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Journal articles on the topic 'Bi-cubic Splines'

Author: Grafiati

Published: 4 June 2021

Last updated: 9 February 2022

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1

Karčiauskas, Kȩstutis, and Jörg Peters. "Rational bi-cubic G2 splines for design with basic shapes." Computer Graphics Forum 30, no. 5 (2011): 1389–95. http://dx.doi.org/10.1111/j.1467-8659.2011.02013.x.

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2

Lavery, John E. "Shape-preserving, multiscale interpolation by bi- and multivariate cubic splines." Computer Aided Geometric Design 18, no. 4 (2001): 321–43. http://dx.doi.org/10.1016/s0167-8396(01)00034-6.

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3

Prenosil, Thomas, and H. G. Becker. "Über die Grenzen der Effizienz bei der Anwendung von bi-kubischen Splines in Gitterpunktmodellen zur regionalen Wettervorhersage." Meteorologische Zeitschrift 8, no. 6 (2000): 168–77. http://dx.doi.org/10.1127/metz/8/2000/168.

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4

Cooper, A. P. R. "Interpolation Techniques for the Display of Remotely Sensed Glaciological Data (Abstract)." Annals of Glaciology 9 (1987): 237. http://dx.doi.org/10.1017/s0260305500000719.

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The use of many display techniques for remotely sensed glaciological data requires the reduction of the data to a regularly spaced rectangular grid of values. Most remotely sensed data are not immediately suitable for display, because the area of interest is covered by more than one set of data on mutually incompatible grids (e.g. Landsat, AVHRR), or because the data are available as profiles along widely spaced ground tracks (e.g. radio echo-sounding, satellite altimetry). In addition, data may be sparsely and randomly scattered (e.g. surface elevations from TWERLE balloons). A variety of techniques is available to reduce data to a specified grid system. These include spatial averaging, interpolation from nearest neighbours, and surface-fitting techniques, notably polynomial fitting and bi-cubic splines. All of these are useful under differing circumstances.

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Cooper, A. P. R. "Interpolation Techniques for the Display of Remotely Sensed Glaciological Data (Abstract)." Annals of Glaciology 9 (1987): 237. http://dx.doi.org/10.3189/s0260305500000719.

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The use of many display techniques for remotely sensed glaciological data requires the reduction of the data to a regularly spaced rectangular grid of values. Most remotely sensed data are not immediately suitable for display, because the area of interest is covered by more than one set of data on mutually incompatible grids (e.g. Landsat, AVHRR), or because the data are available as profiles along widely spaced ground tracks (e.g. radio echo-sounding, satellite altimetry). In addition, data may be sparsely and randomly scattered (e.g. surface elevations from TWERLE balloons).A variety of techniques is available to reduce data to a specified grid system. These include spatial averaging, interpolation from nearest neighbours, and surface-fitting techniques, notably polynomial fitting and bi-cubic splines. All of these are useful under differing circumstances.

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6

Zhang, B., and J. F. M. Molenbroek. "Representation of a human head with bi-cubic B-splines technique based on the laser scanning technique in 3D surface anthropometry." Applied Ergonomics 35, no. 5 (2004): 459–65. http://dx.doi.org/10.1016/j.apergo.2004.03.012.

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7

Xu, Weizhi. "Elements of Bi-cubic Polynomial Natural Spline Interpolation for Scattered Data: Boundary Conditions Meet Partition of Unity Technique." Statistics, Optimization & Information Computing 8, no. 4 (2020): 994–1010. http://dx.doi.org/10.19139/soic-2310-5070-1083.

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This paper investigates one kind of interpolation for scattered data by bi-cubic polynomial natural spline, in which the integral of square of partial derivative of two orders to x and to y for the interpolating function is minimal (with natural boundary conditions). Firstly, bi-cubic polynomial natural spline interpolations with four kinds of boundary conditions are studied. By the spline function methods of Hilbert space, their solutions are constructed as the sum of bi-linear polynomials and piecewise bi-cubic polynomials. Some properties of the solutions are also studied. In fact, bi-cubic natural spline interpolation on a rectangular domain is a generalization of the cubic natural spline interpolation on an interval. Secondly, based on bi-cubic polynomial natural spline interpolations of four kinds of boundary conditions, and using partition of unity technique, a Partition of Unity Interpolation Element Method (PUIEM) for fitting scattered data is proposed. Numerical experiments show that the PUIEM is adaptive and outperforms state-of-the-art competitions, such as the thin plate spline interpolation and the bi-cubic polynomial natural spline interpolations for scattered data.

