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Journal articles on the topic 'B-spline'

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Author: Grafiati

Published: 4 June 2021

Last updated: 6 September 2023

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1

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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2

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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3

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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4

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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5

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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6

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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7

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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8

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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9

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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10

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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11

N, Gajalakshmi, and Karunanith S. "Image segmentation and preserve the boundary of the image using b-spline basis." Journal of Computational Mathematica 5, no. 2 (December 20, 2021): 121–31. http://dx.doi.org/10.26524/cm115.

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This paper focuses the knot insertion in the B-spline collocation matrix, with nonnegative determinants in all n x n sub-matrices. Further by relating the number of zeros in B-spline basis as well as changes (sign changes) in the sequence of its B-spline coefficients. From this relation, we obtained an accurate characterization when interpolation by B-splines correlates with the changes leads uniqueness and this ensures the optimal solution. Simultaneously we computed the knot insertion matrix and B-spline collocation matrix and its sub-matrices having nonnegative determinants. The totality of the knot insertion matrix and B-spline collocation matrix is demonstrated in the concluding section by using the input image and shows that these concepts are fit to apply and reduce the errors through mean square error and PSNR values

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12

Sihombing, Pardomuan Robinson, and Ade Famalika. "Penerapan Analisis Regresi Nonparametrik dengan Pendekatan Regresi Kernel dan Spline." Jurnal Ekonomi Dan Statistik Indonesia 2, no. 2 (August 29, 2022): 172–81. http://dx.doi.org/10.11594/jesi.02.02.05.

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Penelitian ini bertujuan untuk menerapkan regresi nonparametrik menggunakan regresi kernel dan spline. Regresi kernel menggunakan metode penaksir Nadaraya-Watson (NWE) dan penaksir Polinomial Lokal (LPE), sedangkan untuk regresi spline adalah smoothing spline dan b-splines. Metode ini diterapkan dalam menganalisis pola hubungan Pertumbuhan Produksi Industri (PPI) dan Tingkat Pajak Perusahaan (TPP). 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. TPP berpengaruh signifikan negatif terhadap PPI artinya kenaikan TPP akan menurunkan PPI. Oleh sebab itu perlu kebijakan yang komprehensif dalam menerapkan nilai TPP agar tetap dapat meningkatkan produktivitas industri.

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13

Rajashekar, Naraveni, Sudhakar Chaudhary, and V. V. K. Srinivas Kumar. "Approximation of p-Biharmonic Problem using WEB-Spline based Mesh-Free Method." International Journal of Nonlinear Sciences and Numerical Simulation 20, no. 6 (October 25, 2019): 703–12. http://dx.doi.org/10.1515/ijnsns-2018-0298.

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Abstract We describe and analyze the weighted extended b-spline (WEB-Spline) mesh-free finite element method for solving the p-biharmonic problem. The WEB-Spline method uses weighted extended b-splines as basis functions on regular grids and does not require any mesh generation which eliminates a difficult, time consuming preprocessing step. Accurate approximations are possible with relatively low-dimensional subspaces. We perform some numerical experiments to demonstrate the efficiency of the WEB-Spline method.

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14

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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15

Zhao, Yanchun, Mengzhu Zhang, Qian Ni, and Xuhui Wang. "Adaptive Nonparametric Density Estimation with B-Spline Bases." Mathematics 11, no. 2 (January 5, 2023): 291. http://dx.doi.org/10.3390/math11020291.

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Learning density estimation is important in probabilistic modeling and reasoning with uncertainty. Since B-spline basis functions are piecewise polynomials with local support, density estimation with B-splines shows its advantages when intensive numerical computations are involved in the subsequent applications. To obtain an optimal local density estimation with B-splines, we need to select the bandwidth (i.e., the distance of two adjacent knots) for uniform B-splines. However, the selection of bandwidth is challenging, and the computation is costly. On the other hand, nonuniform B-splines can improve on the approximation capability of uniform B-splines. Based on this observation, we perform density estimation with nonuniform B-splines. By introducing the error indicator attached to each interval, we propose an adaptive strategy to generate the nonuniform knot vector. The error indicator is an approximation of the information entropy locally, which is closely related to the number of kernels when we construct the nonuniform estimator. The numerical experiments show that, compared with the uniform B-spline, the local density estimation with nonuniform B-splines not only achieves better estimation results but also effectively alleviates the overfitting phenomenon caused by the uniform B-splines. The comparison with the existing estimation procedures, including the state-of-the-art kernel estimators, demonstrates the accuracy of our new method.

