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Journal articles on the topic 'B-Spline Curve'

Author: Grafiati

Published: 6 September 2023

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1

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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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

Tirandaz, H., A. Nasrabadi, and J. Haddadnia. "Curve Matching and Character Recognition by Using B-Spline Curves." International Journal of Engineering and Technology 3, no. 2 (2011): 183–86. http://dx.doi.org/10.7763/ijet.2011.v3.221.

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4

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. Application instances were put up in this paper which illustrated that the G1/C1 matching between T-B spline curve and C-B spline curve using the feature of T-B spline curve which can represents semiellipse arc (semicircle arc) precisely can solve the problem that C-B spline curve cannot represents semiellipse arc (semicircle arc) precisely.

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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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6

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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7

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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8

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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9

Cheng, Fuhua, Xuefu Wang, and B. A. Barsky. "Quadratic B-spline curve interpolation." Computers & Mathematics with Applications 41, no. 1-2 (January 2001): 39–50. http://dx.doi.org/10.1016/s0898-1221(01)85004-5.

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10

Lord, Marilyn. "Curve and Surface Representation by Iterative B-Spline Fit to a Data Point Set." Engineering in Medicine 16, no. 1 (January 1987): 29–35. http://dx.doi.org/10.1243/emed_jour_1987_016_008_02.

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The method of B-splines provides a very powerful way of representing curves and curved surfaces. The definition is ideally suited to applications in Computer Aided Design (CAD) where the designer is required to remodel the surface by reference to interactive graphics. This particular facility can be advantageous in CAD of body support surfaces, such as design of sockets of limb prostheses, shoe insoles, and custom seating. The B-spline surface is defined by a polygon of control points which in general do not lie on the surface, but which form a convex hull enclosing the surface. Each control point can be adjusted to remodel the surface locally. The resultant curves are well behaved. However, in these biomedical applications the original surface prior to modification is usually defined by a limited set of point measurements from the body segment in question. Thus there is a need initially to define a B-spline surface which interpolates this set of data points. In this paper, a computer-iterative method of fitting a B-spline surface to a given set of data points is outlined, and the technique is demonstrated for a curve. Extension to a surface is conceptually straightforward.

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11

Pigounakis, Kostis G., Nickolas S. Sapidis, and Panagiotis D. Kaklis. "Fairing Spatial B-Spline Curves." Journal of Ship Research 40, no. 04 (December 1, 1996): 351–67. http://dx.doi.org/10.5957/jsr.1996.40.4.351.

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Three-dimensional curves are playing an increasing role in ship-hull modeling and many other areas of computer-aided design (CAD). The problem of evaluating and improving the fairness of such a curve is considered and three solutions (algorithms) are proposed representing all major methodologies currently pursued by CAD researchers: local fairing by knot removal, and local/global fairing based on "energy" minimization. The performance of the algorithms is studied for both cubic and quintic B-splines using realistic test cases. Finally, a comparison with existing techniques is presented and some visualization tools for spatial-curve fairing are briefly discussed.

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12

Chen, Li Juan, and Ming Zhu Li. "T-B Spline Curves with a Shape Parameter." Applied Mechanics and Materials 241-244 (December 2012): 2144–48. http://dx.doi.org/10.4028/www.scientific.net/amm.241-244.2144.

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A T-B spline curves with a shape parameter λ is presented in this paper, which has simple structure and can be used to design curves. Analogous to the four B-spline curves, each curve segment is generated by five consecutive control points. For equidistant knots, the curves are C^2 continuous, but when the shape parameter λ equals to 0 , the curves are C^3 continuous. Moreover, this spline curve can be used to construct open and closed curves and can express ellipses conveniently.

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13

Chen, Xiao-Diao, Weiyin Ma, and Jean-Claude Paul. "Cubic B-spline curve approximation by curve unclamping." Computer-Aided Design 42, no. 6 (June 2010): 523–34. http://dx.doi.org/10.1016/j.cad.2010.01.008.

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14

Li, Ai Min, and Hai Bo Tian. "A Multiresolution Fairing Approach for NURBS Curves." Applied Mechanics and Materials 215-216 (November 2012): 1205–8. http://dx.doi.org/10.4028/www.scientific.net/amm.215-216.1205.

