Relevant bibliographies by topics / B-spliny

Contents

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

Academic literature on the topic 'B-spliny'

Author: Grafiati
Published: 28 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "B-spliny"

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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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Istiqomatul Fajriyah Yuliati and Pardomuan Sihombing. "Pemodelan Fertilitas Di Indonesia Tahun 2017 Menggunakan Pendekatan Regresi Nonparametrik Kernel dan Spline." Jurnal Statistika dan Aplikasinya 4, no. 1 (June 30, 2020): 48–60. http://dx.doi.org/10.21009/jsa.04105.

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Tujuan dari penelitian ini adalah untuk menganalisis pola hubungan Total Fertility Rate (TFR) dengan Contraceptive Prevalence Rate (CPR). Analisis yang sering digunakan untuk pemodelan adalah analisis regresi. Analisis regresi menurut pendekatannya dapat dibedakan menjadi dua, parametrik dan nonparametrik. Metode regresi nonparametrik yang sering digunakan adalah regresi kernel dan spline. Pada penelitian ini untuk regresi kernel yang digunakan adalah regresi kernel dengan metode penaksir Nadaraya-Watson (NWE) dan penaksir polinomial lokal (LPE), sedangkan untuk regresi spline yang digunakan adalah smoothing spline dan b-splines. Hasil pengepasan kurva (fitting curve) menunjukkan bahwa model regresi nonparametrik terbaik adalah model regresi b-splines dengan degree 2 dan jumlah knot 5. Hal ini dikarenakan model regresi b-splines memiliki kurva yang halus dan terlihat lebih mengikuti sebaran data dibandingkan kurva model regresi lainnya. Model regresi b-splines terpilih memiliki nilai koefisien determinasi R2 sebesar 76.86%, artinya besarnya variasi variabel TFR yang dijelaskan oleh model regresi b-splines sebesar 76.86%, sedangkan sisanya 23.14% dijelaskan oleh variabel lainnya yang tidak dimasukkan ke dalam model.
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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. "B-splines Algorithms for Solving Fredholm Linear Integro-Differential Equations." Baghdad Science Journal 1, no. 2 (June 6, 2004): 340–46. http://dx.doi.org/10.21123/bsj.1.2.340-346.

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Algorithms using the second order of B -splines [B (x)] and the third order of B -splines [B,3(x)] are derived to solve 1' , 2nd and 3rd linear Fredholm integro-differential equations (F1DEs). These new procedures have all the useful properties of B -spline function and can be used comparatively greater computational ease and efficiency.The results of these algorithms are compared with the cubic spline function.Two numerical examples are given for conciliated the results of this method.
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Ezhov, Nikolaj, Frank Neitzel, and Svetozar Petrovic. "Spline Approximation, Part 2: From Polynomials in the Monomial Basis to B-splines—A Derivation." Mathematics 9, no. 18 (September 8, 2021): 2198. http://dx.doi.org/10.3390/math9182198.

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In a series of three articles, spline approximation is presented from a geodetic point of view. In part 1, an introduction to spline approximation of 2D curves was given and the basic methodology of spline approximation was demonstrated using splines constructed from ordinary polynomials. In this article (part 2), the notion of B-spline is explained by means of the transition from a representation of a polynomial in the monomial basis (ordinary polynomial) to the Lagrangian form, and from it to the Bernstein form, which finally yields the B-spline representation. Moreover, the direct relation between the B-spline parameters and the parameters of a polynomial in the monomial basis is derived. The numerical stability of the spline approximation approaches discussed in part 1 and in this paper, as well as the potential of splines in deformation detection, will be investigated on numerical examples in the forthcoming part 3.
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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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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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Dokken, T., V. Skytt, and O. Barrowclough. "LOCALLY REFINED SPLINES REPRESENTATION FOR GEOSPATIAL BIG DATA." ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XL-3/W3 (August 20, 2015): 565–70. http://dx.doi.org/10.5194/isprsarchives-xl-3-w3-565-2015.

