Journal articles: 'Non-uniform B-spline 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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Munira, Ali, Nur Najmiyah Jaafar, Abdul Aziz Fazilah, and Z. Nooraizedfiza. "Review on Non Uniform Rational B-Spline (NURBS): Concept and Optimization." Advanced Materials Research 903 (February 2014): 338–43. http://dx.doi.org/10.4028/www.scientific.net/amr.903.338.

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This paper is to provide literature review of the Non Uniform Rational B-Splines (NURBS) formulation in the curve and surface constructions. NURBS curves and surfaces have a wide application in Computer Aided Geometry Design (CAGD), Computer Aided Design (CAD), image processing and etc. The formulation of NURBS showing that NURBS curves and surfaces requires three important parameters in controlling the curve and also modifying the shape of the curves and surfaces. Yet, curves and surfaces fitting are still the major problems in the geometrical modeling. With this, the researches that have been conducted in optimizing the parameters in order to construct the intended curves and surfaces are highlighted in this paper.

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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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Majeed, Abdul, Muhammad Abbas, Faiza Qayyum, Kenjiro T. Miura, Md Yushalify Misro, and Tahir Nazir. "Geometric Modeling Using New Cubic Trigonometric B-Spline Functions with Shape Parameter." Mathematics 8, no. 12 (November 24, 2020): 2102. http://dx.doi.org/10.3390/math8122102.

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Trigonometric B-spline curves with shape parameters are equally important and useful for modeling in Computer-Aided Geometric Design (CAGD) like classical B-spline curves. This paper introduces the cubic polynomial and rational cubic B-spline curves using new cubic basis functions with shape parameter ξ∈[0,4]. All geometric characteristics of the proposed Trigonometric B-spline curves are similar to the classical B-spline, but the shape-adjustable is additional quality that the classical B-spline curves does not hold. The properties of these bases are similar to classical B-spline basis and have been delineated. Furthermore, uniform and non-uniform rational B-spline basis are also presented. C3 and C5 continuities for trigonometric B-spline basis and C3 continuities for rational basis are derived. In order to legitimize our proposed scheme for both basis, floating and periodic curves are constructed. 2D and 3D models are also constructed using proposed curves.

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Wang, Kai, and Guicang Zhang. "New Trigonometric Basis Possessing Denominator Shape Parameters." Mathematical Problems in Engineering 2018 (October 24, 2018): 1–25. http://dx.doi.org/10.1155/2018/9569834.

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Four new trigonometric Bernstein-like bases with two denominator shape parameters (DTB-like basis) are constructed, based on which a kind of trigonometric Bézier-like curve with two denominator shape parameters (DTB-like curves) that are analogous to the cubic Bézier curves is proposed. The corner cutting algorithm for computing the DTB-like curves is given. Any arc of an ellipse or a parabola can be exactly represented by using the DTB-like curves. A new class of trigonometric B-spline-like basis function with two local denominator shape parameters (DT B-spline-like basis) is constructed according to the proposed DTB-like basis. The totally positive property of the DT B-spline-like basis is supported. For different shape parameter values, the associated trigonometric B-spline-like curves with two denominator shape parameters (DT B-spline-like curves) can be C2 continuous for a non-uniform knot vector. For a special value, the generated curves can be C(2n-1) (n=1,2,3,…) continuous for a uniform knot vector. A kind of trigonometric B-spline-like surfaces with four denominator shape parameters (DT B-spline-like surface) is shown by using the tensor product method, and the associated DT B-spline-like surfaces can be C2 continuous for a nonuniform knot vector. When given a special value, the related surfaces can be C(2n-1) (n=1,2,3,…) continuous for a uniform knot vector. A new class of trigonometric Bernstein–Bézier-like basis function with three denominator shape parameters (DT BB-like basis) over a triangular domain is also constructed. A de Casteljau-type algorithm is developed for computing the associated trigonometric Bernstein–Bézier-like patch with three denominator shape parameters (DT BB-like patch). The condition for G1 continuous jointing two DT BB-like patches over the triangular domain is deduced.

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Dung, Van Than, and Tegoeh Tjahjowidodo. "A direct method to solve optimal knots of B-spline curves: An application for non-uniform B-spline curves fitting." PLOS ONE 12, no. 3 (March 20, 2017): e0173857. http://dx.doi.org/10.1371/journal.pone.0173857.

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Hu, Liangchen, Huahao Shou, and Shiaofen Fang. "A PIA optimization algorithm for non-uniform B-spline curves and surfaces." International Journal of Modelling and Simulation 37, no. 3 (April 10, 2017): 167–77. http://dx.doi.org/10.1080/02286203.2017.1309260.

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Tuo, Ming-Xiu, Gui-Cang Zhang, and Kai Wang. "A New Quasi Cubic Rational System with Two Parameters." Symmetry 12, no. 7 (June 30, 2020): 1070. http://dx.doi.org/10.3390/sym12071070.

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The purpose of this article is to develop a new system for the construction of curves and surfaces. Making the new system not only has excellent properties of the orthodox Bézier and the B-spline method but also has practical properties such as variation diminishing and local shape adjustability. First, a new set of the quasi-cubic rational (QCR) system with two parameters is given, which is verified on an optimal normalized totally positive system (B-system). The related QCR Bézier curve is defined, and the de Casteljau-type algorithm are given. Next, a group of non-uniform QCR B-spline system is shown based on the linear combination of the proposed QCR system, the relative properties of the B-spline system are analyzed. Then, the definition and properties of non-uniform QCR B-spline curves are discussed in detail. Finally, the proposed QCR system is extended to the triangular domain, which is called the quasi-cubic rational Bernstein-Bézier (QCR-BB) system, and its related definition and properties of patches are given at length. The experimental image obtained by using MATLAB shows that the newly constructed system has excellent properties such as symmetry, totally positive, and C 2 continuity, and its corresponding curve has the properties of local shape adjustability and C 2 continuity. These extended systems in the extended triangular domain have symmetry, linear independence, etc. Hence, the methods in this article are suitable for the modeling design of complex curves and surfaces.