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Curve fairing has an important influence on curve editing and geometric modeling. Though there has been several different kinds of fairing methods, Multiresolution curve fairing has higher efficiency and simpler algorithms. Different from existing multiresolution curve fairing, a new multiresolution approach is presented based on non-uniform semiorthogonal B-spline wavelets, which can be applied for NURBS curve fairing. It has no restriction to B-spline curves’ knot sequence. This method effectively overcomes the limit of uniform or quasi-uniform B-spline wavelets for fairing. A detailed example is given to show the effectiveness of this multiresolution fairing method.

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15

Srinivasan, L. N., and Q. Jeffrey Ge. "Fine Tuning of Rational B-Spline Motions." Journal of Mechanical Design 120, no. 1 (March 1, 1998): 46–51. http://dx.doi.org/10.1115/1.2826675.

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This paper presents two algorithms for fine-tuning rational B-spline motions suitable for Computer Aided Design. The problem of fine-tuning of rational motions is studied as that of fine-tuning rational curves in a projective dual three-space, called the image curves. The path-smoothing algorithm automatically detects and smoothes out the third order geometric discontinuities in the path of a cubic rational B-spline image curve. The speed-smoothing algorithm uses a quintic rational spline image curve to obtain a second-order geometric approximation of the path of a cubic rational B-spline image curve while allowing specification of the speed and the rate of change of speed at the key points to obtain a near constant kinetic energy parameterization. The results have applications in Cartesian trajectory planning in robotics, spatial navigation in visualization and virtual reality systems, as well as mechanical system simulation.

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16

Ojo, Adebayo, Maurizio Collu, and Andrea Coraddu. "Parametric Curve Comparison for Modeling Floating Offshore Wind Turbine Substructures." Energies 16, no. 14 (July 14, 2023): 5371. http://dx.doi.org/10.3390/en16145371.

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The drive for the cost reduction of floating offshore wind turbine (FOWT) systems to the levels of fixed bottom foundation turbine systems can be achieved with creative design and analysis techniques of the platform with free-form curves to save numerical simulation time and minimize the mass of steel (cost of steel) required for design. This study aims to compare four parametric free-form curves (cubic spline, B-spline, Non-Uniform Rational B-Spline and cubic Hermite spline) within a design and optimization framework using the pattern search gradient free optimization algorithm to explore and select an optimal design from the design space. The best performance free-form curve within the framework is determined using the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS). The TOPSIS technique shows the B-spline curve as the best performing free-form curve based on the selection criteria, amongst which are design and analysis computational time, estimated mass of platform and local shape control properties. This study shows that free-form curves like B-spline can be used to expedite the design, analysis and optimization of floating platforms and potentially advance the technology beyond the current level of fixed bottom foundations.

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17

XIAO, YIJUN, MINGYUE DING, and JIAXIONG PENG. "B-SPLINE BASED STEREO FOR 3D RECONSTRUCTION OF LINE-LIKE OBJECTS USING AFFINE CAMERA MODEL." International Journal of Pattern Recognition and Artificial Intelligence 15, no. 02 (March 2001): 347–58. http://dx.doi.org/10.1142/s0218001401000915.

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This paper presents a novel curve based algorithm of stereo vision to reconstruct 3D line-like objects. B-spline approximations of 2D edge curves are selected as primitives for the reconstruction of their corresponding space curves so that, under the assumption of affine camera model, a 3D curve can be derived from reconstructing its control points according to the affine invariant property of B-Spline curves. The superiority of B-spline model in representing free-form curves gives good geometric properties of reconstruction results. Both theoretical analysis and experimental results demonstrate the validity of our approach.

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18

Zhang, Wan Jun, Feng Zhang, and Jun Hai Zhao. "Research on Modification Algorithm of Cubic B-Spline Curve Interpolation Technology." Applied Mechanics and Materials 687-691 (November 2014): 1596–99. http://dx.doi.org/10.4028/www.scientific.net/amm.687-691.1596.

