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Artykuły w czasopismach na temat „B-spline”

Autor: Grafiati

Data publikacji: 4 czerwca 2021

Data aktualizacji: 25 lipca 2025

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1

Jena, Hrushikesh. "A Constructive Approach to Bivariate Hyperbolic Box Spline Functions." Armenian Journal of Mathematics 17, no. 1 (2025): 1–18. https://doi.org/10.52737/18291163-2025.17.1-1-18.

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This article is based on the construction procedure of bivariate hyperbolic box spline functions. Generally, box splines are considered as the multivariate generalizations of univariate B-splines. Both B-splines and box splines are refinable functions. Two different kinds of box splines like the polynomial box splines and the trigonometric box splines along with their usefulness are well studied in literature. However, another variant of box splines named as the class of hyperbolic box spline functions, has not gained much attention. This article focuses on the construction of bivariate hyperb

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2

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 (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, a

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3

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

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Spline adaptive filter has a different architecture than linear-in-parameter nonlinear filters like Volterra filter. There are various kinds of splines like Bezier spline, B-spline and rational B-spline. Rational B spline has weights associated with control points and hence, provides more flexibility than B-spline to create a curve. This paper presents development of rational b-spline adaptive filter for active noise control. Updating equations to update control points and weights of control points are derived. A simulation study is presented to study performance of proposed rational B-spline

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4

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

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5

Speleers, Hendrik. "Algorithm 1020: Computation of Multi-Degree Tchebycheffian B-Splines." ACM Transactions on Mathematical Software 48, no. 1 (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

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6

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 (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

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7

Budakçı, Gülter, and Halil Oruç. "Further Properties of Quantum Spline Spaces." Mathematics 8, no. 10 (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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8

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 (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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9

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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10

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 (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 a

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11

Korotkiy, V. A. "CUBIC B-SPLINES: PRACTICAL APPLICATION." Vestnik komp'iuternykh i informatsionnykh tekhnologii, no. 235 (January 2024): 12–21. http://dx.doi.org/10.14489/vkit.2024.01.pp.012-021.

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Two constructive algorithms for forming cubic B-splines passing through given points with tangents indicated at these points are proposed. The first algorithm provides a composite cubic B-spline curve passing through n reference points. The composite curve is formed by 3(n-1) elementary cubic segments. At the reference points, the curvature of all segments is zero. Controlling the shape of the curve (with given tangents at the reference points) is achieved by moving auxiliary control points along the given tangents. The second algorithm allows the formation of a cubic B-spline that passes only

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12

Journal, Baghdad Science. "B-splines Algorithms for Solving Fredholm Linear Integro-Differential Equations." Baghdad Science Journal 1, no. 2 (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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13

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 (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

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14

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 (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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15

Sihombing, Pardomuan Robinson, and Ade Famalika. "Penerapan Analisis Regresi Nonparametrik dengan Pendekatan Regresi Kernel dan Spline." Jurnal Ekonomi Dan Statistik Indonesia 2, no. 2 (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-spl

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16

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

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17

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

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Strelkovskaya, Irina, Irina Solovskaya, and Juliya Strelkovska. "Application of real and complex splines in infocommunication problems." Problemi telekomunìkacìj, no. 1(28) (December 22, 2021): 3–19. http://dx.doi.org/10.30837/pt.2021.1.01.

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The work offers the solution to problems of analysis and synthesis of infocommunication systems with the help of real and complex spline functions. The use of the spline approximation method for solving problems of recovery of random signals and self-similar traffic, management of network objects and network as a whole, and procedures of infocommunication objects and networks functioning is offered. To solve the problems of forecasting, in particular, forecasting the characteristics of network traffic and maintaining the QoS characteristics in its service and formation of requirements for netw

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19

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 (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 symm

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20

XING, JUN, JIAHAN LI, RUNQING YANG, XIAOJING ZHOU, and SHIZHONG XU. "Bayesian B-spline mapping for dynamic quantitative traits." Genetics Research 94, no. 2 (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

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21

Zhao, Yanchun, Mengzhu Zhang, Qian Ni, and Xuhui Wang. "Adaptive Nonparametric Density Estimation with B-Spline Bases." Mathematics 11, no. 2 (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

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22

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 (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-spli

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23

Ganchuk, S. N., A. S. Starkova, O. V. Krivosheev, S. V. Mavrin, and Ryzhov S. A. "SMOOTH B-SPLINE MATCHING WITH ADDITIONAL CONSTRAINTS. PART 1: B-SPLINE AND ITS DERIVATIVES." Vestnik komp'iuternykh i informatsionnykh tekhnologii, no. 251 (May 2025): 10–14. https://doi.org/10.14489/vkit.2025.05.pp.010-014.