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Li, J.-G., M.-M. Qiu, T.-H. Zhang, and Z.-X. Li. "A practical real-time non-uniform rational B-spline curve interpolator for computer numerical control machining." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 226, no. 4 (September 7, 2011): 1068–83. http://dx.doi.org/10.1177/0954406211418026.

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Non-uniform rational B-spline (NURBS) interpolator, a key technique in computer numerical control (CNC) machining, has many advantages over linear and circular interpolator. A practical real-time NURBS interpolator based on an off-line algorithm, which is developed to handle the limitation of velocity and acceleration, is presented in this article. Two processing modules are employed to realize the real-time interpolator. In one module, a NURBS curve is split into shorter NURBS curves or approximated as continuous line segments according to the minimum splitting length first, and then the velocity planning of a short curve is applied. Inthe other module, the interpolation according to the velocity planning results is implemented. The proposed algorithm realizes the real-time velocity planning and interpolation of a NURBS curve regardless of the curve length or the continuity. It is also applicable to three-dimensional surface designed by computer-aided design system, which is composed of multiple NURBS curves or both NURBS curves and continuous line segments. Both the simulation and experiment results have proved the effectiveness of the proposed practical real-time NURBS interpolator.

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Zhang, Wen Jie. "The Research of the NURBS Curve Interpolation Algorithm." Advanced Engineering Forum 2-3 (December 2011): 614–18. http://dx.doi.org/10.4028/www.scientific.net/aef.2-3.614.

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In this article, the definition, the nature and the parameter of the NURBS (Non-Uniform Rational B-spline) curves are defined, the more thorough analysis and research of the real-time NURBS curve interpolation algorithm and the feed rate adaptive control are carried out.

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Ülker, Erkan, and İsmail Babaoğlu. "Gravitational Search Algorithm for NURBS Curve Fitting." KnE Social Sciences 3, no. 1 (January 15, 2018): 33. http://dx.doi.org/10.18502/kss.v3i1.1395.

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By providing great flexibility non-uniform rational B-spline (NURBS) curves and surfaces are reason of preferability on areas like computer aided design, medical imaging and computer graphics. Knots, control points and weights provide this flexibility. Computation of these parameters makes the problem as a non-linear combinational optimization problem on a process of reverse engineering. The ability of solving these problems using meta-heuristics instead of conventional methods attracts researchers. In this paper, NURBS curve estimation is carried out by a novel optimization method namely gravitational search algorithm. Both knots and knots together weights simultaneous optimization process is implemented by using research agents. The high performance of the proposed method on NURBS curve fitting is showed by obtained results.Keywords: Non-uniform rational B-spline, gravitational search algorithm, meta-heuristic

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Chen, Chang Liang, Sheng Sun Hu, and Dong Lin He. "Trajectory Model of J-Type Groove and its Curve Fitting of B-Spline." Applied Mechanics and Materials 58-60 (June 2011): 1396–401. http://dx.doi.org/10.4028/www.scientific.net/amm.58-60.1396.

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This paper describes the complexity and particularity of the trajectory of tube-sphere intersection and derives mathematical model of the track; according to characteristics of B-Spline curve, the track intersecting curve is partitioned ,and determine the mathematical relationship between the control points (deBoor point) and the data points of J-type groove; using cubic non-uniform irrational B-Spline theory, generate segments of approximation curves, then first and last point of each segment are constrained, so that combination curves can be seen as a whole curve with C1continuity; programming the trajectory of the preprocess module with C# language, it has advantages of approximate accuracy and high efficiency, thereby it can increase accuracy and precision of welding terminal position, so that the overall system has a metronomic characteristic.

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McGarva, J. R. "Non-Uniform Motion by Mechanical Means." Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture 209, no. 4 (August 1995): 295–303. http://dx.doi.org/10.1243/pime_proc_1995_209_086_02.

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In this paper a methodology for designing mechanical non-uniform motion generators is presented. The basic requirements for four-bar and six-bar linkages are established and it is shown how the performance can be evaluated by harmonic analysis applied to the output angular velocity function. A means of creating and searching a library of mechanisms based on normalized output functions is presented. B-spline curves are used as a means of defining a desired performance and it is shown how minimum acceleration can be achieved with continuity in the derivatives. Finally, a means of increasing the quality of motion transmission in the selected mechanisms is given. The techniques are used to synthesize a six-bar linkage.

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Chen, Chin Sheng, Chih Wei Chu, and Yen Shin Lai. "Real-Time Coplanar NURBS Curves Fitting in Motion Controller." Advanced Materials Research 740 (August 2013): 105–11. http://dx.doi.org/10.4028/www.scientific.net/amr.740.105.

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This paper proposes a real-time coplanar Non-Uniform Rational B-Spline (NURBS) curves fitting in CAD/CAM system to improve the fitting quality and reduce the calculation effort. The real-time NURBS curve fitting process consists of (1) the reading discrete points, (2) curve segmentation and data reshaping, (3) curve fitting, and (4) local and global modulation. According to the simulation and experimental results, the proposed approach certainly raises the fitting quality and the efficiency of calculation.

