Relevant bibliographies by topics / B-spline functions

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Academic literature on the topic 'B-spline functions'

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Published: 4 June 2021
Last updated: 28 September 2024

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Journal articles on the topic "B-spline functions"

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Tsay, D. M., and C. O. Huey. "Application of Rational B-Splines to the Synthesis of Cam-Follower Motion Programs." Journal of Mechanical Design 115, no. 3 (September 1, 1993): 621–26. http://dx.doi.org/10.1115/1.2919235.

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A procedure employing rational B-spline functions for the synthesis of cam-follower motion programs is presented. It differs from earlier techniques that employ spline functions by using rational B-spline basis functions to interpolate motion constraints. These rational B-splines permit greater flexibility in refining motion programs. Examples are provided to illustrate application of the approach.
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Pool, Maryam Khazaei, and Lori Lewis. "A SURVEY ON RECENT HIGHER ORDER SPLINE TECHNIQUES FOR SOLVING BURGERS EQUATION USING B-SPLINE METHODS AND VARIATION OF B-SPLINE TECHNIQUES." Journal of Mathematical Sciences: Advances and Applications 70, no. 1 (April 10, 2022): 1–26. http://dx.doi.org/10.18642/jmsaa_7100122245.

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This is a summary of articles based on higher order B-splines methods and the variation of B-spline methods such as Quadratic B-spline finite elements method, Exponential cubic B-spline method, Septic B-spline technique, Quintic B-spline Galerkin method, and B-spline Galerkin method based on the Quadratic B-spline Galerkin method (QBGM) and Cubic B-spline Galerkin method (CBGM). In this paper, we study the B-spline methods and variations of B-spline techniques to find a numerical solution to the Burgers’ equation. A set of fundamental definitions including Burgers equation, spline functions, and B-spline functions are provided. For each method, the main technique is discussed as well as the discretization and stability analysis. A summary of the numerical results is provided and the efficiency of each method presented is discussed. A general conclusion is provided where we look at a comparison between the computational results of all the presented schemes. We describe the effectiveness and advantages of these methods.
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Budakçı, Gülter, and Halil Oruç. "Further Properties of Quantum Spline Spaces." Mathematics 8, no. 10 (October 14, 2020): 1770. http://dx.doi.org/10.3390/math8101770.

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We construct q-B-splines using a new form of truncated power functions. We give basic properties to show that q-B-splines form a basis for quantum spline spaces. On the other hand, we derive algorithmic formulas for 1/q-integration and 1/q-differentiation for q-spline functions. Moreover, we show a way to find the polynomial pieces on each interval of a q-spline function.
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Journal, Baghdad Science. "Solving B- spline functions." Baghdad Science Journal 3, no. 4 (December 3, 2006): 713–21. http://dx.doi.org/10.21123/bsj.3.4.713-721.

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In this paper, we proposed to zoom Volterra equations system Altfazlah linear complementarity of the first type in this approximation were first forming functions notch Baschtdam matrix and then we discussed the approach and stability, to notch functions
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AL-Faour, Omar M. "Solving B- spline functions." Baghdad Science Journal 3, no. 4 (December 1, 2006): 713–21. http://dx.doi.org/10.21123/bsj.2006.758.

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In this paper, we proposed to zoom Volterra equations system Altfazlah linear complementarity of the first type in this approximation were first forming functions notch Baschtdam matrix and then we discussed the approach and stability, to notch functions
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Strelkovskaya, Irina, Irina Solovskaya, and Juliya Strelkovska. "Application of real and complex splines in infocommunication problems." Problemi telekomunìkacìj, no. 1(28) (December 22, 2021): 3–19. http://dx.doi.org/10.30837/pt.2021.1.01.