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16

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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17

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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18

Sukri, Nursyazni Binti Mohamad, Puteri Ainna Husna Binti Megat Mohd, Siti Musliha Binti Nor-Al-Din, and Noor Khairiah Binti Razali. "Irregular Symmetrical Object Designed By Using Lambda Miu B-Spline Degree Four." Journal of Physics: Conference Series 2084, no. 1 (November 1, 2021): 012018. http://dx.doi.org/10.1088/1742-6596/2084/1/012018.

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Abstract In Computer Aided Geometry Design (CAGD), B-splines curves are piecewise polynomial parametric curves that play an important role. CAGD involves the interpolation and approximation curves and surfaces. CAGD has been widely used which brings good impact of computers to industries in manufacturing. There are many improved methods in the B-spline curve such as extended cubic B-spline, trigonometric B-spline, quasi trigonometric B-spline, and λμ-B-spline. Each of the methods has its behaviour and advantage. In this paper, λμ-B-spline was used to be implemented in generating irregular symmetrical objects. λμ-B-spline has a shape parameter that can change the global shape by manipulating the value of the shape parameter. The bottle has been chosen as an irregular symmetrical object. The 2-dimensional symmetrical curves of Bottle design were formed by using λμ-B-spline degree 4. The curves designed are dependent on the shape parameter which can be adjusted. Then, the curves generated were revolved using the Sweep Surface method to form 3-dimensional objects. Every object has its volume and this research focused on the numerical method which was Simpson’s 3/8 to compute the volume. The volumes obtained were compared to the actual volume to determine the best shape parameter used. The results show that the λμ-B-spline curve with a shape parameter of 1 is the best shape parameter in designing symmetrical irregular objects with the desired volume.

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19

XU, Gang. "Extended Cubic Uniform B-spline and α-B-spline." Acta Automatica Sinica 34, no. 8 (March 2, 2009): 980–83. http://dx.doi.org/10.3724/sp.j.1004.2008.00980.

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20

XU, Gang, and Guo-Zhao WANG. "Extended Cubic Uniform B-spline and α-B-spline." Acta Automatica Sinica 34, no. 8 (August 2008): 980–84. http://dx.doi.org/10.1016/s1874-1029(08)60047-6.

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21

Zhao, Yuming, Zhongke Wu, Xingce Wang, and Xinyue Liu. "G2 Blending Ball B-Spline Curve by B-Spline." Proceedings of the ACM on Computer Graphics and Interactive Techniques 6, no. 1 (May 12, 2023): 1–16. http://dx.doi.org/10.1145/3585504.

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Blending two Ball B-Spline Curves(BBSC) is an important tool in modeling tubular objects. In this paper, we propose a new BBSC blending method. Our method has the following three main contributions: First, we use BBSC instead of ball Bézier to model the blending part to expand the solution space and make the resultant BBSC have better fairness. Second, we consider both the skeleton line and radius of BBSC, which makes the skeleton line and radius consistent. Thirdly, we propose a two-step optimization process to solve the problem of excessive amount of parameters brought by expanding the solution space, so that our method satisfies the real-time.

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22

Bien, Ai-Ping, and Fuhua Cheng. "Alternate spline: A generalized B-spline." Journal of Approximation Theory 51, no. 2 (October 1987): 138–59. http://dx.doi.org/10.1016/0021-9045(87)90028-1.

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23

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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Sissouno, N. "Anisotropic spline approximation with non-uniform B-splines." Applicable Analysis 97, no. 2 (November 14, 2016): 135–44. http://dx.doi.org/10.1080/00036811.2016.1254774.

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25

TSIANOS, KONSTANTINOS I., and RON GOLDMAN. "BEZIER AND B-SPLINE CURVES WITH KNOTS IN THE COMPLEX PLANE." Fractals 19, no. 01 (March 2011): 67–86. http://dx.doi.org/10.1142/s0218348x11005221.