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8

LAC, ETIENNE, ARNAUD MOREL, and DOMINIQUE BARTHÈS-BIESEL. "Hydrodynamic interaction between two identical capsules in simple shear flow." Journal of Fluid Mechanics 573 (February 2007): 149–69. http://dx.doi.org/10.1017/s0022112006003739.

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We present a numerical model of the hydrodynamic interactions between two capsules freely suspended in a simple shear flow. The capsules are identical and each consists of a liquid droplet enclosed by a thin hyperelastic membrane, devoid of bending resistance and obeying a neo-Hookean constitutive law. The two capsules are slightly prestressed with a given inflation ratio in order to avoid the small deformation instability due to compression observed for a single capsule in simple shear flow. The viscosity ratio between the interior and exterior fluids of the capsule is taken to be unity and creeping flow conditions are assumed to prevail. The boundary-element method is used with bi-cubic B-splines as basis functions on a structured mesh in order to discretize the capsule surface. A new method using two grids with initially orthogonal pole axes is developed to eliminate polar singularities in the load calculation and to allow for long computation times. Two capsules suspended in simple shear flow usually have different velocities and thus eventually pass each other. We study this crossing process as a function of flow strength and initial particle separation. We find that hydrodynamic interactions during crossing lead to large shape alterations, elevated elastic tensions in the membrane and result in an irreversible trajectory shift of the capsules. Furthermore, a tendency towards buckling is observed, particularly during the separation phase where large pressure differences occur. Our results are in qualitative agreement with those obtained for a pair of interacting liquid droplets but show the specific role played by the membrane of capsules.

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9

Rohila, Rajni, and R. C. Mittal. "An efficient Bi-cubic B-spline ADI method for numerical solutions of two-dimensional unsteady advection diffusion equations." International Journal of Numerical Methods for Heat & Fluid Flow 28, no. 11 (2018): 2620–49. http://dx.doi.org/10.1108/hff-12-2017-0511.

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Purpose This paper aims to develop a novel numerical method based on bi-cubic B-spline functions and alternating direction (ADI) scheme to study numerical solutions of advection diffusion equation. The method captures important properties in the advection of fluids very efficiently. C.P.U. time has been shown to be very less as compared with other numerical schemes. Problems of great practical importance have been simulated through the proposed numerical scheme to test the efficiency and applicability of method. Design/methodology/approach A bi-cubic B-spline ADI method has been proposed to capture many complex properties in the advection of fluids. Findings Bi-cubic B-spline ADI technique to investigate numerical solutions of partial differential equations has been studied. Presented numerical procedure has been applied to important two-dimensional advection diffusion equations. Computed results are efficient and reliable, have been depicted by graphs and several contour forms and confirm the accuracy of the applied technique. Stability analysis has been performed by von Neumann method and the proposed method is shown to satisfy stability criteria unconditionally. In future, the authors aim to extend this study by applying more complex partial differential equations. Though the structure of the method seems to be little complex, the method has the advantage of using small processing time. Consequently, the method may be used to find solutions at higher time levels also. Originality/value ADI technique has never been applied with bi-cubic B-spline functions for numerical solutions of partial differential equations.

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10

Abbas, Muhammad, Ahmad Abd Majid, Mohd Nain Hj Awang, and Jamaludin Md Ali. "Monotonicity-preserving rational bi-cubic spline surface interpolation." ScienceAsia 40S, no. 1 (2014): 22. http://dx.doi.org/10.2306/scienceasia1513-1874.2014.40s.022.

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Abbas, Muhammad, Ahmad Abd Majid, Mohd Nain Hj Awang, and Jamaludin Md Ali. "Convex data modelling using rational bi-cubic spline function." ScienceAsia 40S, no. 1 (2014): 31. http://dx.doi.org/10.2306/scienceasia1513-1874.2014.40s.031.

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Mittal, R. C., and Amit Tripathi. "Numerical solutions of two-dimensional Burgers’ equations using modified Bi-cubic B-spline finite elements." Engineering Computations 32, no. 5 (2015): 1275–306. http://dx.doi.org/10.1108/ec-04-2014-0067.