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Xu, Jia Chuan, Shang Peng Gao, and Yong Fu Yin. "Representation Method and Degree Selection of Class A Surfaces for Auto-Body." Advanced Materials Research 156-157 (October 2010): 451–55. http://dx.doi.org/10.4028/www.scientific.net/amr.156-157.451.

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To represent curves and surfaces unified, many commercial soft-wares adopt non-uniform rational B-spline (NURBS) as the method. The NURBS method includes Bézier, B-spline and so forth. In surfaces smoothing Class A surfaces of auto-body are a kind of surfaces that have high desire. While different representing methods can fit curves and surfaces with prodigiously different qualities and efficiency. So the representing methods and degree selection of curves and surfaces for auto-body are fundamental issues that auto-body engineers must be solved. Based on analyzing the character of Bézier and B-spline representing methods, Bézier method is adopted to represent Class A surfaces of auto-body according to the desire of auto-body surfaces. At the same time, the degree of curves and surfaces for auto-body is limited between 2nd-7th according to the oscillation of high degree curves and surfaces and continuity desire. The example verified that the Bézier method can improve the quality and efficiency.

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Hamdan, Wisam Kadhum, and Mustafa Mohammed Abdulrazaq. "Sculptured Surface Design and Implementation by Lofting Design Method Using Cross-sectional B-Spline Curves." Al-Khwarizmi Engineering Journal 14, no. 2 (March 14, 2019): 92–82. http://dx.doi.org/10.22153/kej.2018.11.004.

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This research presents a particular designing strategy for a free form of surfaces, constructed by the lofting design method. The regarded surfaces were created by sliding a B-spline curves (profile curves), in addition to describing an automatic procedure for selective identification of sampling points in reverse engineering applications using Coordinate Measurement Machine. Two models have been implemented from (Ureol material) to represent the different cases of B-spline types to clarify its scope of application. The interior data of the desired surfaces was designed by MATLAB software, which then were transformed to UG-NX9 software for connecting the sections that were designed in MATLAB program and obtaining G-code programs for the models In addition, a virtual machining process was simulated to show the machining pitfalls, using VERICUT software. The samples were machined using 3-axis vertical CNC machine (Isel) type. Finally, the samples were measured using Faro arm (CMM inspection) and it was found that the average of errors was equal to (0.0589 mm) for the cross-sectional uniform B-spline model, and (0.1337 mm) for the lofted non-uniform B-spline model. It can be concluded that the whole steps task which built in the present research can be programmed in a single block of the part program where any surface at minimum designing time can be created from it.

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Dong, Jin Hua, and Hui Qin Cao. "NURBS Curves Interpolation Based on Dynamic Characteristics of Machine Tools." Advanced Materials Research 102-104 (March 2010): 353–57. http://dx.doi.org/10.4028/www.scientific.net/amr.102-104.353.

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This paper presents an interpolation algorithm for non-uniform rational B-spline (NURBS) curves. A real-time look-ahead function is introduced to deal with the abrupt change of feedrate. In the proposed algorithm, feedrate can be adaptively adjusted according to the radius of curvature of curves. Dynamic characteristic of machine tools is considered while the feedrate is adjusted. The experimental results show that this algorithm significantly reduced the machining error brought about by the instantaneous acceleration fluctuations of machine tools.

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Ge, Rong Yu, and P. Q. Guo. "Flexible Cam Profile Synthesis Method Using NURBS and its Optimization Based on Genetic Algorithm." Advanced Materials Research 426 (January 2012): 69–72. http://dx.doi.org/10.4028/www.scientific.net/amr.426.69.

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This paper describes a synthesis method of designing flexible cam profiles by using quintic non-uniform rational B spline (NURBS) curves. The cam profile curve can be optimized by adjusting knot vector, control points and weight factors of NURBS curve. The multiobjective optimization for a cam curve was described to satisfy both kinematic and dynamic requirements. To solve the optimization model for NURBS cam curve, an improved genetic algorithm (GA) called INSGA in the paper was proposed. Application examples on the kinematical and dynamical optimization of cam curves are presented together with detailed discussions. These examples, especial the dynamic optimization to control the residual vibration for a cam curve used in an indexing cam mechanism, sufficiently illustrate the effectiveness of the proposed approach.

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Yang, Lin, Shuai Nan Ren, Zhen Yu Wang, and Peng Zhang. "Research on Spiral Bevel Gear Tooth Surface Reconstruction Based on NURBS." Applied Mechanics and Materials 130-134 (October 2011): 701–5. http://dx.doi.org/10.4028/www.scientific.net/amm.130-134.701.

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The tooth surface shape of spiral bevel gear is complex. In the detection process of errors tooth surface model is constructed based on coordinate data of limited the actual tooth surface sampling points. The model is used to analysis and manufacture of gear to meet the processing requirements. NURBS (non-uniform rational B-Spline) method is the most effective reconstruction method for geometry there are both freedom and analytic curves and surfaces. NURBS method is used to calculate non-uniform knot vector, NURBS control points and B-Spline inverse and reconstruct tooth surface. Reconstructionof spiral bevel gears in using NURBS is achieved and the tooth surface reconstruction is drawn out in Open GL in VC environment. And then reconstruction error on the tooth surface is analyzed. It proves that using the method of NURBS to reconstruct spiral bevel gear tooth surface is correct and feasible.

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Yang, Jian Zhong, Jian Tang, Wei Qiang Wang, and Ji Hong Chen. "Fast Discretization Algorithm of Densely Subdivided NURBS Curves." Applied Mechanics and Materials 543-547 (March 2014): 1872–75. http://dx.doi.org/10.4028/www.scientific.net/amm.543-547.1872.