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We extend some well known algorithms for planar Bezier and B-spline curves, including the de Casteljau subdivision algorithm for Bezier curves and several standard knot insertion procedures (Boehm's algorithm, the Oslo algorithm, and Schaefer's algorithm) for B-splines, from the real numbers to the complex domain. We then show how to apply these polynomial and piecewise polynomial algorithms in a complex variable to generate many well known fractal shapes such as the Sierpinski gasket, the Koch curve, and the C-curve. Thus these fractals also have Bezier and B-spline representations, albeit in the complex domain. These representations allow us to change the shape of a fractal in a natural manner by adjusting their complex Bezier and B-spline control points. We also construct natural parameterizations for these fractal shapes from their Bezier and B-spline representations.

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26

Gou, Zhi Jian, and Cheng Wang. "The Trajectory Planning and Simulation for Industrial Robot Based on Fifth-Order B-Splines." Applied Mechanics and Materials 538 (April 2014): 367–70. http://dx.doi.org/10.4028/www.scientific.net/amm.538.367.

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The trajectory is planned with fifth-order uniform B-splines for the industrial robot aimed to assure the motion is smooth and the trajectory is fourth-order continuous. Under the premise to satisfy the initial kinematic parameters of the robot as zero, its speed, acceleration and jerk are continuous. Based on B-spline theory, process five B-spline curve function is calculated inversely in joint space. Under the robot kinematics parameter constraints, using fifth-order B-spline interpolates to plan robot trajectory when known interpolation points and the kinematic parameters are simulated and validated by the software of ADAMS.So it provides an effective new method for the trajectory planning.

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27

Le-Thi-Thu, Nga, Khoi Nguyen-Tan, and Thuy Nguyen-Thanh. "Reconstruction of Low Degree B-spline Surfaces with Arbitrary Topology Using Inverse Subdivision Scheme." Journal of Science and Technology: Issue on Information and Communications Technology 3, no. 1 (March 31, 2017): 82. http://dx.doi.org/10.31130/jst.2017.41.

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Multivariate B-spline surfaces over triangular parametric domain have many interesting properties in the construction of smooth free-form surfaces. This paper introduces a novel approach to reconstruct triangular B-splines from a set of data points using inverse subdivision scheme. Our proposed method consists of two major steps. First, a control polyhedron of the triangular B-spline surface is created by applying the inverse subdivision scheme on an initial triangular mesh. Second, all control points of this B-spline surface, as well as knotclouds of its parametric domain are iteratively adjusted locally by a simple geometric fitting algorithm to increase the accuracy of the obtained B-spline. The reconstructed B-spline having the low degree along with arbitrary topology is interpolative to most of the given data points after some fitting steps without solving any linear system. Some concrete experimental examples are also provided to demonstrate the effectiveness of the proposed method. Results show that this approach is simple, fast, flexible and can be successfully applied to a variety of surface shapes.

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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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29

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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30

Lin, Hongwei, Yunyang Xiong, and Hongwei Liao. "Semi-structured B-spline for blending two B-spline surfaces." Computers & Mathematics with Applications 68, no. 7 (October 2014): 706–18. http://dx.doi.org/10.1016/j.camwa.2014.07.013.

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31

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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32

JENA, M. K. "CONSTRUCTION OF COMPACTLY SUPPORTED WAVELETS FROM TRIGONOMETRIC B-SPLINES." International Journal of Wavelets, Multiresolution and Information Processing 09, no. 05 (September 2011): 843–65. http://dx.doi.org/10.1142/s021969131100433x.

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We construct a class of semiorthogonal wavelets by taking a normalized trigonometric B-spline of any order as the scaling function. The construction is based on generalized Euler–Frobenius polynomial and generalized autocorrelation function. We also show that the odd order normalized trigonometric B-spline satisfies convex hull property as well as partition of unity property. Moreover, we also present a subdivision algorithm for the convolution of normalized trigonometric B-splines. Several examples of wavelet are also provided.

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33

Lamnii, A., M. Lamnii, and H. Mraoui. "Constructing B-spline representation of quadratic Sibson–Thomson splines." Computer Aided Geometric Design 33 (February 2015): 66–81. http://dx.doi.org/10.1016/j.cagd.2015.02.001.

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34

Xu, Huixia, and Qianqian Hu. "Approximating uniform rational B-spline curves by polynomial B-spline curves." Journal of Computational and Applied Mathematics 244 (May 2013): 10–18. http://dx.doi.org/10.1016/j.cam.2012.11.019.