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Purpose – The purpose of this paper is to develop an efficient numerical scheme for non-linear two-dimensional (2D) parabolic partial differential equations using modified bi-cubic B-spline functions. As a test case, method has been applied successfully to 2D Burgers equations. Design/methodology/approach – The scheme is based on collocation of modified bi-cubic B-Spline functions. The authors used these functions for space variable and for its derivatives. Collocation form of the partial differential equation results into system of first-order ordinary differential equations (ODEs). The obtained system of ODEs has been solved by strong stability preserving Runge-Kutta method. The computational complexity of the method is O(p log(p)), where p denotes total number of mesh points. Findings – Obtained numerical solutions are better than those available in literature. Ease of implementation and very small size of computational work are two major advantages of the present method. Moreover, this method provides approximate solutions not only at the grid points but also at any point in the solution domain. Originality/value – First time, modified bi-cubic B-spline functions have been applied to non-linear 2D parabolic partial differential equations. Efficiency of the proposed method has been confirmed with numerical experiments. The authors conclude that the method provides convergent approximations and handles the equations very well in different cases.

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13

Taghipour, M., and H. Aminikhah. "A B-Spline Quasi Interpolation Crank–Nicolson Scheme for Solving the Coupled Burgers Equations with the Caputo–Fabrizio Derivative." Mathematical Problems in Engineering 2021 (January 22, 2021): 1–14. http://dx.doi.org/10.1155/2021/8837846.

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In this paper, a Crank–Nicolson finite difference scheme based on cubic B-spline quasi-interpolation has been derived for the solution of the coupled Burgers equations with the Caputo–Fabrizio derivative. The first- and second-order spatial derivatives have been approximated by first and second derivatives of the cubic B-spline quasi-interpolation. The discrete scheme obtained in this way constitutes a system of algebraic equations associated with a bi-pentadiagonal matrix. We show that the proposed scheme is unconditionally stable. Numerical examples are provided to verify the efficiency of the method.

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14

Amiri-Simkooei, A. R., M. Hosseini-Asl, and A. Safari. "Least squares 2D bi-cubic spline approximation: Theory and applications." Measurement 127 (October 2018): 366–78. http://dx.doi.org/10.1016/j.measurement.2018.06.005.

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15

Jin, Yong Qiao, Yu Han Wang, and Jian Guo Yang. "Real-Time B-Spline Interpolator with Look-Ahead Scheme for High-Speed CNC Machine Tools." Key Engineering Materials 455 (December 2010): 599–605. http://dx.doi.org/10.4028/www.scientific.net/kem.455.599.

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NC tool paths of digital CAD models are currently generated as a set of discrete data points. The CNC interpolator must convert these points into continuous machine tool axis motions. In order to achieve high-speed and high-accuracy machining, the development of a real-time interpolation algorithm is really indispensable, which can deal with a large number of short blocks and still maintain smooth interpolation with an optimal speed. In this paper, a real-time local cubic B-spline interpolator with look-ahead scheme is proposed for consecutive micro-line blocks interpolation. First, the consecutive micro-line blocks that satisfy the bi-chord error constraints are fitted into a C1 continuous cubic B-spline curve. Second, machining dynamics and tool path contour constrains are taken into consideration. Third, local cubic B-spline interpolator with an optimal look-ahead scheme is proposed to generate the optimal speed profile. Simulation and experiment are performed in real-time environment to verify the effectiveness of the proposed method. Compared with the conventional interpolation algorithm, the proposed algorithm reduces the machining time by 70%.

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Li, Zhong, Li-zhuang Ma, Wu-zheng Tan, and Ming-xi Zhao. "Reconstruction from contour lines based on bi-cubic Bézier spline surface." Journal of Zhejiang University-SCIENCE A 7, no. 7 (2006): 1241–46. http://dx.doi.org/10.1631/jzus.2006.a1241.

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Abbas, Muhammad, Ahmad Abd Majid, and Jamaludin Md Ali. "Positivity-preserving rational bi-cubic spline interpolation for 3D positive data." Applied Mathematics and Computation 234 (May 2014): 460–76. http://dx.doi.org/10.1016/j.amc.2014.02.031.

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Abdul Karim, Samsul Ariffin, Azizan Saaban, and Vaclav Skala. "Range-Restricted Surface Interpolation Using Rational Bi-Cubic Spline Functions With 12 Parameters." IEEE Access 7 (2019): 104992–5007. http://dx.doi.org/10.1109/access.2019.2931454.