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When viewed from distance, large parts of the topography of landmasses and the bathymetry of the sea and ocean floor can be regarded as a smooth background with local features. Consequently a digital elevation model combining a compact smooth representation of the background with locally added features has the potential of providing a compact and accurate representation for topography and bathymetry. The recent introduction of Locally Refined B-Splines (LR B-splines) allows the granularity of spline representations to be locally adapted to the complexity of the smooth shape approximated. This allows few degrees of freedom to be used in areas with little variation, while adding extra degrees of freedom in areas in need of more modelling flexibility. In the EU fp7 Integrating Project IQmulus we exploit LR B-splines for approximating large point clouds representing bathymetry of the smooth sea and ocean floor. A drastic reduction is demonstrated in the bulk of the data representation compared to the size of input point clouds. The representation is very well suited for exploiting the power of GPUs for visualization as the spline format is transferred to the GPU and the triangulation needed for the visualization is generated on the GPU according to the viewing parameters. The LR B-splines are interoperable with other elevation model representations such as LIDAR data, raster representations and triangulated irregular networks as these can be used as input to the LR B-spline approximation algorithms. Output to these formats can be generated from the LR B-spline applications according to the resolution criteria required. The spline models are well suited for change detection as new sensor data can efficiently be compared to the compact LR B-spline representation.
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WULANDARY, SEPTIE, and DRAJAT INDRA PURNAMA. "PERBANDINGAN REGRESI NONPARAMETRIK KERNEL DAN B-SPLINES PADA PEMODELAN RATA-RATA LAMA SEKOLAH DAN PENGELUARAN PERKAPITA DI INDONESIA." Jambura Journal of Probability and Statistics 1, no. 2 (November 18, 2020): 89–97. http://dx.doi.org/10.34312/jjps.v1i2.7501.

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Analisis regresi merupakan salah satu alat statistik yang banyak digunakan untuk mengetahui hubungan antara dua variabel acak atau lebih. Metode penaksiran model regresi terbagi atas regresi parametrik dan nonparametrik. Penelitian ini bertujuan menganalisis pola hubungan pengeluaran perkapita terhadap rata-rata lama sekolah di Indonesia tahun 2018 melalui perbandingan regresi nonparametrik, yaitu regresi kernel dan spline. Regresi kernel yang digunakan adalah regresi kernel dengan metode penaksir Nadaraya-Watson (NWE), sedangkan regresi spline yang digunakan adalah B-Splines. Berdasarkan nilai Generalized Cross Validation (GCV) yang minimum dari model regresi B-Splines, digunakan model dengan degree 2. Perbandingan model terbaik antara model NWE dan B-Splines dilakukan berdasarkan nilai RMSE terkecil dan kurva yang dihasilkan. Pada penelitian ini, model yang terbaik adalah model B-Splines karena memiliki RMSE 0,705, lebih kecil dibandingkan NWE dengan RMSE 1,854. Selain itu, regresi B-Splines memiliki kurva yang halus dan mengikuti sebaran data dibandingkan kurva NWE.
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XING, JUN, JIAHAN LI, RUNQING YANG, XIAOJING ZHOU, and SHIZHONG XU. "Bayesian B-spline mapping for dynamic quantitative traits." Genetics Research 94, no. 2 (April 2012): 85–95. http://dx.doi.org/10.1017/s0016672312000249.

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SummaryOwing to their ability and flexibility to describe individual gene expression at different time points, random regression (RR) analyses have become a popular procedure for the genetic analysis of dynamic traits whose phenotypes are collected over time. Specifically, when modelling the dynamic patterns of gene expressions in the RR framework, B-splines have been proved successful as an alternative to orthogonal polynomials. In the so-called Bayesian B-spline quantitative trait locus (QTL) mapping, B-splines are used to characterize the patterns of QTL effects and individual-specific time-dependent environmental errors over time, and the Bayesian shrinkage estimation method is employed to estimate model parameters. Extensive simulations demonstrate that (1) in terms of statistical power, Bayesian B-spline mapping outperforms the interval mapping based on the maximum likelihood; (2) for the simulated dataset with complicated growth curve simulated by B-splines, Legendre polynomial-based Bayesian mapping is not capable of identifying the designed QTLs accurately, even when higher-order Legendre polynomials are considered and (3) for the simulated dataset using Legendre polynomials, the Bayesian B-spline mapping can find the same QTLs as those identified by Legendre polynomial analysis. All simulation results support the necessity and flexibility of B-spline in Bayesian mapping of dynamic traits. The proposed method is also applied to a real dataset, where QTLs controlling the growth trajectory of stem diameters in Populus are located.
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Dissertations / Theses on the topic "B-spliny"