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35

WANG, Hui, Chun-Gang ZHU, and Cai-Yun LI. "Construction of B-spline surface from cubic B-spline asymptotic quadrilateral." Journal of Advanced Mechanical Design, Systems, and Manufacturing 11, no. 4 (2017): JAMDSM0044. http://dx.doi.org/10.1299/jamdsm.2017jamdsm0044.

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36

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

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Analogous to the quartic B-splines curve, a piecewise quartic trigonometric polynomial B-spline curve with two shape parameters is presented in this paper. Each curve segment is generated by three consecutive control points. The given curve posses many properties of the B-spline curve. These curves are closer to the control polygon than the different other curves considered in this paper, for different values of shape parameters for each curve. With the increase of the value of shape parameters, the curve approach to the control polygon. For nonuniform and uniform knot vector the given curves have C0, G3; C1, G3; C1, G7; and C3 continuity for different choice of shape parameters. A quartic trigonometric Bézier curves are also introduced as a special case of the given trigonometric spline curves. A comparison of quartic trigonometric polynomial curve is made with different other curves. In the last, quartic trigonometric spline surfaces with two shape parameters are constructed. They have most properties of the corresponding curves.

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37

Gondegaon, Sangamesh, and Hari K. Voruganti. "Spline Parameterization of Complex Planar Domains for Isogeometric Analysis." Journal of Theoretical and Applied Mechanics 47, no. 1 (March 1, 2017): 18–35. http://dx.doi.org/10.1515/jtam-2017-0002.

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Abstract Isogeometric Analysis (IGA) involves unification of modelling and analysis by adopting the same basis functions (splines), for both. Hence, spline based parametric model is the starting step for IGA. Representing a complex domain, using parametric geometric model is a challenging task. Parameterization problem can be defined as, finding an optimal set of control points of a B-spline model for exact domain modelling. Also, the quality of parameterization, too has significant effect on IGA. Finding the B-spline control points for any given domain, which gives accurate results is still an open issue. In this paper, a new planar B-spline parameterization technique, based on domain mapping method is proposed. First step of the methodology is to map an input (non-convex) domain onto a unit circle (convex) with the use of harmonic functions. The unique properties of harmonic functions: global minima and mean value property, ensures the mapping is bi-jective and with no self-intersections. Next step is to map the unit circle to unit square to make it apt for B-spline modelling. Square domain is re-parameterized by using conventional centripetal method. Once the domain is properly parameterized, the required control points are computed by solving the B-spline tensor product equation. The proposed methodology is validated by applying the developed B-spline model for a static structural analysis of a plate, using isogeometric analysis. Different domains are modelled to show effectiveness of the given technique. It is observed that the proposed method is versatile and computationally efficient.

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38

Ezhov, Nikolaj, Frank Neitzel, and Svetozar Petrovic. "Spline approximation, Part 1: Basic methodology." Journal of Applied Geodesy 12, no. 2 (April 25, 2018): 139–55. http://dx.doi.org/10.1515/jag-2017-0029.

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Abstract In engineering geodesy point clouds derived from terrestrial laser scanning or from photogrammetric approaches are almost never used as final results. For further processing and analysis a curve or surface approximation with a continuous mathematical function is required. In this paper the approximation of 2D curves by means of splines is treated. Splines offer quite flexible and elegant solutions for interpolation or approximation of “irregularly” distributed data. Depending on the problem they can be expressed as a function or as a set of equations that depend on some parameter. Many different types of splines can be used for spline approximation and all of them have certain advantages and disadvantages depending on the approximation problem. In a series of three articles spline approximation is presented from a geodetic point of view. In this paper (Part 1) the basic methodology of spline approximation is demonstrated using splines constructed from ordinary polynomials and splines constructed from truncated polynomials. In the forthcoming Part 2 the notion of B-spline will be explained in a unique way, namely by using the concept of convex combinations. The numerical stability of all spline approximation approaches as well as the utilization of splines for deformation detection will be investigated on numerical examples in Part 3.

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Wang, Zhihua, Falai Chen, and Jiansong Deng. "Evaluation Algorithm of PHT-Spline Surfaces." Numerical Mathematics: Theory, Methods and Applications 10, no. 4 (September 12, 2017): 760–74. http://dx.doi.org/10.4208/nmtma.2017.0003.