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The work offers the solution to problems of analysis and synthesis of infocommunication systems with the help of real and complex spline functions. The use of the spline approximation method for solving problems of recovery of random signals and self-similar traffic, management of network objects and network as a whole, and procedures of infocommunication objects and networks functioning is offered. To solve the problems of forecasting, in particular, forecasting the characteristics of network traffic and maintaining the QoS characteristics in its service and formation of requirements for network buffer devices, developed spline extrapolation based on different types of real spline functions, namely: linear, quadratic, quadratic B-splines, cubic, cubic B-splines, cubic Hermite splines. As a criterion for choosing the type of spline function, the prediction error is selected, the accuracy of which can be increased by using a particular kind of spline, depending on the object being predicted. The use of complex flat spline functions is considered to solve the class of user positioning problems in the radio access network. In general, the use of real and complex spline functions allows obtaining the results of improving the Quality of Service in the infocommunication network and ensuring the scalability of the obtained solutions.
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MacCarthy, B. L., and N. D. Burns. "An Evaluation of Spline Functions for use in Cam Design." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 199, no. 3 (July 1985): 239–48. http://dx.doi.org/10.1243/pime_proc_1985_199_118_02.

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This paper shows how spline functions can be employed for kinematic motion specification in cam design. The polynomial spline is introduced as a special case of a continuous piecewise function. Cubic and quintic splines are derived and their properties are discussed in the cam design context. It is shown how standard cam laws can be approximated extremely accurately with a small number of points and appropriate boundary conditions. The modified sinusoidal acceleration cam law is used as an example. The application of quintic splines to non-standard and special motions is discussed. The algebraic and B-spline representations of spline functions are compared. The former is considered preferable in this context and a list of useful algorithms is given. The real power of the spline function, in particular the algebraic quintic spline, is its simplicity, ease of computation and adaptability to non-standard design problems. The use of parametrized, deficient and exponential splines is proposed for specific applications.
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Che, Xiang Jiu, Gerald Farin, Zhan Heng Gao, and Dianne Hansford. "The Product of Two B-Spline Functions." Advanced Materials Research 186 (January 2011): 445–48. http://dx.doi.org/10.4028/www.scientific.net/amr.186.445.

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A method for calculating the product of two B-spline functions is presented. The product is computed by solving a linear system. The coefficient matrix of the system is a Gramian, which guarantees that the system has a unique solution. Every element of the coefficient matrix and the righthand vector of the system is an inner product of B-splines. The inner product can be computed accurately by making use of numerical methods.
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Speleers, Hendrik. "Algorithm 1020: Computation of Multi-Degree Tchebycheffian B-Splines." ACM Transactions on Mathematical Software 48, no. 1 (March 31, 2022): 1–31. http://dx.doi.org/10.1145/3478686.

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Multi-degree Tchebycheffian splines are splines with pieces drawn from extended (complete) Tchebycheff spaces, which may differ from interval to interval, and possibly of different dimensions. These are a natural extension of multi-degree polynomial splines. Under quite mild assumptions, they can be represented in terms of a so-called multi-degree Tchebycheffian B-spline (MDTB-spline) basis; such basis possesses all the characterizing properties of the classical polynomial B-spline basis. We present a practical framework to compute MDTB-splines, and provide an object-oriented implementation in Matlab . The implementation supports the construction, differentiation, and visualization of MDTB-splines whose pieces belong to Tchebycheff spaces that are null-spaces of constant-coefficient linear differential operators. The construction relies on an extraction operator that maps local Tchebycheffian Bernstein functions to the MDTB-spline basis of interest.
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Strelkovskaya, Irina, Irina Solovskaya, and Anastasiya Makoganiuk. "Spline-Extrapolation Method in Traffic Forecasting in 5G Networks." Journal of Telecommunications and Information Technology 3 (September 30, 2019): 8–16. http://dx.doi.org/10.26636/jtit.2019.134719.