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Lorenczyk, Jiří. "Matematický popis trajektorie pohybu vozidla." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2020. http://www.nusl.cz/ntk/nusl-445453.

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The goal of this thesis is to nd types of curves which would allow for the construction of a path that could be traversed by a vehicle. It seems that a minimal constraint for such a path is the continuity of curve's curvature. This leads to a closer look at the three types of curves: Clothoids, which are able to smoothly connect straights with arcs of a constant curvature, interpolation quintic splines, which are C2 smooth in the interpolation nodes and -splines, these belong to the family of quintic polynomial curves too, however, they are characterised by the vector of parameters which modies the shape of the curve. The thesis is accompanied by an application allowing for manual construction of the path composed of spline curves.
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Hladíková, Hana. "Metody konstrukce výnosové křivky státních dluhopisů na českém dluhopisovém trhu." Doctoral thesis, Vysoká škola ekonomická v Praze, 2008. http://www.nusl.cz/ntk/nusl-71673.

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The zero coupon yield curve is one of the most fundamental tools in finance and is essential in the pricing of various fixed-income securities. Zero coupon rates are not observable in the market for a range of maturities. Therefore, an estimation methodology is required to derive the zero coupon yield curves from observable data. If we deal with approximations of empirical data to create yield curves it is necessary to choose suitable mathematical functions. We discuss the following methods: the methods based on cubic spline functions, methods employing linear combination of the Fourier or exponential basis functions and the parametric model of Nelson and Siegel. The current mathematical apparatus employed for this kind of approximation is outlined. In order to find parameters of the models we employ the least squares minimization of computed and observed prices. The theoretical background is applied to an estimation of the zero-coupon yield curves derived from the Czech coupon bond market. Application of proper smoothing functions and weights of bonds is crucial if we want to select a method which performs best according to given criteria. The best performance is obtained for Bspline models with smoothing.
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Pereira, Larissa Rocha. "Ajuste de curva B-spline fechada com peso." Universidade Federal de Uberlândia, 2014. https://repositorio.ufu.br/handle/123456789/14947.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
The aim of this work is to develop a method of curve fitting using closed B-spline closed for application on reconstruction of cross-sections of objects. For this study specifically where the sections are closed curves, it has been implemented a method to close the curve B-spline curve, in such way that the curve is smooth on the closing point. The developed method is based on least squares approximation with weights, which defines that the curve should be as close as possible to the real curve. The weights in this case are responsible for the tightness of the approximation to each data points, whose points represent the coordinate of the object section that will be rebuild. Moreover, adjustments and impositions on the curve have been proposed so that it has a better result and represent more accurately the desired cross section. Particular characteristics of the curve were used to help enforce and define the settings. For the analysis, B-spline curves using the developed method, were obtained showing good results.
O objetivo desse trabalho é desenvolver um método de ajuste de curvas B-spline fechada para a aplicação na reconstrução de seções transversais de um objeto. Por especificamente nesse trabalho as seções serem seções fechadas, foi implementado um método para o fechamento da curva B-spline, de modo que a mesma possuía suavidade no seu fechamento. O método desenvolvido e utilizado foi baseado na aproximação por mínimos quadrados com pesos, que define que a curva obtida deva ser mais próxima possível da curva real. Os pesos nesse caso são responsáveis pela aproximação ou afastamento da curva em relação aos pontos dados, pontos esses que melhor representam as coordenadas da seção do objeto que se deseja reconstruir. Além disso, foram desenvolvidos ajustes e imposições na curva para que ela tivesse um melhor resultado e representasse de forma mais fiel a seção transversal desejada. Para a imposição e definição dos ajustes foram utilizadas características particulares da curva. Para a análise, curvas B-spline utilizando o método desenvolvido, foram traçadas e foram constatados os resultados desejados.
Mestre em Engenharia Mecânica
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Elsaesser, Bernhard. "Approximation mit rationalen B-Spline Kurven und Flaechen. Approximation with rational B-spline curves and surfaces." Phd thesis, Shaker, 1998. https://tuprints.ulb.tu-darmstadt.de/1126/1/elsaesser.pdf.

