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Journal articles on the topic 'Non Uniform Rational B-Splines'

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Author: Grafiati

Published: 6 September 2023

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1

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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Cheng, Ming-Yang, Hung-Wen Wu, and Alvin Wen-Yu Su. "On Non-Uniform Rational B-Splines Surface Neural Networks." Neural Processing Letters 28, no. 1 (May 10, 2008): 1–15. http://dx.doi.org/10.1007/s11063-008-9078-9.

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3

SUN, Shufeng. "Design of Spatial Cam Based on Non-uniform Rational B-splines." Journal of Mechanical Engineering 45, no. 08 (2009): 125. http://dx.doi.org/10.3901/jme.2009.08.125.

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4

Audoux, Y., M. Montemurro, and J. Pailhes. "A surrogate model based on Non-Uniform Rational B-Splines hypersurfaces." Procedia CIRP 70 (2018): 463–68. http://dx.doi.org/10.1016/j.procir.2018.03.234.

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5

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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Xuan, Guantao, Yuanyuan Shao, and Lei Liu. "Optimal Design of Grooved Cam Profile Using Non-uniform Rational B-splines." MATEC Web of Conferences 139 (2017): 00047. http://dx.doi.org/10.1051/matecconf/201713900047.

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Steuben, John C., Cameron J. Turner, and Richard H. Crawford. "Robust engineering design optimization with non-uniform rational B-splines-based metamodels." Engineering Optimization 45, no. 7 (July 2013): 767–86. http://dx.doi.org/10.1080/0305215x.2012.709509.

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8

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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9

Müller, Mario, Mathias Hüsing, Agnes Beckermann, and Burkhard Corves. "Linkage and Cam Design with MechDev Based on Non-Uniform Rational B-Splines." Machines 8, no. 1 (January 21, 2020): 5. http://dx.doi.org/10.3390/machines8010005.

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Several software products exist in order to support engineers during the mechanism design process. The software “Mechanism Developer” (abbr. MechDev) is one of these products. MechDev provides many functionalities concerning the kinematic and kinetostatic analysis of mechanisms based on revolute, prismatic as well as cam joints. This paper will introduce the software MechDev and will outline these functionalities. Furthermore, it will name the advantages of MechDev compared to other software products. In order to give an impression of the functionality of the software, this paper also includes a special use case. This use case describes a cam mechanism with a prismatic roller-follower. In order to optimize the transmission angle of the cam mechanism, the cam is actuated by a servo drive. To mathematically model the angular input of the servo drive, Non-Uniform Rational B-Splines (NURBS) are described and applied. Thus, a nearly arbitrary input function can be described by few parameters.

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10

Lan, Peng, Zuqing Yu, Liang Du, and Nianli Lu. "Integration of non-uniform Rational B-splines geometry and rational absolute nodal coordinates formulation finite element analysis." Acta Mechanica Solida Sinica 27, no. 5 (October 2014): 486–95. http://dx.doi.org/10.1016/s0894-9166(14)60057-4.

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11

Zerrouki, Nadjib, Noureddine Goléa, and Nabil Benoudjit. "Particle Swarm Optimization of Non Uniform Rational B-Splines for Robot Manipulators Path Planning." Periodica Polytechnica Electrical Engineering and Computer Science 61, no. 4 (November 9, 2017): 337. http://dx.doi.org/10.3311/ppee.8682.

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The path-planning problem is commonly formulated to handle the obstacle avoidance constraints. This problem becomes more complicated when further restrictions are added. It often requires efficient algorithms to be solved. In this paper, a new approach is proposed where the path is described by means of Non Uniform Rational B-Splines (NURBS for short) with more additional constraints. An evolutionary technique called Particle Swarm Optimization (PSO) with three options of particles velocity updating offering three alternatives namely the PSO with inertia weight (PSO-W), the constriction factor PSO (PSO-C) and the combination of the two(PSO-WC); are used to optimize the weights of the control points that serve as parameters of the algorithm describing the path. Simulation results show how the mixture of the first two options produces a powerful algorithm, specifically (PSO-WC), in producing a compromise between fast convergence and large number of potential solution. In addition, the whole approach seems to be flexible, powerful and useful for the generation of successful smooth trajectories for robot manipulator which are independent from environment conditions.