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19

Zhou, Shifei, Hao Wang, Jerome Yen, and Kin Keung Lai. "Bi-cubic B-spline fitting-based local volatility model with mean reversion process." Journal of Systems Science and Complexity 29, no. 1 (2016): 119–32. http://dx.doi.org/10.1007/s11424-015-3066-8.

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20

Zhang, De Qiang, Li Ying Su, Jie Cheng, and Yong Qi Su. "Research on Mold’s Reverse Modeling and Basic Surface Repair." Advanced Materials Research 299-300 (July 2011): 992–96. http://dx.doi.org/10.4028/www.scientific.net/amr.299-300.992.

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Reverse engineering is used to obtain mold’s numerical point cloud. The key is to get mold’s defective area and boundary’s features information. Then its original model of mold’s defective parts is built, and combined with bi-cubic B-spline to control vertex, the abutting of curves and surfaces, and value iteration technologies for integrate modeling of defect molds.Using finite element analysis and multiple technologies to analyze and amend, the model is repeated revised until a mold’s complete model is obtained.

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Aaslid, Per, Frederik Geth, Magnus Korpås, Michael M. Belsnes, and Olav B. Fosso. "Non-linear charge-based battery storage optimization model with bi-variate cubic spline constraints." Journal of Energy Storage 32 (December 2020): 101979. http://dx.doi.org/10.1016/j.est.2020.101979.

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22

Luo, Yuan, and Yuan Liu. "A Fast Interpolation Algorithm Based on the Fractal in the Digital Speckle Sub-Pixel Displacement Measurement." Applied Mechanics and Materials 344 (July 2013): 238–41. http://dx.doi.org/10.4028/www.scientific.net/amm.344.238.

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The Digital Speckle Correlation Method is a non-contact in-plane displacement measurement method based on machine vision. The spline, the linear or the bi-cubic interpolation algorithm is often used in the sub-pixel algorithm. The block effect or the edges blurring, however, could occur in these algorithms. Therefore, a fast interpolation algorithm based on fractal theory is proposed in this paper. The results indicate that this algorithm can overcome either the blocking effect or the edge blurring caused by the traditional interpolation algorithm. In addition, with the same sub-pixel accuracy, the shortest time is required.

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Singh, Suruchi, and Swarn Singh. "High order convergent modified nodal bi‐cubic spline collocation method for elliptic partial differential equation." Numerical Methods for Partial Differential Equations 36, no. 5 (2020): 1028–43. http://dx.doi.org/10.1002/num.22463.

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Li, Xiao Da, and Xiang Hui Zhan. "A Method of Die Surface Compensation after Spring Back Prediction in Sheet Metal Forming." Applied Mechanics and Materials 313-314 (March 2013): 157–63. http://dx.doi.org/10.4028/www.scientific.net/amm.313-314.157.

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Spring back in the process of sheet metal forming leads to deviations between design sizes and actual dimensions of stamping parts, to meet the precision requirements of deviations, the shape of die surface needs to be compensated in the opposite direction according to the predicted spring back by numerical simulation. In this article, the R S coordinate mapping method is used to revise coordinates of finite element nodes according to the predicted spring back, and the bi-cubic B spline surface interpolation method is applied to reconstruct die surface with CAD data format. An example shows that the algorithms are feasible and have some practical values.

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Arora, Rajni, Swarn Singh, and Suruchi Singh. "Numerical solution of second-order two-dimensional hyperbolic equation by bi-cubic B-spline collocation method." Mathematical Sciences 14, no. 3 (2020): 201–13. http://dx.doi.org/10.1007/s40096-020-00331-y.

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Ковтун, Александр Михайлович. "Exploration of describing the vector-parametric bi-spline, defined by the cubic spline with control points incident with surface of appropriate smoothness." Technology audit and production reserves 3, no. 1(23) (2015): 69. http://dx.doi.org/10.15587/2312-8372.2015.44416.

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Zhu, Zhongxia, Edgar Janunts, Timo Eppig, Tomas Sauer, and Achim Langenbucher. "Iteratively re-weighted bi-cubic spline representation of corneal topography and its comparison to the standard methods." Zeitschrift für Medizinische Physik 20, no. 4 (2010): 287–98. http://dx.doi.org/10.1016/j.zemedi.2010.07.002.

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Gardner, L. R. T., and G. A. Gardner. "A two dimensional bi-cubic B-spline finite element: used in a study of MHD-duct flow." Computer Methods in Applied Mechanics and Engineering 124, no. 4 (1995): 365–75. http://dx.doi.org/10.1016/0045-7825(94)00760-k.