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This paper develops a discretization algorithm for non-uniform rational B-spline (NURBS) curves. The algorithm is used for CAM software which is developed for HNC-3000 five-axis woodworking NC milling machine. Functions from the CAM software divide the NURBS into dense segments with equal arc length by vertex set p1, p2pn. The algorithm simultaneously considers chord error δ and curvature of the NURBS curve to maximize the arc length of the segments to get vertex set p'1, p'2 pm'. The algorithm can be described as f (p1, p2pn, δ) = (p1', p2'pm'). The complexity of the algorithm is O (n).

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Yang, Yue, Wen-sheng Qiu, Wei Zeng, Huan Xie, and Su-chao Xie. "A prediction method of rail grinding profile using non-uniform rational B-spline curves and Kriging model." Journal of Central South University 25, no. 1 (January 2018): 230–40. http://dx.doi.org/10.1007/s11771-018-3732-9.

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Abdelmoety, Ahmed K., Taha H. A. Naga, and Youssef F. Rashed. "Isogeometric boundary integral formulation for Reissner’s plate problems." Engineering Computations 37, no. 1 (July 19, 2019): 21–53. http://dx.doi.org/10.1108/ec-11-2018-0507.

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Purpose This paper aims to develop a new isogeometric boundary element formulation based on non-uniform rational basis splines (NURBS) curves for solving Reissner’s shear-deformable plates. Design/methodology/approach The generalized displacements and tractions along the problem boundary are approximated as NURBS curves having the same rational B-spline basis functions used to describe the geometrical boundary of the problem. The source points positions are determined over the problem boundary by the well-known Greville abscissae definition. The singular integrals are accurately evaluated using the singularity subtraction technique. Findings Numerical examples are solved to demonstrate the validity and the accuracy of the developed formulation. Originality/value This formulation is considered to preserve the exact geometry of the problem and to reduce or cancel mesh generation time by using NURBS curves employed in computer aided designs as a tool for isogeometric analysis. The present formulation extends such curves to be implemented as a stress analysis tool.

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Chen, Liang Ji, Hui Ying Li, and Hai Jun Zhang. "Study on Tool Path Generation and Direct Interpolation Method." Advanced Materials Research 945-949 (June 2014): 1657–60. http://dx.doi.org/10.4028/www.scientific.net/amr.945-949.1657.

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At present, Non-Uniform Rational B-Spline (NURBS) curves are mostly used to generate arbitrary contour of a complex shape in the CAD field. In this article, a new method with NURBS technology is presented and realized in a location and federate controlling system. In the method, the tool paths and the cutter locations (CL) were represented into NURBS curves based on the same knot vector. The above CL data was firstly calculated and then transformed to five motion commands of five axes of machine through the real-time post-procession algorithm. The acceleration/deceleration controlling method is also presented to avoid the impact of machine. The proposed 5-axis spline interpolation method is realized and the experimental result of machining shows that the method is valid.

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Zhang, Yin Juan, and Yong Ke Wang. "Research of Accurate NURBS Curve Fitting Based on Genetic Algorithm." Advanced Materials Research 479-481 (February 2012): 1927–30. http://dx.doi.org/10.4028/www.scientific.net/amr.479-481.1927.

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In order to control the curve modality of non-uniform rational B-spline accurately, the genetic algorithm is presented to the manipulative precision of NURBS curve fitting. The manipulative precision of curve fitting and the overall side-by-side search ability of genetic algorithm were researched; the excellent unit is founded in the field of weight coefficient. The precision result and the curve figure of curve fitting using the excellent weight coefficient are better. The examples of data fitting are given to show that the curves fitting used genetic algorithms are better in approximation. The precision result of curve fitting is improved. The global optimal search of genetic algorithm provides a reliable tool for scientific data processing.

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Zheng, Peng, Lian Qiang Yang, and Zhen Ni Dai. "Term Structure of Interest Rates with B-Spline Model during the Money-Shortage-Event in China." Advanced Materials Research 989-994 (July 2014): 5634–37. http://dx.doi.org/10.4028/www.scientific.net/amr.989-994.5634.

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Using the price data of bonds’ transactions during June 2013, the discounting function is fitted by non-uniform cubic B-Splines and yield curves are modeled. Models’ single parametric test and total test are both significant. Furthermore, the structural change’s test shows that there is no significant structural change between adjacent transaction days, which means that the bonds’ market is relatively steady during June 2013.

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Hui, Ji Zhuang, Yan Ma, and Ze Feng Liu. "Study on the Algorithm for Real-Time Interpolation of NURBS Curve." Advanced Engineering Forum 1 (September 2011): 262–67. http://dx.doi.org/10.4028/www.scientific.net/aef.1.262.

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In order to meet the needs of high speed and high precision computerized numerical control machining, a calculation based on the control of contour error and feeding acceleration for the real-time interpolation of Non-uniform rational B-spline (NURBS) curves was presented in this paper. On the premise of meeting the error requirement, machine can process parts with the highest feeding speed to achieve interpolation precision and interpolation speed optimization, and improve processing quality and efficiency.

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Jiang, Yulin, Qingmin Pu, and Wenbin Ding. "Reconstruction of Velocity Distribution in Partially-Filled Pipe Based on Non-Uniform Under-Sampling." Advances in Mathematical Physics 2020 (January 22, 2020): 1–8. http://dx.doi.org/10.1155/2020/6961286.

