Relevant bibliographies by topics / B-spline

Contents

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

Academic literature on the topic 'B-spline'

Author: Grafiati
Published: 4 June 2021
Last updated: 6 September 2023

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Journal articles on the topic "B-spline"

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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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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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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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Liu, Xinyue, Xingce Wang, Zhongke Wu, Dan Zhang, and Xiangyuan Liu. "Extending Ball B-spline by B-spline." Computer Aided Geometric Design 82 (October 2020): 101926. http://dx.doi.org/10.1016/j.cagd.2020.101926.

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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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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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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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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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Loe, K. F. "?B-spline: a linear singular blending B-spline." Visual Computer 12, no. 1 (January 1, 1996): 18–25. http://dx.doi.org/10.1007/s003710050044.

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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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Dissertations / Theses on the topic "B-spline"

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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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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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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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Mößner, Bernhard. "B-splines als Finite Elemente /." Aachen : Shaker, 2006. http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&doc_number=015210875&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA.

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Lampis, Alberto. "Sul Calcolo di B-Spline Tchebycheffiane Multi-Order." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2021. http://amslaurea.unibo.it/23217/.

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Viene descritto un nuovo algoritmo numericamente stabile per il calcolo di B-spline Tchebycheffiane multi-order, basato sull'espressione delle matrici relative alla procedura di knot insertion in termini dei coefficienti di Greville generalizzati dello spazio in analisi.
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Armstrong, Curtis A. "Vectorization of Raster Images Using B-Spline Surfaces." Diss., CLICK HERE for online access, 2006. http://contentdm.lib.byu.edu/ETD/image/etd1513.pdf.

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Aggarwal, Bhavya. "B-spline finite elements for plane elasticity problems." Texas A&M University, 2006. http://hdl.handle.net/1969.1/4849.

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The finite element method since its development in the 1950’s has been used extensively in solving complex problems involving partial differential equations. The conventional finite element methods use piecewise Lagrange interpolation functions for approximating displacements. The aim of this research is to explore finite element analysis using B-spline interpolation. B-splines are piecewise defined polynomial curves which provide higher continuity of derivatives than piecewise Lagrange interpolation functions. This work focuses on the implementation and comparison of the B-spline finite elements in contrast with the conventional finite elements. This thesis observes that the use of B-spline interpolation functions can reduce the computational cost significantly. It is an efficient technique and can be conveniently implemented into the existing finite element programs.
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Books on the topic "B-spline"

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

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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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1928-, Boehm Wolfgang, and Paluszny Marco 1950-, eds. Bézier and B-spline techniques. Berlin: Springer, 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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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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Goldman, Ronald N., and Tom Lyche, eds. Knot Insertion and Deletion Algorithms for B-Spline Curves and Surfaces. Philadelphia, PA: Society for Industrial and Applied Mathematics, 1992. http://dx.doi.org/10.1137/1.9781611971583.

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Book chapters on the topic "B-spline"

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

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AbstractThe univariate minimal support B-spline basis (UMB) has been used in Computer Aided Design (CAD) since the 1970s. Freeform curves use UMB, while sculptured surfaces are represented using a tensor product of two UMBs. The coefficients of a B-spline curve and surface are respectively represented in a vector and a rectangular grid. In CAD-intersection algorithms for UMB represented objects, a divide-and-conquer strategy is often used. Refinement by knot insertion is used to split the objects intersected into objects of the same type with a smaller geometric extent. In many cases the intersection of the resulting sub-objects has simpler topology than the original problem. The sub-objects created are represented using their parents’ UMB format and deleted when the sub-problem is solved. Consequently, no global representations of the locally refined bases are needed. This is contrary to when locally refined splines are used for approximation of large point sets. As soon as a B-spline is locally refined, the regular structure of UMB objects in CAD is no longer valid. In this chapter we discuss how Locally Refined B-splines (LR B-splines) address this challenge and present the properties of LR B-splines.
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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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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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Kermarrec, Gaël, Vibeke Skytt, and Tor Dokken. "LR B-Spline Surfaces and Volumes for Deformation Analysis of Terrain Data." In Optimal Surface Fitting of Point Clouds Using Local Refinement, 81–107. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-16954-0_6.