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Liu, Jian Ping, Bang Yan Ye, and Jian Xi Peng. "3D Reconstruction from Orthographic Image and Optimization Processing of NC Machining for Reconstructed Part." Key Engineering Materials 392-394 (October 2008): 619–23. http://dx.doi.org/10.4028/www.scientific.net/kem.392-394.619.

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For inverse constructing object from its orthographic image, a new method of 3D reconstruction based on image vectorization and bi-arc approximation of cubic B-spline is investigated. A 3D CAD model is automatically acquired from 2D views by means of 2D primitive recognition, 3D reconstruction of primitive and combination of 3D primitive bodies. With the help of CimatronE8.0 software, reasonable procedure design and optimization toolpath planning are applied to increase machining accuracy and productivity during automatic programming for reconstructed 3D solid. Reconstructed parts are machined on the VMC-600 type machine center with FANUC system. The results of application indicate that this method has many advantages, such as quickly obtaining the CAD model of part, getting smooth machined surface, efficient machining without invalid or reduplicate feed and so on. As a result, it can be applied widely in NC machining field.

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Xu, Y., B. Liu, J. Liu, and S. Riemenschneider. "Two-dimensional empirical mode decomposition by finite elements." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 462, no. 2074 (2006): 3081–96. http://dx.doi.org/10.1098/rspa.2006.1700.

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Empirical mode decomposition (EMD) is a powerful tool for analysis of non-stationary and nonlinear signals, and has drawn significant attention in various engineering application areas. This paper presents a finite element-based EMD method for two-dimensional data analysis. Specifically, we represent the local mean surface of the data, a key step in EMD, as a linear combination of a set of two-dimensional linear basis functions smoothed with bi-cubic spline interpolation. The coefficients of the basis functions in the linear combination are obtained from the local extrema of the data using a generalized low-pass filter. By taking advantage of the principle of finite-element analysis, we develop a fast algorithm for implementation of the EMD. The proposed method provides an effective approach to overcome several challenging difficulties in extending the original one-dimensional EMD to the two-dimensional EMD. Numerical experiments using both simulated and practical texture images show that the proposed method works well.

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Suzuki, Sho, R. U. Gobithaasan, Péter Salvi, Shin Usuki, and Kenjiro T. Miura. "Minimum variation log-aesthetic surfaces and their applications for smoothing free-form shapes." Journal of Computational Design and Engineering 5, no. 2 (2017): 243–48. http://dx.doi.org/10.1016/j.jcde.2017.08.003.

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Abstract The log-aesthetic curve, which includes the logarithmic (equiangular) spiral, clothoid, and involute of a circle, achieves a control over curvature distribution by defining its shape as an integral form of its curvature and they are expected to be utilized for the field of design. However, it is very difficult to extend it to surfaces and the existing formulations have some problems that they cannot use arbitrary boundary curves. In this paper, we propose “minimum variation log-aesthetic surface” as a new formulation for the log-aesthetic surface. Based on variational principle our method can generate surfaces by minimizing the objective function newly proposed in this paper for given arbitrary boundary curves. Highlights We propose a “minimum variation log-aesthetic surface” as a new formulation of log-aesthetic surface. We derived a new objective function based on variational principle and our method can generate surfaces by minimizing the objective function. We generate bi-cubic B-spline surfaces by minimizing the new objective function. Numerical examples indicate that it can be used for practical aesthetic design.

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Upadhaya, Brijesh, Floran Martin, Paavo Rasilo, Paul Handgruber, Anouar Belahcen, and Antero Arkkio. "Modelling anisotropy in non-oriented electrical steel sheet using vector Jiles–Atherton model." COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 36, no. 3 (2017): 764–73. http://dx.doi.org/10.1108/compel-09-2016-0399.