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12

Yau, Hong-Tzong. "A model-based approach to form tolerance evaluation using non-uniform rational B-splines." Robotics and Computer-Integrated Manufacturing 15, no. 4 (August 1999): 283–95. http://dx.doi.org/10.1016/s0736-5845(99)00012-5.

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13

Teufel, Edgar. "Designing optical devices based on non-uniform rational Béziers splines." Renewable Energy 63 (March 2014): 69–75. http://dx.doi.org/10.1016/j.renene.2013.09.001.

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14

Xuan, Guan Tao, Yuan Yuan Shao, and Zhao Qin Lü. "Reduction of Residual Vibrations in High-Speed Cam Mechanisms Using Non-Uniform Rational B-Splines." Advanced Materials Research 510 (April 2012): 90–95. http://dx.doi.org/10.4028/www.scientific.net/amr.510.90.

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In high-speed cam mechanisms, the output motion and positioning accuracy are affected greatly by residual vibrations. To reduce residual vibration, non-uniform rational B-splines (NURBS) is employed to reconstruct the cam profile. Based on elastic dynamic theory, this paper designs the multi-objective dynamic optimization model of high-speed cam mechanisms, and proposes an improved artificial fish swarm algorithm (IAFSA) to optimize the cam profile. Utilizing the taboo search strategy, NURBS profile is optimized twice with variable parameters. By adjusting parameters of NURBS, dynamic characteristics of the follower motion curve are improved, and the residual vibration is reduced. Finally, an optimization simulation example is given to demonstrate the usefulness and effectiveness of the approach.

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Shih, Alan M., Tzu-Yi Yu, Sankarappan Gopalsamy, Yasushi Ito, and Bharat Soni. "Geometry and mesh generation for high fidelity computational simulations using non-uniform rational B-splines." Applied Numerical Mathematics 55, no. 3 (November 2005): 368–81. http://dx.doi.org/10.1016/j.apnum.2005.04.036.

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Martín, M. J., E. Andrés, M. Widhalm, P. Bitrián, and C. Lozano. "Non-uniform rational B-splines-based aerodynamic shape design optimization with the DLR TAU code." Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering 226, no. 10 (December 7, 2011): 1225–42. http://dx.doi.org/10.1177/0954410011421704.

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17

Steuben, John C., and Cameron J. Turner. "Graph analysis of non-uniform rational B-spline-based metamodels." Engineering Optimization 47, no. 9 (September 26, 2014): 1157–76. http://dx.doi.org/10.1080/0305215x.2014.954565.

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Taheri, Alireza H., Saeed Abolghasemi, and Krishnan Suresh. "Generalizations of non-uniform rational B-splines via decoupling of the weights: theory, software and applications." Engineering with Computers 36, no. 4 (June 20, 2019): 1831–48. http://dx.doi.org/10.1007/s00366-019-00799-w.

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Wang, Jing Jing, and Hong Jun Wang. "A Non-Rigid Image Registration Algorithm Based on NURBS." Applied Mechanics and Materials 170-173 (May 2012): 3521–24. http://dx.doi.org/10.4028/www.scientific.net/amm.170-173.3521.

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Non-rigid image registration is an interesting and challenging research work in medical image processing, computer vision and remote sensing fields. In this paper we present a free form deformable algorithm based on NURBS because NURBS (Non-uniform Rational B Spline ) with a non-uniform grid has a higher registration precision and a higher registration speed in comparison with B spline. In our experiment we compare the NURBS based FFD method with the B spline based FFD method quantitatively. The experiment result shows that the algorithm can improve highly the registration precision.

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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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Deng, Chongyang, Zhihao Wang, Jianzhen Liu, Huixia Xu, and Qianqian Hu. "FC-NURBS curves: fullness control non-uniform rational B-spline curves." Communications in Information and Systems 22, no. 1 (2022): 131–46. http://dx.doi.org/10.4310/cis.2022.v22.n1.a6.

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22

Cheng, C. W., M. C. Tsai, and J. Maciejowski. "Feedrate control for non-uniform rational B-spline motion command generation." Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture 220, no. 11 (November 2006): 1855–61. http://dx.doi.org/10.1243/09544054jem401.