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Dag, Idris. "Studies of B-spline finite elements." Thesis, Bangor University, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.358041.

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Rojas, Roberto. "Geometric trimming of B-spline surfaces." Thesis, Virginia Tech, 1994. http://hdl.handle.net/10919/40634.

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Elsässer, Bernhard [Verfasser]. "Approximation mit rationalen B-Spline Kurven und Flaechen. Approximation with rational B-spline curves and surfaces / Bernhard Elsaesser." Darmstadt : Universitäts- und Landesbibliothek Darmstadt, 2008. http://d-nb.info/1104177943/34.

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Aggarwal, Aditya Mohan. "B-Spline Boundary Element Method for Ships." ScholarWorks@UNO, 2008. http://scholarworks.uno.edu/td/853.

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The development of a three dimensional B-Spline based method, which is suitable for the steady-state potential flow analysis of free surface piercing bodies in hydrodynamics, is presented. The method requires the B-Spline or Non Uniform Rational B-Spline (NURBS) representation of the body as an input. In order to solve for the unknown potential, the source surface, both for the body as well as the free surface, is represented by NURBS surfaces. The method does not require the body surface to be discritized into flat panels. Therefore, instead of a mere panel approximation, the exact body geometry is utilized for the computation. The technique does not use a free surface Green's function, which already satisfies the linear free surface boundary conditions, but uses a separate source patch for the free surface. By eliminating the use of a free surface Green's function, the method can be extended to considering non-linear free surface conditions, thus providing the possibility for wave resistance calculations. The method is first applied to the double body flow problem around a sphere and a Wigley hull. Some comparisons are made with exact solutions to validate the accuracy of the method. Results of linear free surface conditions are then presented.
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Junger, Jean-Claude. "Modélisation et réalisation d'une prothèse de genou." Vandoeuvre-les-Nancy, INPL, 1993. http://www.theses.fr/1993INPL052N.

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La complexité du mouvement des os de l'articulation du genou requiert une étude anatomique pour construire une prothèse de genou. Une bonne prothèse repose sur des surfaces permettant tous les mouvements du genou. Le nouveau type de prothèse présenté ici, est le résultat de cette approche scientifique. Dans un premier temps, nous mesurons les surfaces des condyles et de la trochlée d'une population significative d'os humains en utilisant une machine triaxiale. Puis, nous déterminons une surface moyenne servant de base à la réalisation de notre prothèse. Ensuite, en utilisant les techniques des fonctions b-splines, nous étudions les paramètres permettant de reconstruire la surface des condyles tout en respectant la cinématique ligamentaire et la transmission des contraintes. Notre prothèse respecte la position de la rotule sur les condyles et la trochlée et présente une forme proche de la forme anatomique. En relation avec cette étude, nous avons développé de nouveaux types de tiges intramédullaires ainsi que la technique de pose associée
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Tazeroualti, Mohammed. "Modélisation de surfaces à l'aide de fonctions splines : conception d'un verre progressif." Grenoble 1, 1993. http://tel.archives-ouvertes.fr/tel-00343495.