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Purpose Non-oriented electrical steel presents anisotropic behaviour. Modelling such anisotropic behaviour has become a necessity for accurate design of electrical machines. The main aim of this study is to model the magnetic anisotropy in the non-oriented electrical steel sheet of grade M400-50A using a phenomenological hysteresis model. Design/methodology/approach The well-known phenomenological vector Jiles–Atherton hysteresis model is modified to correctly model the typical anisotropic behaviour of the non-oriented electrical steel sheet, which is not described correctly by the original vector Jiles–Atherton model. The modification to the vector model is implemented through the anhysteretic magnetization. Instead of the commonly used classical Langevin function, the authors introduced 2D bi-cubic spline to represent the anhysteretic magnetization for modelling the magnetic anisotropy. Findings The proposed model is found to yield good agreement with the measurement data. Comparisons are done between the original vector model and the proposed model. Another comparison is also made between the results obtained considering two different modifications to the anhysteretic magnetization. Originality/value The paper presents an original method to model the anhysteretic magnetization based on projections of the anhysteretic magnetization in the principal axis, and apply such modification to the vector Jiles–Atherton model to account for the magnetic anisotropy. The replacement of the classical Langevin function with the spline resulted in better fitting. The proposed model could be used in the numerical analysis of magnetic field in an electrical application.

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Mittal, Sanjay, Varun Bhatt, and D. N. Srinath. "Aerodynamic shape optimization using stabilized finite element method." Mathematical Models and Methods in Applied Sciences 25, no. 12 (2015): 2319–48. http://dx.doi.org/10.1142/s0218202515400102.

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An algorithm for aerodynamic shape optimization using a gradient-based approach is presented. A stabilized finite element method is utilized to solve the equations governing the fluid flow and adjoint variables. The effectiveness of the method in finding nontrivial designs that satisfy the posed objectives and constraints is demonstrated. It is shown that the initial guess plays an important role in the optimal solution that is realized. Shapes of bumps that are associated with a specified volume, lift and drag are determined and presented. The method is applied to design of airfoils in unsteady flows. The objective function is based on time-averaged force coefficients. The effect of enriching the design space is studied. It is shown that this being a local method, where the search direction is based on gradient of the objective function, the gradual enrichment of design space leads to superior performance. The idea is demonstrated via spontaneous appearance of corrugations on an airfoil surface during the optimization, for maximum lift, by gradually increasing the number of control points. The method is extended to three dimensions. Its application is demonstrated via optimization of the planform of a finite wing for maximum lift-to-drag ratio. A bi-parametric tensorial NURBS (non-uniform rational bi-cubic spline) surface is interpolated on a 3D control net to represent a wing surface. It is shown that for low Reynolds number, it is possible to design a planform that is more efficient than an ellipse. Unlike the elliptic planform, the optimal wing computed by the present method, is associated with a short winglet-like structure at the wing-tip and the maximum chord length at around mid-span.

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Choi, Boo-Kyeong, Nuwan Madusanka, Heung-Kook Choi, et al. "Convolutional Neural Network-based MR Image Analysis for Alzheimer’s Disease Classification." Current Medical Imaging Formerly Current Medical Imaging Reviews 16, no. 1 (2020): 27–35. http://dx.doi.org/10.2174/1573405615666191021123854.

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Background: In this study, we used a convolutional neural network (CNN) to classify Alzheimer’s disease (AD), mild cognitive impairment (MCI), and normal control (NC) subjects based on images of the hippocampus region extracted from magnetic resonance (MR) images of the brain. Materials and Methods: The datasets used in this study were obtained from the Alzheimer's Disease Neuroimaging Initiative (ADNI). To segment the hippocampal region automatically, the patient brain MR images were matched to the International Consortium for Brain Mapping template (ICBM) using 3D-Slicer software. Using prior knowledge and anatomical annotation label information, the hippocampal region was automatically extracted from the brain MR images. Results: The area of the hippocampus in each image was preprocessed using local entropy minimization with a bi-cubic spline model (LEMS) by an inhomogeneity intensity correction method. To train the CNN model, we separated the dataset into three groups, namely AD/NC, AD/MCI, and MCI/NC. The prediction model achieved an accuracy of 92.3% for AD/NC, 85.6% for AD/MCI, and 78.1% for MCI/NC. Conclusion: The results of this study were compared to those of previous studies, and summarized and analyzed to facilitate more flexible analyses based on additional experiments. The classification accuracy obtained by the proposed method is highly accurate. These findings suggest that this approach is efficient and may be a promising strategy to obtain good AD, MCI and NC classification performance using small patch images of hippocampus instead of whole slide images.

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Zhang, Y., F. L. Litvin, N. Maruyama, R. Takeda, and M. Sugimoto. "Computerized Analysis of Meshing and Contact of Gear Real Tooth Surfaces." Journal of Mechanical Design 116, no. 3 (1994): 677–82. http://dx.doi.org/10.1115/1.2919435.