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This paper considers the problem of predicting self-similar traffic with a significant number of pulsations and the property of long-term dependence, using various spline functions. The research work focused on the process of modeling self-similar traffic handled in a mobile network. A splineextrapolation method based on various spline functions (linear, cubic and cubic B-splines) is proposed to predict selfsimilar traffic outside the period of time in which packet data transmission occurs. Extrapolation of traffic for short- and long-term forecasts is considered. Comparison of the results of the prediction of self-similar traffic using various spline functions has shown that the accuracy of the forecast can be improved through the use of cubic B-splines. The results allow to conclude that it is advisable to use spline extrapolation in predicting self-similar traffic, thereby recommending this method for use in practice in solving traffic prediction-related problems.
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Dissertations / Theses on the topic "B-spline functions"

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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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Andriamaro, Miangaly Gaelle. "Vector refinable splines and subdivision." Thesis, Stellenbosch : Stellenbosch University, 2008. http://hdl.handle.net/10019.1/1747.

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Thesis (MSc (Mathematics))--Stellenbosch University, 2008.
In this thesis we study a standard example of refinable functions, that is, functions which can be reproduced by the integer shifts of their own dilations. Using the cardinal B-spline as an introductory example, we prove some of its properties, thereby building a basis for a later extension to the vector setting. Defining a subdivision scheme associated to the B-spline refinement mask, we then present the proof of a well-known convergence result. Subdivision is a powerful tool used in computer-aided geometric design (CAGD) for the generation of curves and surfaces. The basic step of a subdivision algorithm consists of starting with a given set of points, called the initial control points, and creating new points as a linear combination of the previous ones, thereby generating new control points. Under certain conditions, repeated applications of this procedure yields a continuous limit curve. One important goal of this thesis is to study a particular extension of scalar subdivision to matrix subdivision ...
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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 Superior
O 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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Flores, Melvin Estuardo Murray Richard M. Murray Richard M. "Real-time trajectory generation for constrained nonlinear dynamical systems using non-uniform rational B-spline basis functions /." Diss., Pasadena, Calif. : California Institute of Technology, 2008. http://resolver.caltech.edu/CaltechETD:etd-02192008-153449.

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You, C. F. "An investigation of the use of B-spline shaped functions for the analysis of large deformations of structures." Thesis, Cranfield University, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.381051.

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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.
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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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Phan, Anh cang. "Crack removal and hole filling on composite subdivision meshes." Thesis, Aix-Marseille, 2013. http://www.theses.fr/2013AIXM4068/document.

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Construire une surface lisse d'un objet 3D est un problème important dans de nombreuses applications graphiques. En particulier, les méthodes de subdivision permettent de passer facilement d'un maillage discret à une surface continue. Un problème général résultant de la subdivision de deux maillages initialement connectés le long d'un bord est l'apparition de fissures ou de trous entre eux. Ces fissures produisent non seulement des formes indésirables, mais induisent aussi des difficultés pour les traitements ultérieurs. Il faut donc réparer ces défauts de sorte que la surface obtenue soit lisse et puisse être subdivisée ou modifiée. Nous proposons de nouvelles méthodes pour relier deux maillages avec des résolutions différentes en utilisant une transformée en ondelettes B-splines et une approximation locale ou une interpolation locale à l'aide de fonctions de base radiales (RBF). Ces procédés génèrent un maillage de connexion où la continuité est contrôlée. La résolution du maillage est ajustable pour respecter le changement de résolution entre les zones grossières et fines. En outre, nous présentons des méthodes pour combler les trous à n-côtés, et le raffinement des maillages grâce à un schéma de subdivision adaptative. Nous avons conçu, implémenté et testé les algorithmes en MatLab pour illustrer nos méthodes et montrer des résultats expérimentaux. Ces algorithmes sont mis en oeuvre sur de nombreux modèles d'objets 3D avec des formes complexes. En outre, nous avons fourni des approches différentes pour chaque problème. Ainsi, les résultats des différentes approches sont comparés et évalués afin d'exploiter les avantages et les inconvénients de ces approches
Constructing a smooth surface of a 3D object is an important problem in many graphical applications. In particular, subdivision methods permit to pass easily from a discrete mesh to a continuous surface. A generic problem arising from subdividing two meshes initially connected along a common boundary is the occurrence of cracks or holes between them. These cracks not only produce undesired shapes, but also bring serious trouble for further mesh processing. They must be removed or filled so that the produced surface is smooth and can be further subdivided or edited. In order to remove cracks, we propose new methods for joining two meshes with different resolutions using a Lifted B-spline wavelet transform and a local approximation or radial basis function (RBF) local interpolation. These methods generate a connecting mesh where continuity is controlled from one boundary to the other and the connecting mesh can change gradually in resolution between coarse and fine areas. Additionally, we introduce methods for filling n-sided holes, and refining meshes with an adaptive subdivision scheme. We have designed, implemented, and tested the algorithms in MatLab to illustrate our proposed methods and show experimental results. These algorithms are implemented on many 3D object models with complex shapes. Additionally, we have provided some different approaches for each problem. Thus, results from the different approaches are compared and evaluated to exploit the advantages and disadvantages of these approaches
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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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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 2D
Isogeometric 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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Bahari, Mustapha. "Transport optimal pour la génération de maillage et le r-raffinement." Electronic Thesis or Diss., Université Côte d'Azur, 2024. http://www.theses.fr/2024COAZ5032.