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Ce travail se décompose en trois parties distinctes. Dans la première partie, on introduit un algorithme du type Gauss-Seidel pour la minimisation de fonctionnelles symétriques semi-définies positives. La convergence de cet algorithme est démontrée. En application, on donne deux méthodes de lissage de surfaces. Ces méthodes sont basées sur l'idée de ramener un probleme de lissage a deux dimensions a la resolution d'une suite de problèmes a une dimension faciles a résoudre. Pour cela on utilise l'opération d'inf-convolution spline. Dans la deuxième partie, on introduit une nouvelle methode pour la conception d'un verre progressif. Ce verre est représente par une surface suffisamment régulière, a laquelle on impose des conditions sur ses courbures principales dans certaines zones (zone de vision de loin et zone de vision de pres), et des conditions sur ses directions principales de courbure dans d'autres zones (zone nasale et zone temporale). La surface est écrite sous forme de produit tensoriel de b-splines de degré quatre. Pour la calculer, on est amené a minimiser un opérateur non quadratique. Cette minimisation est alors effectuée par un procédé itératif dont on a teste numériquement la convergence rapide
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Books on the topic "B-spliny"

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

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

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Prautzsch, Hartmut, Wolfgang Boehm, and Marco Paluszny. Bézier and B-Spline Techniques. Berlin, Heidelberg: Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/978-3-662-04919-8.

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Prautzsch, Hartmut. Bézier and B-Spline Techniques. Berlin, Heidelberg: Springer Berlin Heidelberg, 2002.

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Gregory, John A. The weighted v-spline as a double knot B-spline. Uxbridge: Brunel University,Department of Mathematics and Statistics, 1991.

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Harries, Stefan. Parametric design and hydrodynamic optimization of ship hull forms. Berlin: Mensch-und-Buch-Verl., 1998.

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Hllig, Klaus. Finite element methods with B-splines. Philadelphia, PA: Society for Industrial and Applied Mathematics, 2003.

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Höllig, Klaus, and Jörg Hörner. Approximation and Modeling with B-Splines. Philadelphia, PA: Society for Industrial and Applied Mathematics, 2013. http://dx.doi.org/10.1137/1.9781611972955.

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Finite element methods with B-splines. Philadelphia: Society Industrial and Applied Mathematics, 2003.

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Ennis, Marguerite. Modelling non-negative outcomes using B-splines. Toronto: [s.n.], 1996.

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Book chapters on the topic "B-spliny"

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Singh, Dhananjay, Madhusudan Singh, and Zaynidinov Hakimjon. "B-Spline Approximation for Polynomial Splines." In Signal Processing Applications Using Multidimensional Polynomial Splines, 13–19. Singapore: Springer Singapore, 2018. http://dx.doi.org/10.1007/978-981-13-2239-6_2.

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Guha, Sumanta. "B-Spline." In Computer Graphics Through OpenGL, 557–90. Third edition. | Boca Raton : Taylor & Francis, a CRC title, part of the Taylor & Francis imprint, a member of the Taylor & Francis Group, the academic division of T&F Informa, plc, 2018.: Chapman and Hall/CRC, 2018. http://dx.doi.org/10.1201/9780429464171-18.

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Lyche, Tom, Carla Manni, and Hendrik Speleers. "Foundations of Spline Theory: B-Splines, Spline Approximation, and Hierarchical Refinement." In Lecture Notes in Mathematics, 1–76. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-94911-6_1.

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Prautzsch, Hartmut, Wolfgang Boehm, and Marco Paluszny. "B-spline representation." In Bézier and B-Spline Techniques, 59–75. Berlin, Heidelberg: Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/978-3-662-04919-8_5.

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Prautzsch, Hartmut, Wolfgang Boehm, and Marco Paluszny. "B-spline techniques." In Bézier and B-Spline Techniques, 77–89. Berlin, Heidelberg: Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/978-3-662-04919-8_6.

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Salomon (emeritus), David. "B-Spline Approximation." In Texts in Computer Science, 731–801. London: Springer London, 2011. http://dx.doi.org/10.1007/978-0-85729-886-7_14.

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de Boor, Carl, and Manfred R. Trummer. "B-Splines." In Splinefunktionen, 49–57. Basel: Birkhäuser Basel, 1990. http://dx.doi.org/10.1007/978-3-0348-9133-2_7.

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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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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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Christensen, Ole. "B-splines." In Frames and Bases, 1–11. Boston: Birkhäuser Boston, 2008. http://dx.doi.org/10.1007/978-0-8176-4678-3_6.