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Based on cubic B-Spline curve mathematical properties, theoretical analysis the cubic B-Spline curve recursive formula of Taylor development of first-order, derivation of two order in the interpolation cycle under the condition of certain interpolation increment only and interpolation speed, change the interpolation increments can be amended cubic times B-Spline curves purpose The simulation results show that meet the high-speed and high-accuracy NC machine tool require-ments of CNC systems.

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19

Wang, C. H., H. Y. Liu, and R. S. Wen. "Pipelined computations of B-spline curve." IEEE Transactions on Systems, Man, and Cybernetics 22, no. 2 (1992): 327–31. http://dx.doi.org/10.1109/21.148406.

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20

Haron, H., A. Rehman, D. I. S. Adi, S. P. Lim, and T. Saba. "Parameterization Method on B-Spline Curve." Mathematical Problems in Engineering 2012 (2012): 1–22. http://dx.doi.org/10.1155/2012/640472.

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The use of computer graphics in many areas allows a real object to be transformed into a three-dimensional computer model (3D) by developing tools to improve the visualization of two-dimensional (2D) and 3D data from series of data point. The tools involved the representation of 2D and 3D primitive entities and parameterization method using B-spline interpolation. However, there is no parameterization method which can handle all types of data points such as collinear data points and large distance of two consecutive data points. Therefore, this paper presents a new parameterization method that is able to solve those drawbacks by visualizing the 2D primitive entity of scanned data point of a real object and construct 3D computer model. The new method has improved a hybrid method by introducing exponential parameterization method in the beginning of the reconstruction process, followed by computing B-spline basis function to find maximum value of the function. The improvement includes solving a linear system of the B-spline basis function using numerical method. Improper selection of the parameterization method may lead to the singularity matrix of the system linear equations. The experimental result on different datasets show that the proposed method performs better in constructing the collinear and two consecutive data points compared to few parameterization methods.

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21

Jung, Hyung Bae, and Kwangsoo Kim. "The redefinition of B-spline curve." International Journal of Advanced Manufacturing Technology 57, no. 1-4 (August 11, 2011): 265–70. http://dx.doi.org/10.1007/s00170-010-3128-y.

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22

Lara-Ramirez, Jose Edgar, Carlos Hugo Garcia-Capulin, Maria de Jesus Estudillo-Ayala, Juan Gabriel Avina-Cervantes, Raul Enrique Sanchez-Yanez, and Horacio Rostro-Gonzalez. "Parallel Hierarchical Genetic Algorithm for Scattered Data Fitting through B-Splines." Applied Sciences 9, no. 11 (June 6, 2019): 2336. http://dx.doi.org/10.3390/app9112336.

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Curve fitting to unorganized data points is a very challenging problem that arises in a wide variety of scientific and engineering applications. Given a set of scattered and noisy data points, the goal is to construct a curve that corresponds to the best estimate of the unknown underlying relationship between two variables. Although many papers have addressed the problem, this remains very challenging. In this paper we propose to solve the curve fitting problem to noisy scattered data using a parallel hierarchical genetic algorithm and B-splines. We use a novel hierarchical structure to represent both the model structure and the model parameters. The best B-spline model is searched using bi-objective fitness function. As a result, our method determines the number and locations of the knots, and the B-spline coefficients simultaneously and automatically. In addition, to accelerate the estimation of B-spline parameters the algorithm is implemented with two levels of parallelism, taking advantages of the new hardware platforms. Finally, to validate our approach, we fitted curves from scattered noisy points and results were compared through numerical simulations with several methods, which are widely used in fitting tasks. Results show a better performance on the reference methods.

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23

Li, Jun Cheng, Guo Hua Chen, and Lian Yang. "The Quadratic Trigonometric B-Spline Curve with a Shape Parameter." Advanced Materials Research 468-471 (February 2012): 2463–66. http://dx.doi.org/10.4028/www.scientific.net/amr.468-471.2463.

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A quadratic trigonometric B-spline curve analogous to the standard quadratic uniform B-spline curve, with a shape parameter, is presented in this work. The shape of the proposed curve can be adjusted by altering the value of the shape parameter while the control polygon is kept unchanged. With the shape parameter, the quadratic trigonometric B-spline curve can be closer to given polygon than the standard quadratic uniform B-spline curve. The proposed curve can be used to accurately represent the ellipse.