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In the process of research on the flow velocity distribution in a partially filled pipe, the under-sampling of measurement data often occurs. For the first time, this problem is solved by the improved non-uniform B-spline curve fitting approximation (NBSC) method. The main innovation of this method is to reconstruct the flow velocity distribution fitting curve with a small amount of non-uniform feature points containing flow velocity information. First, the curvature of a whole discrete sampled data is analyzed, then the weighted threshold is set, and the sampled points that satisfy the threshold are extracted as the initial velocity distribution feature points. Next the node vectors were constructed according to the initial feature points, and the initial interpolation fitting curves are generated. Secondly, by using the relative deviation between the initial approximation curve and each sampled point, new feature points were added where the curve allowable deviation exceeded the specified tolerance, and then a new interpolation fitting curve was obtained. The above procedure was repeated until the fitting curve reached expected accuracy, thus the appropriate feature points were determined. Experimental results showed that, in the case of the same approximation deviation, the proposed NBSC method can solve the problem of under-sampling of measurement data better.

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Li, Hui Ying, and Liang Ji Chen. "Study on Five-Axis NURBS Path Generation Method and Direct-Interpolation for CNC System." Applied Mechanics and Materials 621 (August 2014): 162–66. http://dx.doi.org/10.4028/www.scientific.net/amm.621.162.

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In this article, a new method with Non-Uniform Rational B-Spline (NURBS) technology is presented and realized in a location and federate controlling system. In the method, the tool paths and the cutter locations (CL) were represented into NURBS curves based on the same knot vector. The above CL data was firstly calculated and then transformed to five motion commands of five axes of machine through the real-time post-procession algorithm. The acceleration/deceleration controlling method is also presented to avoid the impact of machine. The proposed 5-axis spline interpolation method is realized and the experimental result of machining shows that the method is valid.

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Jang, Jeongki, and Kyungmok Kim. "Modeling of a Microscale Surface Using NURBS Technique." Coatings 9, no. 12 (November 20, 2019): 775. http://dx.doi.org/10.3390/coatings9120775.

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This article describes microscale surface modeling using the Non-Uniform Rational B-Spline (NURBS) surface interpolation technique. A three-dimensional surface model was generated on the basis of measured surface profile data. To validate this model, three brass specimens having different roughness values were used. Direct comparison between measured profiles and the curves modeled with NURBS was employed. It was identified that the proposed method allows the generation of microscale models similar to actual surfaces. Finally, a method to extract the Bearing Area Curve (BAC) from a 3D model was detailed. The proposed modeling will be useful for the characterization of bearing capacity of the surface and for contact analysis.

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Thilmany, Jean. "No Mesh, No Fuss." Mechanical Engineering 128, no. 05 (May 1, 2006): 46–48. http://dx.doi.org/10.1115/1.2006-may-5.

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This paper highlights the design of finite element analysis (FEA) without the finite element. The analysis can use the same information, the CAD system used to create the geometry in the first place. The geometry as well as the analysis fields-like displacement or temperature all uses the non-uniform rational B-spline mathematical representation. Software makers generally use the NURBS mathematical model to generate curves and surfaces in a digitized image. The framework lets mechanical engineers run quick, what-if scenarios to determine how changing a piece of a subassembly would affect the entire assembly. The full assembly need not be remeshed.

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Sharifi, Mohsen, Ali Aminfar, and Elnaz Abdollahzadeh. "A Minimalist Path Detection Approach for Wireless Sensor Networks." International Journal of Distributed Sensor Networks 5, no. 5 (October 1, 2009): 576–95. http://dx.doi.org/10.1080/15501320802300198.

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Most object tracking techniques find the exact locations of an object, while many other applications are only interested in the object's path rather than its locations. This provides an opportunity to reduce the existing tracking methods' resource usage by only focusing on the path detection. Taking advantage of this opportunity, this article presents two new minimalist approaches for accurately detecting unknown available passages in a sensor field without requiring the exact locations of the objects. In the first approach, each sensor sends its own location to a base station when it senses an object of interest. The base station uses b-spline curves to build the object's path online. Since each sensor sends its location data just once per new path, the first approach is a minimalist approach. The second approach is offline and uses non-uniform rational b-spline (NURBS) curves. Since NURBS needs weighted locations, each sensor sends its own location in addition to the number of times it has sensed an object based on the object's weight. Using the same simulation models, both approaches greatly reduce power consumption and improve the accuracy of the computed paths. The NURBS approach has proved to be robust on false alarms and improves the accuracy of path detection up to 95 percent, which is very close to detecting the object's actual path.

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Tsai, Mi-Ching, and Chung-Wei Cheng. "A Real-Time Predictor-Corrector Interpolator for CNC Machining." Journal of Manufacturing Science and Engineering 125, no. 3 (July 23, 2003): 449–60. http://dx.doi.org/10.1115/1.1578670.

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This paper presents a predictor-corrector interpolator (PCI) for the CNC machining of parts with parametric curves or surfaces. In contrast to existing parametric interpolators, the proposed method uses a simple algorithm as a predictor and the current feedrate command feedback compensation scheme as the corrector. The predictor adjusts itself according to the current feedrate command feedback, it also has the capability of predicting the next reference point of the parametric curves from the current reference point. As a result, the deviations between the current and desired feedrate commands will always fall within the specified feedrate command tolerances. This study aims at developing the mathematical analysis of the PCI, where the convergence condition is derived for the corrector. In this present approach, the user can specify either constant or variable federate and also its feedrate command accuracy. Both the simulation and experiment results are presented to demonstrate the feasibility of the proposed PCI for machining the parametric curves represented in the Non-Uniform Rational B-Spline (NURBS) form.