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Conference papers on the topic "B-spliny"

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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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Wang, Mingming, and Xiaoping Qian. "Efficient Filtering in Topology Optimization via B-Splines." In ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/detc2014-34712.

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This paper presents a B-spline based approach for topology optimization of three-dimensional (3D) problems where the density representation is based on B-splines. Compared with the usual density filter in topology optimization, the new B-spline based density representation approach is advantageous in both memory usage and CPU time. This is achieved through the use of tensor-product form of B-splines. As such, the storage of the filtered density variables is linear with respect to the effective filter size instead of the cubic order as in the usual density filter. Numerical examples of 3D topology optimization of minimal compliance and heat conduction problems are demonstrated. We further reveal that our B-spline based density representation resolves the bottleneck challenge in multiple density per element optimization scheme where the storage of filtering weights had been prohibitively expensive.
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Carminelli, Antonio, and Giuseppe Catania. "PB-Spline Hybrid Surface Fitting Technique." In ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-87195.

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This work considers the fitting of data points organized in a rectangular array to parametric spline surfaces. Point Based (PB) splines, a generalization of tensor product splines, are adopted. The basic idea of this paper is to fit large scale data with a tensorial B-spline surface and to refine the surface until a specified tolerance is met. Since some isolated domains exceeding tolerance may result, detail features on these domains are modeled by a tensorial B-spline basis with a finer resolution, superimposed by employing the PB-spline approach. The present method leads to an efficient model of free form surfaces, since both large scale data and local geometrical details can be efficiently fitted. Two application examples are presented. The first one concerns the fitting of a set of data points sampled from an interior car trim with a central geometrical detail. The second one refers to the modification of the tensorial B-spline surface representation of a mould in order to create a local adjustment. Considerations regarding strengths and limits of the approach then follow.
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Fujioka, Hiroyuki, and Hiroyuki Kano. "Constrained smoothing and interpolating spline surfaces using normalized uniform B-splines." In 2009 IEEE International Conference on Industrial Technology - (ICIT). IEEE, 2009. http://dx.doi.org/10.1109/icit.2009.4939537.

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Fujioka, Hiroyuki, and Hiroyuki Kano. "Recursive construction of smoothing spline surfaces using normalized uniform B-splines." In 2009 Joint 48th IEEE Conference on Decision and Control (CDC) and 28th Chinese Control Conference (CCC). IEEE, 2009. http://dx.doi.org/10.1109/cdc.2009.5399523.

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de Menezes, Fa´bio G. T., and Prota´sio Dutra Martins. "B-Splines Geometric Modeling for Dynamic Analysis Behaviour in Offshore Systems." In 25th International Conference on Offshore Mechanics and Arctic Engineering. ASMEDC, 2006. http://dx.doi.org/10.1115/omae2006-92091.

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This work reports a study of B-Spline curves and surfaces applied to the geometric definition of hulls of ships and oil drilling and production platforms. The research aims at defining mathematically the floating body surface in suitable formats for the analysis of functional behaviour of the design object with sophisticated methods and tools. The WAMIT system was chosen as a reference in the research due to its reliability as a professional tool for hydrodynamic behaviour of floating systems in practice. The B-Spline model is input to the WAMIT system in the required format for the analysis of hull motion response to waves. The quality of the results obtained with B-Splines modeling was compared the ones obtained with flat panels. B-Splines have shown to be an effective approach, more efficient in computing terms when compared with the flat panels approach and suitable to optimization scripts. It revealed itself as a more adequate procedure to the design work as it simplifies the hull form mathematical definition of floating systems.
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Yang, Yanli, De Ma, and Ting Yu. "Interpolation by nonuniform B-spline through uniform B-spline filter banks." In 2016 IEEE International Conference on Digital Signal Processing (DSP). IEEE, 2016. http://dx.doi.org/10.1109/icdsp.2016.7868582.

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Forsey, David R., and Richard H. Bartels. "Hierarchical B-spline refinement." In the 15th annual conference. New York, New York, USA: ACM Press, 1988. http://dx.doi.org/10.1145/54852.378512.