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24

Li, Ai Min, Wei Guo, Hai Bo Tian, and Fa Rong Kou. "Wavelet-Based Multiresolution NURBS Curve Fairing." Advanced Materials Research 314-316 (August 2011): 1562–65. http://dx.doi.org/10.4028/www.scientific.net/amr.314-316.1562.

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A multiresolution approach is presented for NURBS curve fairing based on nonuniform semiorthogonal B-spline wavelets built. This method provides greater flexibility and applicability than uniform B-spline wavelets for multiresolution curve fairing. An example is presented to validate effectiveness of this multiresolution fairing method. Furthermore, the algorithm can be easily applied to NURBS curves in three dimensions as well as in two.

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25

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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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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Liu, Tzu-Chi, Ming-Hsiu Hsu, and Kuo-Tung Lin. "Chiller Performance Curve, Online Modeling Using B-spline Curve." Energy Engineering 108, no. 6 (September 22, 2011): 46–58. http://dx.doi.org/10.1080/01998595.2011.10412167.

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28

Lin, Hongwei, Wei Chen, and Guojin Wang. "Curve reconstruction based on an interval B-spline curve." Visual Computer 21, no. 6 (July 2005): 418–27. http://dx.doi.org/10.1007/s00371-005-0304-4.

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29

Shahriman, A. B., A. K. M. Syafiq, M. S. M. Hashim, D. Hazry, Z. M. Razlan, K. Wan, R. Daud, E. M. Cheng, S. K. Zaaba, and Azizi Azizan. "Improvement of cam performance curve using B-Spline curve." Journal of Physics: Conference Series 908 (October 2017): 012043. http://dx.doi.org/10.1088/1742-6596/908/1/012043.

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30

Munir, N. A. A. A., N. A. Hadi, and M. A. S. Nasir. "C1 Cubic Trigonometric Spline with a Shape Parameter for Positive Shape Preservation." Malaysian Journal of Mathematical Sciences 16, no. 1 (January 31, 2022): 55–66. http://dx.doi.org/10.47836/mjms.16.1.05.

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This paper presents a new construction of C1 cubic trigonometric spline interpolation. Instead of repositioning control points, a shape parameter is introduced in the spline to control the shape and behaviour of the curves. The built basis functions fulfil all the geometric properties of the standard cubic Bezier curve, and the proof is included in this paper. Then, the interpolation of the spline is illustrated using suitable parameter values. Every curve segment comprises four successive control points with a cubic trigonometric spline that carries out all the curve properties. The result showed effective approximation since the developed C1 cubic trigonometric spline produced a smooth and pleasant interpolating curve while preserving the positive data features. The flexibility of the developed spline is compared with the other two existing works: b-spline and bezier-like curves. The analysis shows that the proposed spline gives greater flexibility since it has a broader parameter value range. Therefore, this helps the spline interpolation build opened and closed curves, as incorporated in the paper.Munir, N. A. A. A

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Amna Abdul Sittar, Abdul Majeed, and Abd Rahni Mt Piah. "Shape Designing Using Quadratic Trigonometric B-Spline Curves." Scientific Inquiry and Review 3, no. 2 (June 5, 2019): 36–49. http://dx.doi.org/10.32350/sir.32.05.

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The B-spline curves, particularly trigonometric B-spline curves, have attained remarkable significance in the field of Computer Aided Geometric Designing (CAGD). Different researchers have developed different interpolants for shape designing using Ball, Bezier and ordinary B-spline. In this paper, quadratic trigonometric B-spline (piecewise) curve has been developed using a new basis for shape designing. The proposed method has one shape parameter which can be used to control and change the shape of objects. Different objects like flower, alphabet and vase have been designed using the proposed method. The effects of shape parameter and control points have been discussed also.

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Shu, Si Hui, Zi Zhi Lin, and Yun Ding. "B-Spline Curve Approximation with Nearly Arc-Length Parameterization." Applied Mechanics and Materials 513-517 (February 2014): 3372–76. http://dx.doi.org/10.4028/www.scientific.net/amm.513-517.3372.