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Dans cette thèse, nous développons des solveurs rapides et des procédures de génération de maillage adaptatif basés sur le transport optimal dans le contexte de l'Analyse Isogéométrique, en utilisant les B-Splines comme base des éléments finis. Notre approche garantit la construction d'une bijection, abordant ainsi un défi majeur de l'Analyse Isogéométrique. Nous utilisons des éléments finis standard pour résoudre l'équation de Monge-Ampère. Cependant, une analyse de cette approche montre des limitations significatives, notamment lorsqu'elle est confrontée à des variations importantes au voisinage de la frontière. Pour surmonter ce défi, nous dérivons une nouvelle formulation utilisant une discrétisation B-Splines compatible basée sur la suite de DeRham. De plus, nous introduisons de nouveaux solveurs rapides utilisant la méthode de diagonalisation rapide pour aborder efficacement cette question.Nous proposons une variété de tests et d'applications pour illustrer la performance et l'efficacité de notre approche. Celles-ci incluent des tests utilisant des solutions construites de l'équation de Monge-Ampère ainsi que des fonctions de densité analytiques. De plus, nous appliquons notre solveur à des problèmes elliptiques et à des problèmes dépendant du temps, en relevant des défis tels que l'obtention d'une précision élevée, la capture précise des interfaces, et la réduction efficace des oscillations.Finalement, la paramétrisation B-spline de presque toutes les géométries présentées repose sur les informations donnnées par le bord, utilisant une nouvelle approche basée sur le transport optimal
In this thesis, we develop fast solvers and adaptive mesh generation procedures based on the Optimal Transport using B-Splines Finite Elements within the Isogeometric Analysis framework. Our approach ensures the construction of a bijection mapping, addressing a major challenge in Isogeometric Analysis.Initially, we employ standard B-Splines Finite Elements to solve the Monge-Ampère Equation. However, an analysis of this approach reveals significant limitations, particularly when confronted with high variations near the boundary. To overcome this challenge, we derive a new formulation utilizing compatible B-Splines discretization based on a discrete DeRham sequence. Furthermore, we introduce new fast solvers using the Fast Diagonalization method to address this issue effectively.We provide various tests and applications to demonstrate the performance and efficiency of our novel approach. These include testing our approach using manufactured solutions of the Monge-Ampère equation and employing analytical density functions. Additionally, we apply our solver to elliptic problems and time-dependent problems, addressing challenges such as achieving higher accuracy, accurately capturing sharp interfaces, and effectively reducing oscillations.Finally, the parameterization of nearly all presented geometries relies on CAD-boundary information, employing a novel approach based on optimal transport
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Books on the topic "B-spline functions"

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deLancey, Moser Robert, and United States. National Aeronautics and Space Administration., eds. Two-dimensional mesh embedding for Galerkin B-spline methods. [Washington, DC]: National Aeronautics and Space Administration, 1995.

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deLancey, Moser Robert, and United States. National Aeronautics and Space Administration., eds. Two-dimensional mesh embedding for Galerkin B-spline methods. [Washington, DC]: National Aeronautics and Space Administration, 1995.