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Du, Xu, Jie Huang, and Li-Min Zhu. "A complete S-shape feed rate scheduling approach for NURBS interpolator." Journal of Computational Design and Engineering 2, no. 4 (June 20, 2015): 206–17. http://dx.doi.org/10.1016/j.jcde.2015.06.004.

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Abstract This paper presents a complete S-shape feed rate scheduling approach (CSFA) with confined jerk, acceleration and command feed rate for parametric tool path. For a Non-Uniform Rational B-Spline (NURBS) tool path, the critical points of the tool path where the radius of curvature reaches extreme values are found firstly. Then, the NURBS curve is split into several NURBS sub-curves or blocks by the critical points. A bidirectional scanning strategy with the limitations of chord error, normal/tangential acceleration/jerk and command feed rate is employed to make the feed rate at the junctions between different NURBS blocks continuous. To improve the efficiency of the feed rate scheduling, the NURBS block is classified into three types: short block, medium block and long block. The feed rate profile corresponding to each NURBS block is generated according to the start/end feed rates and the arc length of the block and the limitations of tangential acceleration/jerk. In addition, two compensation strategies are proposed to make the feed rate more continuous and the arc increment more precise. Once the feed rate profile is determined, a second-order Taylor׳s expansion interpolation method is applied to generate the position commands. Finally, experiments with two free-form NURBS curves are conducted to verify the applicability and accuracy of the proposed method.

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Liu, Yunzhen, Zhiqiang Wan, Chao Yang, and Xiaozhe Wang. "NURBS-Enhanced Meshfree Method with an Integration Subtraction Technique for Complex Topology." Applied Sciences 10, no. 7 (April 9, 2020): 2587. http://dx.doi.org/10.3390/app10072587.

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In this paper, we present an integration subtraction technique to model holes interactively in a predesigned domain for adaptive problems. This technique involves two approaches, the normal subtraction technique and the moving subtraction technique. In the basic normal subtraction technique, the predesigned domain can be meshed using any methods as an initial integration background cell for meshfree analysis. Holes are described using closed non-uniform rational B-spline (NURBS) curves to preserve the exact computer-aided design (CAD) geometry and are meshed alone using the homotopic method, so they can easily be subtracted from the predesigned domain with no refinement. On the other hand, when the hole size is varying, the moving subtraction technique, in which only the changing part between the new and old boundaries needs to be integrated and subtracted, is more efficient. Compared with the standard radial point interpolation method (RPIM) and finite element method (FEM) in three linear elastic examples with different holes, the excellent accuracy and good efficiency of the proposed method are demonstrated, and its feasibility in complex topology problems is verified.

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Xu, Libo, Feifei Zhao, Jingli Du, and Hong Bao. "Two-Step Calibration Method for Inverse Finite Element with Small Sample Features." Sensors 20, no. 16 (August 16, 2020): 4602. http://dx.doi.org/10.3390/s20164602.

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When the inverse finite element method (inverse FEM) is used to reconstruct the deformation field of a multi-element structure with strain measurements, strain measurement errors can lower the reconstruction accuracy of the deformation field. Furthermore, the calibration ability of a self-structuring fuzzy network (SSFN) is weak when few strain samples are used to train the SSFN. To solve this problem, a novel two-step calibration method for improving the reconstruction accuracy of the inverse FEM method is proposed in this paper. Initially, the errors derived from measured displacements and reconstructed displacements are distributed to the degrees of freedom (DOFs) of nodes. Then, the DOFs of nodes are used as knots, in order to produce non-uniform rational B-spline (NURBS) curves, such that the sample size employed to train the SSFN can be enriched. Next, the SSFN model is used to determine the relationship between the measured strain and the DOFs of the end nodes. A loading deformation experiment using a three-element structure demonstrates that the proposed algorithm can significantly improve the accuracy of reconstruction displacement.

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Liao, Huanyu, Pavan Kumar Vaitheeswaran, Tao Song, and Ganesh Subbarayan. "Algebraic Point Projection for Immersed Boundary Analysis on Low Degree NURBS Curves and Surfaces." Algorithms 13, no. 4 (March 31, 2020): 82. http://dx.doi.org/10.3390/a13040082.

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Point projection is an important geometric need when boundaries described by parametric curves and surfaces are immersed in domains. In problems where an immersed parametric boundary evolves with time as in solidification or fracture analysis, the projection from a point in the domain to the boundary is necessary to determine the interaction of the moving boundary with the underlying domain approximation. Furthermore, during analysis, since the driving force behind interface evolution depends on locally computed curvatures and normals, it is ideal if the parametric entity is not approximated as piecewise-linear. To address this challenge, we present in this paper an algebraic procedure to project a point on to Non-uniform rational B-spline (NURBS) curves and surfaces. The developed technique utilizes the resultant theory to construct implicit forms of parametric Bézier patches, level sets of which are termed algebraic level sets (ALS). Boolean compositions of the algebraic level sets are carried out using the theory of R-functions. The algebraic level sets and their gradients at a given point on the domain are then used to project the point onto the immersed boundary. Beginning with a first-order algorithm, sequentially refined procedures culminating in a second-order projection algorithm are described for NURBS curves and surfaces. Examples are presented to illustrate the efficiency and robustness of the developed method. More importantly, the method is shown to be robust and able to generate valid solutions even for curves and surfaces with high local curvature or G 0 continuity—problems where the Newton–Raphson method fails due to discontinuity in the projected points or because the numerical iterations fail to converge to a solution, respectively.