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23

Zang, Ting, and Anping Xu. "An approach to representing heterogeneous non-uniform rational B-spline objects." Transactions of Tianjin University 17, no. 4 (August 2011): 275–79. http://dx.doi.org/10.1007/s12209-011-1629-x.

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24

Rajamohan, G., M. Shunmugam, and G. Samuel. "Practical Measurement Strategies for Verification of Freeform Surfaces Using Coordinate Measuring Machines." Metrology and Measurement Systems 18, no. 2 (January 1, 2011): 209–22. http://dx.doi.org/10.2478/v10178-011-0004-y.

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Practical Measurement Strategies for Verification of Freeform Surfaces Using Coordinate Measuring MachinesFreeform surfaces have wider engineering applications. Designers use B-splines, Non-Uniform Rational B-splines, etc. to represent the freeform surfaces in CAD, while the manufacturers employ machines with controllers based on approximating functions or splines. Different errors also creep in during machining operations. Therefore the manufactured freeform surfaces have to be verified for conformance to design specification. Different points on the surface are probed using a coordinate measuring machine and substitute geometry of surface established from the measured points is compared with the design surface. The sampling points are distributed according to different strategies. In the present work, two new strategies of distributing the points on the basis of uniform surface area and dominant points are proposed, considering the geometrical nature of the surfaces. Metrological aspects such as probe contact and margins to be provided along the sides have also been included. The results are discussed in terms of deviation between measured points and substitute surface as well as between design and substitute surfaces, and compared with those obtained with the methods reported in the literature.

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Wu, Lei, Jianqiao Liu, Manicka Dhanasekar, Hengyu Wang, and Zefeng Wen. "Optimisation of railhead profiles for curved tracks using improved non-uniform rational B-splines and measured profiles." Wear 418-419 (January 2019): 123–32. http://dx.doi.org/10.1016/j.wear.2018.11.012.

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26

Xie, Wei-Cheng, Xiu-Fen Zou, Jian-Dong Yang, and Jie-Bin Yang. "Iteration and optimization scheme for the reconstruction of 3D surfaces based on non-uniform rational B-splines." Computer-Aided Design 44, no. 11 (November 2012): 1127–40. http://dx.doi.org/10.1016/j.cad.2012.05.004.

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27

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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Yang, Zhen Xing, and Jian Jun Zhou. "Mine 3D Geological Interface Modeling by NURBS Technology." Advanced Materials Research 1065-1069 (December 2014): 44–47. http://dx.doi.org/10.4028/www.scientific.net/amr.1065-1069.44.

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It is imperative for 3D modeling of mining or underground engineering to precisely and efficiently describe various interfaces, which is also the precondition for 3D visualization of underground engineering. NURBS (Non-Uniform Rational B-Splines) curve and surface technology are introduced in the paper. With help of analyzing 3D geologic structure of Laohutai mining area and comprehensive treatment of surfaces of tunnels and geologic structures. 3D geological surfaces of mining area are built which is the base of building complex 3D geologic modeling.

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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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Wang, Guirong, Jiahao Chen, Kun Zhou, and Zhihui Pang. "Industrial Robot Contouring Control Based on Non-Uniform Rational B-Spline Curve." Symmetry 14, no. 12 (November 30, 2022): 2533. http://dx.doi.org/10.3390/sym14122533.

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This paper presents a novel algorithm about the industrial robot contouring control based on the NURBS (non-uniform rational B-spline) curve. First, aiming at the error between the industrial robot’s actual trajectory and the desired trajectory, the contour error is proposed as the trajectory evaluation index, and the estimation algorithm of contour error based on the tangent approximation is proposed. Based on the tangent approximation algorithm, the estimation algorithm of contour error in the local task coordinate frame is proposed to realize the transformation from the Cartesian coordinate frame to the local task coordinate frame. Second, according to the configuration of the industrial robot, a modified cross-coupling control scheme based on the local task coordinate frame is designed. Finally, the Bernoulli’s lemniscate curves are constructed by NURBS curve and five-order polynomial curve, respectively, and they are symmetrical. The contrast experiment is designed using the two types of constructed Bernoulli’s lemniscate curves as the incentive trajectory. Through the analysis and comparison between the obtained uniaxial tracking error and the contour error curve of the two incentive trajectories, it is concluded that the incentive trajectory constructed by the NURBS curve has better contour control performance than that constructed by the five-order polynomial curve. The results drawn from this paper lay a certain foundation for the future high-precision contouring control of industrial robots.