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An algorithm of B-spline curve approximation with the three-dimensional data is presented in this paper. In this algorithm, we will get a smooth curve which is nearly arc-length parameterization. The smoothness and uniform parameterization are key factors of the approximating curve, specifically in skinning surface and surface approximation. Firstly, the data points are fitted using local interpolation, this local fitting algorithm yields n Bezier segments, each segment having speed equal to 1 at their end and midpoints. Then segments are composed of a C1 continuous cubic B-spline curve which named controlling curve. But the controlling curves control points are redundancy, so we find another curve to approximate the controlling curve using least square approximation with smoothness

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Poliakoff, Janet F., Yew Kee Wong, and Peter D. Thomas. "An automated curve fairing algorithm for cubic B-spline curves." Journal of Computational and Applied Mathematics 102, no. 1 (February 1999): 73–85. http://dx.doi.org/10.1016/s0377-0427(98)00209-x.

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Xu, Jin. "Smooth B-Spline Curves Extension with Ordered Points Constraint." Advanced Materials Research 311-313 (August 2011): 1439–45. http://dx.doi.org/10.4028/www.scientific.net/amr.311-313.1439.

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An algorithm for extending B-spline curves with a sequence of ordered points constraint is presented based on the curve unclamping algorithm. The ordered points are divided into two categories: interpolation points and approximation points. The number of interpolation points increases gradually during the curve extension process. The most important feature of this algorithm is the ability to optimize the knots of the extended curve segment according to the ordered points. Thus, with minimum number of interpolation points, the maximum deviation of the extended curve segment from the ordered points is less than the given tolerance. The extended curve segment connects to the original curve with maximum continuity intrinsically. Several experimental results have shown the validity and applicability of the proposed algorithm.

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Kong, Xiang, and Jun Chen. "Two Extensions of the Quadratic Nonuniform B-Spline Curve with Local Shape Parameter Series." Mathematical Problems in Engineering 2021 (September 2, 2021): 1–12. http://dx.doi.org/10.1155/2021/9980320.

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Two extensions of the quadratic nonuniform B-spline curve with local shape parameter series, called the W3D3C1P2 spline curve and the W3D4C2P1 spline curve, are introduced in the paper. The new extensions not only inherit most excellent properties of the quadratic nonuniform B-spline curve but also can move locally toward or against the fixed control polygon by varying the shape parameter series. They are C1 and C2 continuous separately. Furthermore, the W3D3C1P2 spline curve includes the quadratic nonuniform B-spline curve as a special case. Two applications, the interpolation of the position and the corresponding tangent direction and the interpolation of a line segment, are discussed without solving a system of linear functions. Several numerical examples indicated that the new extensions are valid and can easily be applied.

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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 validated by the software of ADAMS.So it provides an effective new method for the trajectory planning.

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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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Cheng, Xian Guo. "B-Spline Curve Approximation Using Feature Points." Applied Mechanics and Materials 397-400 (September 2013): 1093–98. http://dx.doi.org/10.4028/www.scientific.net/amm.397-400.1093.

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This paper addresses the problem of B-spline curve approximating to a set of dense and ordered points. We choose local curvature maximum points based on the curvature information. The points and the two end points are viewed as initial feature points, constructing a B-spline curve approximating to the feature points by the least-squares method, refining the feature points according to the shape information of the curve, and updating the curve. This process is repeated until the maximum error is less than the given error bound. The approach adaptively placed fewer knots at flat regions but more at complex regions. Under the same error bound, experimental results showed that our approach can reduce more control points than Parks approach,Piegls approach and Lis approach. The numbers of control points of the curve is equal to that of the feature points after refinement.

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Li, Denggao, Kaihuai Qin, and Hanqiu Sun. "Curve modeling with constrained B-spline wavelets." Computer Aided Geometric Design 22, no. 1 (January 2005): 45–56. http://dx.doi.org/10.1016/j.cagd.2004.08.004.

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Rogers, D. F., and N. R. Fog. "Constrained B-spline curve and surface fitting." Computer-Aided Design 21, no. 10 (December 1989): 641–48. http://dx.doi.org/10.1016/0010-4485(89)90162-0.

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Chen, Xiao Bing, and Kun Yu. "Efficient Algorithm for B-Spline Curve Fitting by Using Feature Data Points." Applied Mechanics and Materials 411-414 (September 2013): 523–26. http://dx.doi.org/10.4028/www.scientific.net/amm.411-414.523.