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AbstractGeospatial data acquisition of terrains with contact-free sensors such as Terrestrial or Airbone Laser Scanners generates scattered and noisy point clouds. Performing a surface approximation is an efficient way to reduce and structure the recorded point clouds. To that end, LR B-splines are attractive as they allow a local refinement, on the contrary to the tensor product B-spline and raster surfaces. By comparing the approximation error with a given tolerance, a local refinement is performed. We apply this adaptive refinement strategy to landslides data sets from Alpine terrain in Austria. We show how different epochs of the point clouds can be analyzed with LR B-spline volumes for spatio-temporal visualisation of deformation. We highlight the potential of a time-differenced LR B-splines volume for analysing geomorphological changes. A further application of this method is the drawing of contour lines.
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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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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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Kermarrec, Gaël, Vibeke Skytt, and Tor Dokken. "Conclusion." In Optimal Surface Fitting of Point Clouds Using Local Refinement, 109–11. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-16954-0_7.

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AbstractIn this SpringerBrief, we went through the mathematical concepts of LR B-splines in all its facets, explaining in details how the spline space can be refined and the different strategies for adaptive approximation.
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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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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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Conference papers on the topic "B-spline"

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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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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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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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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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Gu, Yu, and Xiaoping Qian. "B-Spline Based Robust Topology Optimization." In ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/detc2015-46076.

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In this paper, we present an extension of the B-spline based density representation to a robust formulation of topology optimization. In our B-spline based topology optimization approach, we use separate representations for material density distribution and analysis. B-splines are used as a representation of density and the usual finite elements are used for analysis. The density undergoes a Heaviside projection to reduce the grayness in the optimized structures. To ensure minimal length control so the resulting designs are robust with respect to manufacturing imprecision, we adopt a three-structure formulation during the optimization. That is, dilated, intermediate and eroded designs are used in the optimization formulation. We give an analytical description of minimal length of features in optimized designs. Numerical examples have been implemented on three common topology optimization problems: minimal compliance, heat conduction and compliant mechanism. They demonstrate that the proposed approach is effective in generating designs with crisp black/white transition and is accurate in minimal length control.
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Chen, Yifan, and Klaus-Peter Beier. "B2: An Interactive Quality Visualization and Improvement Technique for B-Spline Surfaces." In ASME 1998 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1998. http://dx.doi.org/10.1115/detc98/dac-5586.

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Abstract A new interactive technique for B-spline surface quality visualization and improvement, called the B2 method, is presented. This method interpolates the control points of a given B-spline surface using a second B-spline surface. If small irregularities exist in the control points of the original surface, they will be magnified through the second B-spline and demonstrated as large distortions in its control points. This facilitates the detection of small surface irregularities. Subsequently, the surface may be improved through direct and interactive adjustment of the second B-spline’s control polyhedron.
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Wei Chen, Ting Chen, and Wentao Wang. "B-spline with shape parameter." In 2010 3rd International Conference on Advanced Computer Theory and Engineering (ICACTE 2010). IEEE, 2010. http://dx.doi.org/10.1109/icacte.2010.5579539.

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da Silva, L. M. C., and M. S. V. de Paiva. "B-spline generation in FPGA." In 2012 VIII Southern Conference on Programmable Logic (SPL). IEEE, 2012. http://dx.doi.org/10.1109/spl.2012.6211798.

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Xin, Wang, and Tu Yunxia. "A faster B spline snake." In 2009 IEEE International Conference on Robotics and Biomimetics (ROBIO). IEEE, 2009. http://dx.doi.org/10.1109/robio.2009.5420738.

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Reports on the topic "B-spline"

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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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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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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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Yapp, Clifford W. An Investigation into Conversion from Non-Uniform Rational B-Spline Boundary Representation Geometry to Constructive Solid Geometry. Fort Belvoir, VA: Defense Technical Information Center, December 2015. http://dx.doi.org/10.21236/ada624518.

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Li, Xin, Eric L. Miller, Carey Rappaport, and Michael Silevich. An Adaptive B-Spline Method for Low-order Image Reconstruction Problems - Final Report - 09/24/1997 - 09/24/2000. Office of Scientific and Technical Information (OSTI), April 2000. http://dx.doi.org/10.2172/791462.

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Vásquez, Diego Mauricio, and Luis Fernando Melo-Velandia. Estimación de la estructura a plazos de las tasas de interés en Colombia por medio del método de funciones B-spline cúbicas. Bogotá, Colombia: Banco de la República, May 2002. http://dx.doi.org/10.32468/be.210.

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