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Wang, Wei, Jianhua Zhu, Ruiyun Zhang, Yuling Li, Feng Ji, and Jianyong Yu. "Numerical characterization and simulation of the three-dimensional tubular woven fabric." Journal of Industrial Textiles 47, no. 8 (July 7, 2017): 2112–27. http://dx.doi.org/10.1177/1528083717720206.

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Three-dimensional tubular woven composite as a kind of special textile structural material is mainly used in oil and natural gas industry due to the advantages of the mechanical uniform circular shape and the provided properties. In order to comprehend the mechanical properties of the fabric in advance, modeling the three-dimensional tubular woven fabric is very important based on the actual weaving process parameters and specific structural data. In this paper, numerical characterization was performed and geometric model was constructed for this kind of three-dimensional tubular woven fabric. The geometric model of the 3D tubular woven fabric was established first based on the minimal repeating structural unit, and then a set of code including the positioning yarn coordinates and the topological relationship of the positioning yarn and non-positioning yarn was described. Furthermore, the three-dimensional tubular woven fabric was simulated under OpenGL platform according to the assumptions of the yarn cross-section and yarn path that was described by cubic B-spline curves. The proposed simulation method will contribute to the fabric structure simulation system used in the calculation of the fiber volume fraction, the distribution of voids and the prediction of composite mechanics.

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Perles, Brian P., and Judy M. Vance. "Interactive Virtual Tools for Manipulating NURBS Surfaces in a Virtual Environment." Journal of Mechanical Design 124, no. 2 (May 16, 2002): 158–63. http://dx.doi.org/10.1115/1.1464132.

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DN-Edit is a virtual environment developed to allow the manipulation of non-uniform rational b-spline (NURBS) surfaces using virtual shaping tools. NURBS have become the industry standard for representation of free-form curves and surfaces. The contribution of the work presented here is in the development of shaping tools which are used to operate directly on the NURBS data and change the shape of the surfaces in a virtual environment. These shaping tools allow surface manipulations to be made using methods that match the shaping of real malleable objects. The virtual shaping tools are three-dimensional shapes that are controlled through a six degree-of-freedom tracking system that converts user hand motions into computer input. The NURBS surface updates itself in real time due to the effect of the tools on the surface. The new shape of the surface is dependent on the position and orientation of the shaping tool relative to the surface. Constraint-based surface manipulation is used to obtain multiple point direct manipulation of NURBS surfaces. In addition, computational methods to allow the user to have direct control of the first derivative of the surface over an area are implemented. This application has been developed using the C2 software libraries and Iowa State University’s C2 surround screen virtual environment.

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WU, Sheng, Xin-yu GUO, Bo-xiang XIAO, Sheng-lian LU, and Wei-liang WEN. "Encryption algorithm based on non-uniform B-spline curve." Journal of Computer Applications 31, no. 2 (April 7, 2011): 517–19. http://dx.doi.org/10.3724/sp.j.1087.2011.00517.

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Liu, Jiankang, Hongya Fu, Jihao Qin, and Hongyu Jin. "Sliding look-ahead window-based real-time feedrate planning for non-uniform rational B-splines curves." Advances in Mechanical Engineering 10, no. 12 (December 2018): 168781401881692. http://dx.doi.org/10.1177/1687814018816926.

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This article presents an online three-axis non-uniform rational B-splines preprocessing and feedrate scheduling method with chord error, axial velocity, acceleration, and jerk limitations. A preprocessing method is proposed to accurately locate the critical points by reducing pre-interpolation feedrate in feedrate limit violation regions. In the preprocessing stage, the non-uniform rational B-splines curve is subdivided into segments by the critical points and the corresponding feedrate constraints are obtained. A sliding look-ahead window-based feedrate scheduling method is proposed to generate smooth feedrate profile for the buffered non-uniform rational B-splines segments. The feedrate profile corresponding to each non-uniform rational B-splines block is constructed according to the block length and the given limits of acceleration and jerk. The feedrate modification method for non-schedulable short blocks is also described which aimed at avoiding feedrate discontinuity at the junction of two non-uniform rational B-splines blocks. With the proposed method, a successful feedrate profile could be generated with sufficient look-ahead trajectory length in the buffer, which enables that the preprocessing and feedrate planning to be performed progressively online. Simulation and experimental tests with different non-uniform rational B-splines curves are carried out to validate the feasibility and advantages of the proposed method. The results show that the proposed method is capable of making a balance between the machining efficiency, machining precision, and computational complexity.

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Wahab, Abd Fatah, Mohammad Izat Emir Zulkifly, and Lim Kah Yong. "EVELOPMENT OF NON-UNIFORM RATIONAL TYPE-2 FUZZY B-SPLINE CURVE MODELING." Advances in Differential Equations and Control Processes 23, no. 2 (November 20, 2020): 261–77. http://dx.doi.org/10.17654/de023020261.

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Zhao, Zhen Yu, Dong Ying Liang, Yong Shan Xiao, and Bai Liu. "Research on CNC Key Technology for High Speed Milling." Key Engineering Materials 467-469 (February 2011): 252–56. http://dx.doi.org/10.4028/www.scientific.net/kem.467-469.252.

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At present, high speed machining (HSM) features in high efficiency, high precision, high flexibility and high quality. HSM technology involves many factors, including cutting mechanisms, machining performance, tool path and other aspects. The key techniques on HSM such as linear interpolation, circular interpolation, cubic B-spline curve interpolation, non-uniform rational B-spline (NURBS) curve interpolation and their respective characteristics are paid more attention and expatiated.