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In order to obtain B-spline curve with fewer control points and higher precision, an efficient algorithm for B-spline curve fitting by using feature data points is proposed. During iterations of the proposed algorithm, the projected points, which are the nearest points on fitting curve to discrete data points, are calculated first, then maximal deviations between B-spline curve and connection lines of the data points are controlled, finally new feature points are determined and parameters of feature points are adjusted by parameters of projected points. According to these, B-spline curve with fewer control points and higher precision are obtained rapidly. Experimental result indicates that the proposed algorithm is feasible and effective.

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Hangjian, Zhang, Zhang Guicang, and Wang Lu. "The Shape Analysis of DTB-like and DT B-spline-like Curves." Journal of Mathematics and Informatics 24 (2023): 01–21. http://dx.doi.org/10.22457/jmi.v24a01216.

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In the field of computer-aided design and related applications, the free curve with parameters shows its strong function. But an excellent curve with parameters need to eliminate unnecessary cusps and inflection points, so shape analysis is needed for some specific curves. We have already shown many excellent properties of the DTB-like curves and DT B-spline-like curves. Thus the shape features like convexity, loops, inflection points, and cusps of the DTB-like curves, and DT B-spline-like curves are further discussed in this paper. And the necessary and sufficient conditions for the existence of shape features of the corresponding DTB-like curves and DT B-spline-like curves are given. And the shape features distribution all be generalized into tables and diagrams, which are useful for industrial design. In addition, the effect of shape parameters on the shape features diagram and its adjustment ability to the shape of corresponding curves are analyzed, respectively. The work in this paper enables users to determine how to set parameter values so that the generated curve could be a global convex or local convex curve, has a required inflection point, or eliminate the unnecessary one, and could be adjusted to another aimed shape.

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Wang, Xi, Cui Cui Gao, and Chen Jiang. "Cubic Uniform B-Spline Curve and Surface with Multiple Shape Parameters." Applied Mechanics and Materials 543-547 (March 2014): 1860–63. http://dx.doi.org/10.4028/www.scientific.net/amm.543-547.1860.

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In order to construct B-spline curves with local shape control parameters, a class of polynomial basis functions with two local shape parameters is presented. Properties of the proposed basis functions are analyzed and the corresponding piecewise polynomial curve is constructed with two local shape control parameters accordingly. In particular, the G1 continuous and the shapes of other segments of the curve can remain unchangeably during the manipulation on the shape of each segment on the curve. Numerical examples illustrate that the constructed curve fit to the control polygon very well. Furthermore, its applications in curve design is discussed and an extend application on surface design is also presented. Modeling examples show that the new curve is very valuable for the design of curves and surfaces.

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Lin, Zi Zhi, and Si Hui Shu. "An Algorithm for Representing Planar Curves in B-Splines." Applied Mechanics and Materials 596 (July 2014): 149–53. http://dx.doi.org/10.4028/www.scientific.net/amm.596.149.

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An algorithm for representing planar curves in B-splines is presented in this paper. The representing problem is different from the approximation to data points; planar curve provided more information than data points. To make full use of the information, we propose a three-step representing approach: 1.Sample data points along with their tangent vectors from the planar curve according to the given accuracy. 2. Fit the sampled points by Bezier segments using local interpolation; compose these segments to an interpolation curve. 3. Approximate the interpolation curve using the best least approximation to get the final B-spline curve. Tangent information is used in the second step to construct the interpolation curve. In the third step, the system is always positive because of using the best least square approximation, so we can get more freedoms to approximate the interpolation curve. Finally, some examples of this algorithm demonstrate its usefulness and quality.

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Ma, Jian-wei, De-ning Song, Zhen-yuan Jia, Guo-qing Hu, and Wei-wei Su. "Conversion method study from cutter-location points to nonuniform rational B-spline toolpath NC file for high-speed machining." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 233, no. 2 (March 14, 2018): 514–25. http://dx.doi.org/10.1177/0954406218762018.