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Qiu, W., J. M. Chuang, and C. C. Hsiung. "Numerical Solution of Wave Diffraction Problem in the Time Domain With the Panel-Free Method." Journal of Offshore Mechanics and Arctic Engineering 126, no. 1 (February 1, 2004): 1–8. http://dx.doi.org/10.1115/1.1641384.

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A panel-free method (PFM) was developed earlier to solve the radiation problem of a floating body in the time domain. In the further development of this method, the diffraction problem has been solved. After removing the singularity in the Rankine source of the Green function and representing the body surface mathematically by Non-Uniform Rational B-Splines (NURBS) surfaces, integral equations were globally discretized over the body surface by Gaussian quadratures. Computed response functions and forces due to diffracted waves for a hemisphere at zero speed were compared with published results.

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Farah, Philipp, Markus Gitterle, Wolfgang A. Wall, and Alexander Popp. "Computational Wear and Contact Modeling for Fretting Analysis with Isogeometric Dual Mortar Methods." Key Engineering Materials 681 (February 2016): 1–18. http://dx.doi.org/10.4028/www.scientific.net/kem.681.1.

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A finite element framework based on dual mortar methods is presented for simulating fretting wear effects in the finite deformation regime. The mortar finite element discretization is realized with Lagrangean shape functions as well as isogeometric elements based on non-uniform rational B-splines (NURBS) in two and three dimensions. Fretting wear effects are modeled in an incremental scheme with the help of Archard’s law and the worn material is considered as additional contribution to the gap function. Numerical examples demonstrate the robustness and accuracy of the presented algorithm.

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Dsouza, S. M., T. Khajah, X. Antoine, S. P. A. Bordas, and S. Natarajan. "Non Uniform Rational B-Splines and Lagrange approximations for time-harmonic acoustic scattering: accuracy and absorbing boundary conditions." Mathematical and Computer Modelling of Dynamical Systems 27, no. 1 (January 2, 2021): 263–94. http://dx.doi.org/10.1080/13873954.2021.1902355.

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Ruiu, Jeremy, Guillaume Caumon, and Sophie Viseur. "Modeling Channel Forms and Related Sedimentary Objects Using a Boundary Representation Based on Non-uniform Rational B-Splines." Mathematical Geosciences 48, no. 3 (December 21, 2015): 259–84. http://dx.doi.org/10.1007/s11004-015-9629-3.

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Hageman, Tim, and René de Borst. "Unequal order T-spline meshes for fracture in poroelastic media." Journal of Mechanics 37 (2021): 669–79. http://dx.doi.org/10.1093/jom/ufab031.

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Abstract Spline-based meshes allow for a higher inter-element continuity. For coupled problems, e.g. poroelasticity, different meshes with different orders of interpolation are normally used for the various fields in order to avoid spurious oscillations. When including discontinuities in these meshes, there exist several options for the discretisation. Herein we will discuss two options which use T-splines, one aiming at a minimum number of degrees of freedom around the crack tip, the other trying to maximise this number. Both meshes retain a higher-order continuity along the fracture, but the mesh which maximises the number of degrees of freedom mesh introduces two additional degrees of freedom around the crack tip to allow for a sharper crack. The two discretisations are used to simulate a pressurised fracture inside a poroelastic material and the results are compared to results obtained using a Non-Uniform Rational B-Spline (NURBS) mesh. A comparison between the two discretisations shows the effect of including additional degrees of freedom close to the crack tip. However, both meshes yield similar results further away from the crack tip. It is shown that both T-spline meshes capture a fully closed discontinuity at the fracture tip, whereas the NURBS mesh retains a small opening due to the discontinuity which exists for the cracked as well as the intact elements. A fully closed fracture aperture results in T-splines with a lower discontinuity pressure compared to NURBS, making T-splines more suitable for simulations in which the fracture propagation is limited by the fluid transport within the fracture.