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AbstractPHT-splines are a type of polynomial splines over hierarchical T-meshes which posses perfect local refinement property. This property makes PHT-splines useful in geometric modeling and iso-geometric analysis. Current implementation of PHT-splines stores the basis functions in Bézier forms, which saves some computational costs but consumes a lot of memories. In this paper, we propose a de Boor like algorithm to evaluate PHT-splines provided that only the information about the control coefficients and the hierarchical mesh structure is given. The basic idea is to represent a PHT-spline locally in a tensor product B-spline, and then apply the de-Boor algorithm to evaluate the PHT-spline at a certain parameter pair. We perform analysis about computational complexity and memory costs. The results show that our algorithm takes about the same order of computational costs while requires much less amount of memory compared with the Bézier representations. We give an example to illustrate the effectiveness of our algorithm.

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40

László, Lajos. "Cubic spline interpolation with quasiminimal B-spline coefficients." Acta Mathematica Hungarica 107, no. 1-2 (February 2005): 77–87. http://dx.doi.org/10.1007/s10474-005-0180-4.

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41

Loe, K. F. "αB-spline: a linear singular blending B-spline." Visual Computer 12, no. 1 (January 1996): 18–25. http://dx.doi.org/10.1007/bf01782216.

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42

Du, Xiaogang, Jianwu Dang, Yangping Wang, Song Wang, and Tao Lei. "A Parallel Nonrigid Registration Algorithm Based on B-Spline for Medical Images." Computational and Mathematical Methods in Medicine 2016 (2016): 1–14. http://dx.doi.org/10.1155/2016/7419307.

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The nonrigid registration algorithm based on B-spline Free-Form Deformation (FFD) plays a key role and is widely applied in medical image processing due to the good flexibility and robustness. However, it requires a tremendous amount of computing time to obtain more accurate registration results especially for a large amount of medical image data. To address the issue, a parallel nonrigid registration algorithm based on B-spline is proposed in this paper. First, the Logarithm Squared Difference (LSD) is considered as the similarity metric in the B-spline registration algorithm to improve registration precision. After that, we create a parallel computing strategy and lookup tables (LUTs) to reduce the complexity of the B-spline registration algorithm. As a result, the computing time of three time-consuming steps including B-splines interpolation, LSD computation, and the analytic gradient computation of LSD, is efficiently reduced, for the B-spline registration algorithm employs the Nonlinear Conjugate Gradient (NCG) optimization method. Experimental results of registration quality and execution efficiency on the large amount of medical images show that our algorithm achieves a better registration accuracy in terms of the differences between the best deformation fields and ground truth and a speedup of 17 times over the single-threaded CPU implementation due to the powerful parallel computing ability of Graphics Processing Unit (GPU).

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43

Ismaeel, Najim. "Trigonometric B-Spline Interpolation." Journal of Garmian University 4, ICBS Conference (July 1, 2017): 122–30. http://dx.doi.org/10.24271/garmian.130.

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44

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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45

He, Xuming, and Peide Shi. "Monotone B-Spline Smoothing." Journal of the American Statistical Association 93, no. 442 (June 1998): 643. http://dx.doi.org/10.2307/2670115.

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46

Forsey, David R., and Richard H. Bartels. "Hierarchical B-spline refinement." ACM SIGGRAPH Computer Graphics 22, no. 4 (August 1988): 205–12. http://dx.doi.org/10.1145/378456.378512.

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47

Engleitner, Nora, and Bert Jüttler. "Patchwork B-spline refinement." Computer-Aided Design 90 (September 2017): 168–79. http://dx.doi.org/10.1016/j.cad.2017.05.021.

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48

Wang, Guozhao, Qinyu Chen, and Minghua Zhou. "NUAT B-spline curves." Computer Aided Geometric Design 21, no. 2 (February 2004): 193–205. http://dx.doi.org/10.1016/j.cagd.2003.10.002.

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49

Shi, Kan-Le, Jun-Hai Yong, Jia-Guang Sun, and Jean-Claude Paul. "B-spline surface interpolation." Computer Aided Geometric Design 28, no. 6 (August 2011): 368–81. http://dx.doi.org/10.1016/j.cagd.2011.06.002.

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50

Pang, D., L. A. Ferrari, and P. V. Sankar. "B-spline FIR filters." Circuits Systems and Signal Processing 13, no. 1 (March 1994): 31–64. http://dx.doi.org/10.1007/bf01183840.

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