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Parts with complex curved surfaces are widely applied and the demands for the machining quality and the machining efficiency of such complex parts become increasingly higher. In order to realize high-speed and high-quality machining, the nonuniform rational B-spline interpolator is widely researched and demonstrated to be superior to the conventional linear or circular interpolators. However, the nonuniform rational B-spline toolpath NC files cannot be directly generated from the computer-aided design (CAD) models by using commercial computer-aided manufacturing (CAM) software. To deal with this problem, a conversion method from the cutter-location points to the nonuniform rational B-spline toolpath numerical control (NC) file is presented. To avoid the bad curve-fitting effect at sharp corners of the toolpath and to meanwhile reduce the computational burden, the cutter-location pre-processing method, consisting data segmentation and data simplification, is provided first. Then, the least-square method is employed to fit the cutter locations to the nonuniform rational B-spline curves, and an iterative fitting approach is proposed for linear/nonuniform rational B-spline hybrid toolpath generation. Finally, a user interface is designed for displaying the fitting results and outputting the NC file with nonuniform rational B-spline toolpaths. By using this method, nonuniform rational B-spline and linear toolpaths hybrid interpolation NC program can be generated for the high-speed machining of complex curved surface parts with the utilization of the nonuniform rational B-spline interpolator. The experimental results demonstrate the feasibility and the advantages of the presented method.

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Yang, Peng, Dong Xing Hui, Zheng Kai, and Li Shu Tian. "Research on Algorithm for Space Weld Reconstruction and Torch Pose Simulation." Advanced Materials Research 1049-1050 (October 2014): 833–37. http://dx.doi.org/10.4028/www.scientific.net/amr.1049-1050.833.

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A path planning algorithm based on B-spline interpolation techniques was constructed for automatic welding system.The system used a B-spline curve to reconstruct the weld,it was achieved by reversing the control points of B-spline curve through the prescribed date points. The weld posture model was then obtained from the osculating plane and normal plane of B-spline curve. By taking a series coordinate transformation to the weld posture model, the torch posture model based on control terminal was provided.Experiments show that the new algorithm can readily be used for various three-dimensional welding tasks.

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XING, JUN, JIAHAN LI, RUNQING YANG, XIAOJING ZHOU, and SHIZHONG XU. "Bayesian B-spline mapping for dynamic quantitative traits." Genetics Research 94, no. 2 (April 2012): 85–95. http://dx.doi.org/10.1017/s0016672312000249.

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

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Páleš, Dušan, Veronika Váliková, Ján Antl, and František Tóth. "Approximation of Vehicle Trajectory with B-Spline Curve." Acta Technologica Agriculturae 19, no. 1 (March 1, 2016): 1–5. http://dx.doi.org/10.1515/ata-2016-0001.

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In this contribution, we present the description of a B-spline curve. We deal with creation of its basis function as well as with creation of the curve itself from entered control points. Following the literature, we formed an algorithm for B-spline modelling and we used it for the planar and spatial curve. The planar curve is made of chosen points. The spatial curve approximates the trajectory of a real vehicle, which trajectory was obtained by the set of measured points. The modelled curve very exactly describes the polygon created from the linked control points. With the lowering degree of the curve, this one is more clamping to the given polygon and for the extreme case it is transformed to the polygon itself. The advantage of the B-spline curve use is, for example in comparison with a Bézier curve, high adaptability, which is expressed in its parameters - besides entered control points, these are knots generated on the curve and degree of the curve.

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Lamberti, Paola, and Sara Remogna. "Quadratic B-Spline Surfaces with Free Parameters for the Interpolation of Curve Networks." Mathematics 10, no. 4 (February 10, 2022): 543. http://dx.doi.org/10.3390/math10040543.

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In this paper, we propose a method for constructing spline surfaces interpolating a B-spline curve network, allowing the presence of free parameters, in order to model the interpolating surface. We provide a constructive algorithm for its generation in the case of biquadratic tensor product B-spline surfaces and bivariate B-spline surfaces on criss-cross triangulations. Finally, we present graphical results.

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Yan, Lanlan. "B\'{e}zier-like Curve and B-spline-like Curve of Order Two." Journal of Information and Computational Science 10, no. 17 (November 20, 2013): 5483–503. http://dx.doi.org/10.12733/jics20101992.

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