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Nemnem, Ahmed F., Mark G. Turner, Kiran Siddappaji, and Marshall Galbraith. "A Smooth Curvature-Defined Meanline Section Option for a General Turbomachinery Geometry Generator." In ASME Turbo Expo 2014: Turbine Technical Conference and Exposition. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/gt2014-26363.

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The blade geometry design process is integral to the development and advancement of compressors and turbines in gas turbines or aeroengines. An airfoil section design feature has been added to a previously developed open source parametric 3D blade design tool. The second derivative of the mean-line (related to the curvature) is controlled using B-splines to create the airfoils. This is analytically integrated twice to obtain the mean-line. A smooth thickness distribution is then added to the airfoil with two options either the Wennerstrom distribution or a quartic B-spline thickness distribution. B-splines have also been implemented to achieve customized airfoil leading and trailing edges. Geometry for a turbine, compressor, and transonic fan are presented along with a demonstration of the importance of airfoil smoothness.
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Tsay, Der Min, Chien Wen Chen, and Jiun Ren Chen. "Surface Generation and Machining With Rational B-Splines for Turbomachinery Components." In ASME Turbo Expo 2002: Power for Land, Sea, and Air. ASMEDC, 2002. http://dx.doi.org/10.1115/gt2002-30485.

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To five-axis point mill turbomachinery components, a least squares approximation procedure for generating tool paths in terms of parametric rational B-splines is presented. The detailed processes of using the appropriate parameters of rational B-splines that will reduce the amount of geometric deviations between the designed and machined part surfaces are proposed. Compared to a traditional linear tool path, a rational B-spline tool path can substantially reduce the number of blocks on machine controllers without compromising the accuracy. As a result, the machining efficiency and machine dynamic behavior can be improved. Numerical and experimental results are given to show such improvements. A practical application example for machining a centrifugal compressor impeller with 12 blades is also illustrated to demonstrate the reliability and usefulness of the developed procedure.
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Reports on the topic "B-spliny"

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

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Ramamurti, Sita, and David Gilsinn. Bicubic b-spline surface approximation of invariant tori. Gaithersburg, MD: National Institute of Standards and Technology, 2010. http://dx.doi.org/10.6028/nist.ir.7731.

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Manke, J. A tensor product B-spline method for numerical grid generation. Office of Scientific and Technical Information (OSTI), October 1989. http://dx.doi.org/10.2172/5005256.

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Dede, Luca, and Hugo A. Santos. B-spline goal-oriented error estimators for geometrically nonlinear rods. Fort Belvoir, VA: Defense Technical Information Center, April 2011. http://dx.doi.org/10.21236/ada555331.

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Siddiqui, Matheen, and Stan Sclaroff. Surface Reconstruction from Multiple Views Using Rational B-Splines. Fort Belvoir, VA: Defense Technical Information Center, June 2001. http://dx.doi.org/10.21236/ada440710.

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Manke, J. A tensor product b-spline method for 3D multi-block elliptic grid generation. Office of Scientific and Technical Information (OSTI), December 1988. http://dx.doi.org/10.2172/5536897.

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DE Boor, Carl. The Exact Condition of the B-Spline Basis May be Hard to Determine. Fort Belvoir, VA: Defense Technical Information Center, July 1988. http://dx.doi.org/10.21236/ada204080.

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Evans, John A., and Thomas J. Hughes. Isogeometric Divergence-conforming B-splines for the Darcy-Stokes-Brinkman Equations. Fort Belvoir, VA: Defense Technical Information Center, January 2012. http://dx.doi.org/10.21236/ada555390.

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Evans, John A., and Thomas J. Hughes. Isogeometric Divergence-conforming B-splines for the Steady Navier-Stokes Equations. Fort Belvoir, VA: Defense Technical Information Center, April 2012. http://dx.doi.org/10.21236/ada560496.

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Evans, John A., and Thomas J. Hughes. Isogeometric Divergence-conforming B-splines for the Unsteady Navier-Stokes Equations. Fort Belvoir, VA: Defense Technical Information Center, April 2012. http://dx.doi.org/10.21236/ada560939.

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