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deLancey, Moser Robert, and United States. National Aeronautics and Space Administration., eds. Two-dimensional mesh embedding for Galerkin B-spline methods. [Washington, DC]: National Aeronautics and Space Administration, 1995.

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Two-dimensional mesh embedding for Galerkin B-spline methods. [Washington, DC]: National Aeronautics and Space Administration, 1995.

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Book chapters on the topic "B-spline functions"

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Piegl, Les, and Wayne Tiller. "B-Spline Basis Functions." In The NURBS Book, 47–79. Berlin, Heidelberg: Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/978-3-642-59223-2_2.

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Piegl, Les, and Wayne Tiller. "B-Spline Basis Functions." In Monographs in Visual Communications, 47–79. Berlin, Heidelberg: Springer Berlin Heidelberg, 1995. http://dx.doi.org/10.1007/978-3-642-97385-7_2.

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Bojanov, B. D., H. A. Hakopian, and A. A. Sahakian. "B-Splines." In Spline Functions and Multivariate Interpolations, 28–44. Dordrecht: Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-015-8169-1_3.

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Bojanov, B. D., H. A. Hakopian, and A. A. Sahakian. "Multivariate B-Splines and Truncated Powers." In Spline Functions and Multivariate Interpolations, 132–48. Dordrecht: Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-015-8169-1_9.

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Qu, Ruibin, and John A. Gregory. "A Subdivision Algorithm For Non—Uniform B—Splines." In Approximation Theory, Spline Functions and Applications, 423–36. Dordrecht: Springer Netherlands, 1992. http://dx.doi.org/10.1007/978-94-011-2634-2_30.

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Szyszka, Anna, and Maciej Woźniak. "Parallel Algorithm for Concurrent Integration of Three-Dimensional B-Spline Functions." In Computational Science – ICCS 2023, 590–96. Cham: Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-36021-3_57.

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Tan, Shunquan. "Steganalysis of LSB Matching Revisited for Consecutive Pixels Using B-Spline Functions." In Digital Forensics and Watermarking, 16–29. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-32205-1_4.

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Tanaka, Satoyuki, and Hiroshi Okada. "An Adaptive Wavelet Finite Element Method with High-Order B-Spline Basis Functions." In The Mechanical Behavior of Materials X, 877–80. Stafa: Trans Tech Publications Ltd., 2007. http://dx.doi.org/10.4028/0-87849-440-5.877.

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Christensen, Ole. "B-splines." In Functions, Spaces, and Expansions, 203–14. Boston: Birkhäuser Boston, 2010. http://dx.doi.org/10.1007/978-0-8176-4980-7_10.

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Frederic, P., G. D’Amore, and E. Pacciani. "Attributing a Paleoanthropological Specimen to a Prehistoric Population: A Bayesian Approach with Multivariate B-Spline Functions." In Applied Bayesian Statistical Studies in Biology and Medicine, 131–52. Boston, MA: Springer US, 2004. http://dx.doi.org/10.1007/978-1-4613-0217-9_8.

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Conference papers on the topic "B-spline functions"

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Du, Huiqian, and Wenbo Mei. "Image Resizing Using Exponential B-Spline Functions." In 2009 2nd International Congress on Image and Signal Processing (CISP). IEEE, 2009. http://dx.doi.org/10.1109/cisp.2009.5305799.

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Brown, Joanna M., Malcolm I. G. Bloor, M. Susan Bloor, and Michael J. Wilson. "Generation and Modification of Non-Uniform B-Spline Surface Approximations to PDE Surfaces Using the Finite Element Method." In ASME 1990 Design Technical Conferences. American Society of Mechanical Engineers, 1990. http://dx.doi.org/10.1115/detc1990-0032.