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Mirhosseini, R. Tabatabaei. "Simulation of Seismic Response of Reinforced Concrete Beam-Column Joints with Nurbs Surface Fitting." Archives of Civil Engineering 63, no. 3 (September 26, 2017): 71–84. http://dx.doi.org/10.1515/ace-2017-0029.

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Abstract This paper presents an approach based on NURBS (non-uniform rational B-splines) to achieve a seismic response surface (SRS) from a group of points obtained by using an analytical model of RC joints. NURBS based on the genetic algorithm is an important mathematical tool and consists of generalizations of Bezier curves and surfaces and B-splines. Generally, the accuracy of the design process of joints depends on the number of control points that are captured in the results of experimental research on real specimens. The values obtained from the specimens are the best tools to use in seismic analysis, though more expensive when compared to values simulated by SRSs. The SRS proposed in this paper can be applied to obtain surfaces that show site effect results on destructions of beam-column joint, taking into account different site conditions for a specific earthquake. The efficiency of this approach is demonstrated by the retrieval of simulated-versus-analytical results.

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Wang, Nan, Haobo Yuan, Mei Xu, and Changhong Liang. "Study on Interface Scheme for Non-Uniform Rational B-Spline Uniform Geometrical Theory of Diffraction Method." Electromagnetics 36, no. 6 (August 3, 2016): 392–99. http://dx.doi.org/10.1080/02726343.2016.1207830.

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Wang, Li Hua, and Guang Wei Liu. "Study on 3D Reconstruction and Static/Dynamic Characteristics of Human Femur." Applied Mechanics and Materials 37-38 (November 2010): 1259–64. http://dx.doi.org/10.4028/www.scientific.net/amm.37-38.1259.

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3D (three-dimensional) reconstruction, the stress distribution and dynamic response characteristics of human femur are important for optimal design of human femur prosthesis. Based on the STL (Stereo Lithography) model, using the method of NURBS (Non-Uniform Rational B-Splines) surfaces modeling, 3D reconstruction of human femur has been discussed in this paper. Then the static and dynamics characteristics of the reconstructed human femur model are analyzed using finite element method. The analytical results revealed that the precision 3D model and the statics and dynamics characteristics of human femur are the key factors for the human femur prostheses design.

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Chen, Leilei, Steffen Marburg, Wenchang Zhao, Cheng Liu, and Haibo Chen. "Implementation of Isogeometric Fast Multipole Boundary Element Methods for 2D Half-Space Acoustic Scattering Problems with Absorbing Boundary Condition." Journal of Theoretical and Computational Acoustics 27, no. 02 (June 2019): 1850024. http://dx.doi.org/10.1142/s259172851850024x.

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Isogeometric Analysis (IGA), which tries to bridge the gap between Computer Aided Engineering (CAE) and Computer Aided Design (CAD), has been widely proposed in recent research. According to the concept of IGA, this work develops a boundary element method (BEM) using non-Uniform Rational B-Splines (NURBS) as basis functions for the 2D half-space acoustic problems with absorbing boundary condition. Fast multipole method (FMM) is applied to accelerate the solution of an isogeometric BEM (IGA-BEM). Several examples are tested and it is shown that this advancement on isogeometric fast multipole boundary element method improves the accuracy of simulations.

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Ouadefli, Lahcen El, Omar El Moutea, Abdeslam El Akkad, Ahmed Elkhalfi, Sorin Vlase, and Maria Luminița Scutaru. "Mixed Isogeometric Analysis of the Brinkman Equation." Mathematics 11, no. 12 (June 17, 2023): 2750. http://dx.doi.org/10.3390/math11122750.

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This study focuses on numerical solution to the Brinkman equation with mixed Dirichlet–Neumann boundary conditions utilizing isogeometric analysis (IGA) based on non-uniform rational B-splines (NURBS) within the Galerkin method framework. The authors suggest using different choices of compatible NURBS spaces, which may be considered a generalization of traditional finite element spaces for velocity and pressure approximation. In order to investigate the numerical properties of the suggested elements, two numerical experiments based on a square and a quarter of an annulus are discussed. The preliminary results for the Stokes problem are presented in References.

