular Bezier splines (rTBS) for developing Kirchhoff-Love plate elements in the context of isogeometric analysis. Triangular isogeometric analysis can provide the C1 continuity over the mesh including elements interfaces, a necessary condition in finite elements formulation based on Kirchhoff-Love shell and plate theory. Using rTBS and macro-element technique, we develop Kirchhoff-Love plate elements, investigate the convergence rate and apply the method on complex geometry. Obtained results demonstrate that the optimal convergence rate is achievable; moreover, this method is applicable to represent thin geometric models of complex topology or thin geometric models in which efficient local refinement is required.
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Hillaire, Robert G., Louis A. Marchetti, and Paul K. Wright. "Geometry for Precision Manufacturing on an Open Architecture Machine Tool (MOSAIC-PC)." In ASME 1998 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 1998. http://dx.doi.org/10.1115/imece1998-1074.

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Abstract Modern machine tools cannot presently machine all the desired geometries modeled by designers. These geometries include free-formed surfaces represented by Bezier, Tensor Product, NURBS, and the like. When these free-formed surfaces are executed on the production floor, they are approximated with straight lines, circles, and in some advanced manufacturing facilities, cubic B-Splines. The work described in this paper provides a machine path interpolator that can traverse complicated free-formed paths represented by NURBS. This NURBS interpolator is implemented on a three axis milling machine with an industrial quality Open Architecture Controller. The system is called MOSAIC-PC (Machine-tool Open System Advanced Intelligent Controller: PC platform).
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Limaiem, Anis, and Hoda A. ElMaraghy. "Analytical Solid Modeling Using Dual Kriging." In ASME 1995 Design Engineering Technical Conferences collocated with the ASME 1995 15th International Computers in Engineering Conference and the ASME 1995 9th Annual Engineering Database Symposium. American Society of Mechanical Engineers, 1995. http://dx.doi.org/10.1115/detc1995-0017.

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Abstract This paper presents a new method for representing analytical or parametric solids based on dual kriging. Complex solids may be represented with a single model without any limitation on the number of data points. The equations of the parametric model are derived in a simple and novel way by considering the combination of three interpolation profiles. Dual kriging was successfully used for curve/surface modeling. It is a general method which incorporates several interpolation techniques in a single formulation, such as piecewise interpolation, cubic splines and Bezier curves/surfaces and solids. We will show that B-splines and NURBS are special cases of dual kriging. The model generated passes through all data points, and elementary shapes such as conics, cylinders are represented exactly. In addition, derivatives and linear constraints may be incorporated in the kriging model as well as uncertainties on data points. Many applications, common to analytical solid modeling are possible, such as solid mesh generation in finite elements analysis, mass property calculations, composite material modeling and computer animation.
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Reports on the topic "Bezier splines"

1

Lasser, Dieter. B-Spline-Bezier Representation of Tau-Splines. Defense Technical Information Center, 1988. http://dx.doi.org/10.21236/ada197937.

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