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Abstract A PDE surface is generated by solving partial differential equations subject to boundary conditions. To obtain an approximation of the PDE surface in the form of a B-spline surface the finite element method, with the basis formed from B-spline basis functions, can be used to solve the equations. The procedure is simplest when uniform B-splines are used, but it is also feasible, and in some cases desirable, to use non-uniform B-splines. It will also be shown that it is possible, if required, to modify the non-uniform B-spline approximation in a variety of ways, using the properties of B-spline surfaces.
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Fahmy, M. F., and G. Fahmy. "C12. Image compression using exponential B-spline functions." In 2012 29th National Radio Science Conference (NRSC). IEEE, 2012. http://dx.doi.org/10.1109/nrsc.2012.6208530.

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Akyel, Cevdet, and Slobodan Babic. "Choice of segments in the B=B(H) approximation using spline functions." In Symposium on Antenna Technology and Applied Electromagnetics [ANTEM 2000]. IEEE, 2000. http://dx.doi.org/10.1109/antem.2000.7851641.

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Stanciu, Lucian, Valentin Stanciu, and Radu Badea. "Digital Crossover Filters Designed by Using B-Spline Functions." In 2019 International Symposium on Signals, Circuits and Systems (ISSCS). IEEE, 2019. http://dx.doi.org/10.1109/isscs.2019.8801810.

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Rohal'-Ilkiv, Boris, Martin Gulan, and Peter Minarcik. "Implementation of Continuous-time MPC Using B-spline Functions." In 2019 22nd International Conference on Process Control (PC19). IEEE, 2019. http://dx.doi.org/10.1109/pc.2019.8815334.

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Santoro, Esamuele. "Digraph and matrix representation or nonuniform B-spline functions." In Wuhan - DL tentative, edited by Shuzi Yang, Ji Zhou, and Cheng-Gang Li. SPIE, 1996. http://dx.doi.org/10.1117/12.235523.

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Nikolos, Ioannis K., Georgios N. Lygidakis, Stavros N. Leloudas, and Sofia Tavla. "Application of B-Spline Basis Functions as Harmonic Functions for the Concurrent Shape and Mesh Morphing of Airfoils." In GPPS Chania22. GPPS, 2022. http://dx.doi.org/10.33737/gpps22-tc-9.

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The automatic deformation of the computational mesh along with the deformed geometry in design optimization cycles is a valuable procedure, as it reduces the required time for the construction of new meshes. The introduction of harmonic coordinates for the deformation of objects included within a closed mesh (cage) has been introduced in computer graphics. Harmonic coordinates result from solutions to the Laplace’s equation (harmonic functions) using a numerical solver. In this work, a modification to the classical harmonic coordinates’ concept is introduced for the deformation of 2D geometries (and the corresponding computational mesh) which are defined as B-spline curves. The B-spline basis functions are used as harmonic functions along the mesh boundary, being also the geometry to be deformed. Thus, any deformation of the B-Spline boundary, through the movement of the curve’s control points, can be successfully propagated to the interior of the computational domain, resulting in the concurrent and conformable modification of the B-Spline boundary and the entire computational mesh. For the computation of harmonic coordinates a node-centered Finite-Volume based Laplace solver for unstructured meshes is used, enhanced with an agglomeration multigrid scheme. The proposed method is applied and assessed for the shape and mesh morphing of airfoils.
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Chihab, N., A. Zergainoh, and J. P. Astruc. "Generalized non-uniform B-spline functions for discrete signal interpolation." In Seventh International Symposium on Signal Processing and Its Applications, 2003. Proceedings. IEEE, 2003. http://dx.doi.org/10.1109/isspa.2003.1224832.

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Martin, Tobias, Elaine Cohen, and Mike Kirby. "Volumetric parameterization and trivariate b-spline fitting using harmonic functions." In the 2008 ACM symposium. New York, New York, USA: ACM Press, 2008. http://dx.doi.org/10.1145/1364901.1364938.

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Reports on the topic "B-spline functions"

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Saunders, Bonita, and Qiming Wang. From b-spline mesh generation to effective visualizations for the NIST digital library of mathematical functions. Gaithersburg, MD: National Institute of Standards and Technology, 2007. http://dx.doi.org/10.6028/nist.ir.7402.

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