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Truong, Thien Tich, Bang Kim Tran, Khuong Duy Nguyen, Minh Ngoc Nguyen, and Nha Thanh Nguyen. "Extended iso geometry analysis of crack propagation." Science and Technology Development Journal 18, no. 2 (June 30, 2015): 76–84. http://dx.doi.org/10.32508/stdj.v18i2.1075.

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The purpose of this paper is simulating the crack propagation in steel structures with isogeometry analysis (IGA). In this method, CAD model is integrated into the CAE model by using non uniform rational B-Splines (NURBS) function. Crack propagation in isotroptic linear elastic material will be presented. The numerical example is a rectangular plate assumed to be plane strain condition with an edge crack under uniform shear loading. The obtained results are investigated and compared with analytical method and reference solutions. Very good agreements on the solutions are found. It is showed that isogometry analysis is better than standard finite element method in modeling and simulating. Consequently, isogometry analysis is an effective numerical method in future, especially when solving the crack propagation problems.

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Yuan, Haobo, Li He, Zhijun Wang, and Xiaojie Dang. "Accurate Solution of Magnetic Field Integral Equation with Higher-Order Basis Functions and Non-Uniform Rational B-Splines Modeling." Electromagnetics 35, no. 7 (October 2, 2015): 474–87. http://dx.doi.org/10.1080/02726343.2015.1084574.

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Eldeeb, Radia, Vikrant Aute, and Reinhard Radermacher. "Pillow plate heat exchanger weld shape optimization using approximation and parallel parameterized CFD and non-uniform rational B-splines." International Journal of Refrigeration 110 (February 2020): 121–31. http://dx.doi.org/10.1016/j.ijrefrig.2019.10.024.

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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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Li Yun, 李云, and 邢廷文 Xing Tingwen. "Surface Error of Optical Components Extended with Non-Uniform Rational B-Spline Surface." Acta Optica Sinica 32, no. 7 (2012): 0722001. http://dx.doi.org/10.3788/aos201232.0722001.

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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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Saravanan, R., S. Ramabalan, P. Sriram, and C. Balamurugan. "Non-uniform rational B-spline-based minimum cost trajectory planning for autonomous robots." International Journal of Intelligent Systems Technologies and Applications 9, no. 2 (2010): 121. http://dx.doi.org/10.1504/ijista.2010.034317.

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Zhang, Yue, Chun-Gang Zhu, and Qing-Jie Guo. "On the limits of non-uniform rational B-spline surfaces with varying weights." Advances in Mechanical Engineering 9, no. 5 (May 2017): 168781401770054. http://dx.doi.org/10.1177/1687814017700547.

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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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Kermarrec, Gaël, Niklas Schild, and Jan Hartmann. "Fitting Terrestrial Laser Scanner Point Clouds with T-Splines: Local Refinement Strategy for Rigid Body Motion." Remote Sensing 13, no. 13 (June 26, 2021): 2494. http://dx.doi.org/10.3390/rs13132494.

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T-splines have recently been introduced to represent objects of arbitrary shapes using a smaller number of control points than the conventional non-uniform rational B-splines (NURBS) or B-spline representatizons in computer-aided design, computer graphics and reverse engineering. They are flexible in representing complex surface shapes and economic in terms of parameters as they enable local refinement. This property is a great advantage when dense, scattered and noisy point clouds are approximated using least squares fitting, such as those from a terrestrial laser scanner (TLS). Unfortunately, when it comes to assessing the goodness of fit of the surface approximation with a real dataset, only a noisy point cloud can be approximated: (i) a low root mean squared error (RMSE) can be linked with an overfitting, i.e., a fitting of the noise, and should be correspondingly avoided, and (ii) a high RMSE is synonymous with a lack of details. To address the challenge of judging the approximation, the reference surface should be entirely known: this can be solved by printing a mathematically defined T-splines reference surface in three dimensions (3D) and modeling the artefacts induced by the 3D printing. Once scanned under different configurations, it is possible to assess the goodness of fit of the approximation for a noisy and potentially gappy point cloud and compare it with the traditional but less flexible NURBS. The advantages of T-splines local refinement open the door for further applications within a geodetic context such as rigorous statistical testing of deformation. Two different scans from a slightly deformed object were approximated; we found that more than 40% of the computational time could be saved without affecting the goodness of fit of the surface approximation by using the same mesh for the two epochs.

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