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Zhao, Zhen Yu, Ming Jun Liu, Yong Shan Xiao, and Bai Liu. "Interpolation Algorithm on Numerical Control Technology." Key Engineering Materials 467-469 (February 2011): 247–51. http://dx.doi.org/10.4028/www.scientific.net/kem.467-469.247.

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High speed machining (HSM) features in high efficiency, high precision, high flexibility and high quality. The key techniques on HSM such as linear interpolation, circular interpolation, cubic B-spline curve interpolation, non-uniform rational B-spline (NURBS) curve interpolation and their respective characteristics are paid more attention and expatiated. Circle arcs are approximated by using intersecting polygons instead of general inscribed polygons. NURBS interpolation algorithms can reduce feedrate fluctuation and improve machining accuracy.

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CHEN, Kaiyun. "Research on How the Knot Vector Influences Non-uniform Rational B-spline Curve." Chinese Journal of Mechanical Engineering 44, no. 10 (2008): 294. http://dx.doi.org/10.3901/jme.2008.10.294.

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LIN, Hongwei. "Constructing iterative non-uniform B-spline curve and surface to fit data points." Science in China Series F 47, no. 3 (2004): 315. http://dx.doi.org/10.1360/02yf0529.

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Peng, Bao Ying, and Qiu Shi Han. "Cam Grinding Interpolation Research Based on Cubic Non-Uniform Rational B-Splines." Advanced Materials Research 443-444 (January 2012): 843–49. http://dx.doi.org/10.4028/www.scientific.net/amr.443-444.843.

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With the development of auto industry and aviation industry,the cam quality requirements higher and higher. The NURBS curve has excellent natures that can smooth the cam grinding path and improve its processing quality. Combined with existing CAD software and CNC systems, respectively, from reverse and forward two aspects of NURBS curve to illustrate the non-uniform B-spline principle and given the relevant formulas. Choosing X-C coordinates points of the cam grinding as the research object, adopt reverse and forward NURBS curve interpolation to fit the cam grinding path. Analysed the fitting error caused by line segment fit NURBS curve and cam lift error caused by NURBS interpolation. Summarized the advantages and disadvantages of two ways Nurbs interpolation discussed the method to improve NURBS interpolation for cam grinding.

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TAKAHASHI, Seiji, Koichi MORISHIGE, and Yoshimi TAKEUCHI. "NC Data Generation for Five-axis Control Machining Using Curved Interpolation - Application of Five-dimensional Non-uniform B-spline Curve." Journal of the Japan Society for Precision Engineering 65, no. 12 (1999): 1740–44. http://dx.doi.org/10.2493/jjspe.65.1740.

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Sudir, P., and M. Ravishankar. "An Effective Edge and Texture Based Approach towards Curved Videotext Detection and Extraction." International Journal of System Dynamics Applications 4, no. 3 (July 2015): 1–29. http://dx.doi.org/10.4018/ijsda.2015070101.

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In present day video text greatly helps video indexing and retrieval system as they often carry significant semantic information. Video text analysis is challenging due to varying background, multiple orientations and low contrast between text and non-text regions. Proposed approach explores a new framework for curved video text detection and recognition where from the observation that curve text regions can be well defined by edges size and uniform texture, Probable curved text edge detection is accomplished by processing wavelet sub bands followed by text localization by utilizing fast texture descriptor LU-transform. Binarization is achieved by maximal H-transform. A Connected Component filtering method followed by B-Spline curve fitting on centroid of each character vertically aligns each oriented character. The aligned text string is recognized by optical character recognition (OCR). Experiments on various curved video frames shows that proposed method is efficacious and robust in detecting and recognizing curved videotext.

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Zhou, Honggen, Jie Cui, Guizhong Tian, Yesheng Zhu, and Changfeng Jia. "Modeling technology of curved surface development for puffer fish." Advances in Mechanical Engineering 12, no. 4 (April 2020): 168781402091602. http://dx.doi.org/10.1177/1687814020916025.

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The drag reduction mechanism of puffer epidermis was closely related to its real geometry. In order to solve the modeling problem of epidermal spines on the puffer surface, a modeling method for the expansion of puffer shape was proposed. The three-dimensional scanning and non-uniform rational B-spline surface modeling technology was used to reconstruct the puffer model. According to the curvature characteristics, the surface mathematical equations including exponential, logarithmic, and sinusoidal functions were established based on the multinomial function. The surface was generated by a mathematical equation, and the surface was divided into several non-uniform rational B-spline patches according to curvature. After discretization, the point cloud Gaussian curvature and average value were calculated based on the implicit equation of moving least square surface, and whether the surface is approximately extensible or not was judged. Finally, the puffer surface was divided into 46 curved patches. In this article, the surface expansion algorithm gave priority to ensure the area unchanged, and four feature surfaces were selected according to the epidermal spines arrangement of the puffer surface. The results showed that the technique can simply and efficiently unfold the curved surface of the puffer fish, thus the mapping relationship between the epidermal spines on the surface and the plane was determined, which established a foundation for the accurate arrangement and modeling of the epidermal spines on the surface.

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Wang, Geng Zhu. "The Real-Time Look-Ahead NURBS Curve Interpolation Algorithm." Advanced Engineering Forum 2-3 (December 2011): 523–26. http://dx.doi.org/10.4028/www.scientific.net/aef.2-3.523.

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To ensure a given chord error, through the division of the cusp, the NURBS (Non-Uniform Rational B-Splins) curve is divided into several sections and the speed of the various sections is planned accordingly. The acceleration and deceleration time period is recalculated, which results in a smooth speed transition curve.

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Journal articles on the topic 'Non-uniform B-spline curves'

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