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Smooth conjugation of B-splines is one of the main functional operations in modern CAD-systems. An analytical method for smooth optimal conjugation of parametric curves represented as B-splines is proposed. Optimality is achieved by minimizing the metric of the difference between the original and conjugate splines. The neighborhood of the conjugation point is a parametric function (B-spline) belonging to the class of functions C ( p – 1), where p is the degree of the original splines. It is possible to supplement the optimization problem with pre-defined constraints that smoothly conjugate fun

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Ni, Qian, and Chen Xie. "Stretch-Energy-Minimizing B-Spline Interpolation Curves and Their Applications." Mathematics 11, no. 21 (2023): 4534. http://dx.doi.org/10.3390/math11214534.

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In this paper, we propose a new method to construct energy-minimizing cubic B-spline interpolation curves by minimizing the approximated stretch energy. The construction of a B-spline interpolation curve with a minimal approximated stretch energy can be addressed by solving a sparse linear system. The proof of both the existence and uniqueness of the solution for the linear system is provided. In addition, we analyze the computational cost of cubic B-spline curves with an approximated stretch energy, which is close to that of the ordinary interpolation method with cubic B-splines without the r

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

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

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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 (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 solut

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

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

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

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

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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 (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 adju

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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

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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 (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 nila

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MacCarthy, B. L., and N. D. Burns. "An Evaluation of Spline Functions for use in Cam Design." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 199, no. 3 (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 algebra

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Strelkovskaya, Irina, Irina Solovskaya та Anastasiya Makoganiuk. "Spline-Extrapolation Method in Traﬃc Forecasting in 5G Networks". Journal of Telecommunications and Information Technology 3 (30 вересня 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 predi

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36

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

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37

JENA, M. K. "CONSTRUCTION OF COMPACTLY SUPPORTED WAVELETS FROM TRIGONOMETRIC B-SPLINES." International Journal of Wavelets, Multiresolution and Information Processing 09, no. 05 (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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Shubhashree Bebarta, Shubhashree Bebarta, Bibhakar Kodamasingh Bibhakar Kodamasingh, and Ranjan Kumar Jati Ranjan Kumar Jati. "A Short Survey on B-spline and Bezier Methods." International Journal of Engineering and Science Invention 14, no. 5 (2025): 15–20. https://doi.org/10.35629/6734-14051520.

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Two effective techniques for approximating data in all areas of engineering problems are the B-spline and Bezier methods. They can be used for data interpolation with a few tweaks and enhancements. Although there are various methods for formulating B-splines in the literature, the B-spline equation is defined by a set of independent functions. The number of pairs of data or control points is equal to the number of coefficients in the B-spline equation. The B-spline method's benefit is that most set functions decrease at specific control points. The governing parametric equations can be drawn t

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Gondegaon, Sangamesh, and Hari K. Voruganti. "Spline Parameterization of Complex Planar Domains for Isogeometric Analysis." Journal of Theoretical and Applied Mechanics 47, no. 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 a

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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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Ezhov, Nikolaj, Frank Neitzel, and Svetozar Petrovic. "Spline approximation, Part 1: Basic methodology." Journal of Applied Geodesy 12, no. 2 (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. Man

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42

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 (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

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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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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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Vasiliev, N. P., and M. R. Vagizov. "Using B-splines for alignment of satellite geolocation elevation data." Geodesy and Cartography 1014, no. 12 (2025): 54–59. https://doi.org/10.22389/0016-7126-2024-1014-12-54-59.

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The possibility of constructing analytical models of terrain elevation is studied with mathematical apparatus of B-splines based on satellite geolocation data. For constructing regression models the main nodes of splines are chosen independently of measurements. An algorithmic approach is discussed to avoid degenerate cases, which may arise from this selection. B-splines can be used to create more accurate digital elevation models; their applications in practical field are land-use planning, disaster risk management and mapping, operational visualization of more accurate geofield data. The pre

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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 regis

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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 (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 l

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Liu, Xu Min, Wei Xiang Xu, Jing Xu, and Yong Guan. "G¹/C¹ Matching of Spline Curves." Applied Mechanics and Materials 20-23 (January 2010): 202–8. http://dx.doi.org/10.4028/www.scientific.net/amm.20-23.202.

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The research is mainly made on the G1/C1 matching condition of spline curves. On the basis of the analysis on the basic function of T-B spline curves and the features of curve endpoints, we proposed the n+1 order T-B spline basic function and the solving method. The G1/C1 matching condition of C-B spline curves and T-B spline curves is put forward in this paper. On this condition, when matching C-B spline curves and T-B spline curves, the controlling vertexes can be added to make C-B spline curve tangent with the first and last edge by the first and last vertex of controlling polygon. Applicat

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49

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

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

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