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The authors propose a technique for computerized simulation and tangency of gears provided with real tooth surfaces. The deviations of real tooth surfaces from the theoretical ones are caused by the distortion of surfaces during the heat treatment and lapping. The main ideas of the proposed technique are as follows: (i) The gear real tooth surface is represented by a sum of two vector functions that determine the theoretical tooth surface and the deviations of the real surface from the theoretical one, respectively. (ii) Both vector functions mentioned above are represented in terms of the same Gaussian surface coordinates (the Gaussian coordinates of the theoretical surface). (iii) The deviations of the real surface are initially determined numerically using the data of surface coordinate measurements. The analytical representation of the vector function of deviations is based on the interpolation of a numerically given vector function by a bi-cubic spline. The interpolation provides a relatively high precision because it is accomplished for the surface of small deviations but not for the whole real surface. (iv) The computerized simulation of meshing and tangency of gears with real tooth surfaces is based on the algorithm that describes the conditions of continuous tangency of real tooth surfaces. The proposed approach is illustrated with application to the hypoid gear drive with real tooth surfaces. The data of surface deviations have been determined experimentally at the Nissan Motor Co.

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36

Quraishi, Sarosh. "New bi-cubic spline wavelet based thin plate finite elements." International Journal for Multiscale Computational Engineering, 2014. http://dx.doi.org/10.1615/intjmultcompeng.2014002616.

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Micula, Sanda, and Ioan Pop. "Free convection inside a porous square cavity with convective boundary condition using spline functions." Boundary Value Problems 2021, no. 1 (2021). http://dx.doi.org/10.1186/s13661-021-01533-6.

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AbstractIn this paper, we consider the problem of free convection in a square cavity filled with a porous medium with convective boundary condition on the left wall of the cavity. We first transform the governing equations transformed in terms of dimensionless variables and then solve them numerically using a cubic spline colocation method. We discuss the effects of two very important parameters, the Biot (Bi) and Rayleigh (Ra) numbers. We perform a comparison of the average Nusselt number $\overline{Nu}$ N u ‾ at the hot wall with results from the open literature. We can notice that the comparison is very good, which gives us strong confidence that this cubic spline collocation method works very efficiently for such problems. We also state that the present problem has not been considered before by any researcher.

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Mariana, DRIÅžCU. "CREATING THE SPATIAL FORM OF THE SHOE LAST WITH 3D BI-CUBIC SURFACES LIKE B-SPLINE FUNCTION." ANNALS OF THE ORADEA UNIVERSITY. Fascicle of Management and Technological Engineering. XIX (IX), 2010/2, no. 2 (2010). http://dx.doi.org/10.15660/auofmte.2010-2.1957.

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Xu, Da. "Observability Inequalities for Hermite Bi-cubic Orthogonal Spline Collocation Methods of 2-D Integro-differential Equations in the Square Domains." Applied Mathematics & Optimization, April 27, 2020. http://dx.doi.org/10.1007/s00245-020-09680-5.

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Yuan, Yuan, Bo Zhou, Shunan Wang, et al. "Adult Body Height and Cardiometabolic Disease Risk: The China National Health Survey in Shaanxi." Frontiers in Endocrinology 11 (December 21, 2020). http://dx.doi.org/10.3389/fendo.2020.587616.

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ObjectivesBased on data from the China National Health Survey, we aimed to examine the association between body height and cardiometabolic disease (CMD) in a large adult population from Shaanxi province, and further to test whether this association was hinged upon other population characteristics.MethodsThis population-based study was conducted in 2014 in Shaanxi Province, China. Utilizing a multi-stage stratified cluster sampling method, total 5,905 adults with complete data were eligible for analysis, and 1,151 (19.5%) of them had CMD. Of 1,151 CMD patients, 895 (15.1%) had one disorder and 256 (4.4%) had ≥2 disorders.ResultsUsing the bi-directional stepwise method and all-subsets regression, five factors—age, body mass index, family histories of CMD, exercise, and height—constituted the optimal model when predicting CMD risk. Restricted cubic spline regression showed a reduced tendency towards CMD with the increase of body height, with per 10 cm increment in body height corresponding to 14% reduced risk. Ordinal Logistic regression supported the contribution of body height on both continuous and categorical scales to CMD risk before and after adjustment, yet this contribution was significantly confounded by exercise and education, especially by exercise, which can explain 65.4% of total impact. For example, short stature was associated with an increased risk of CMD after multivariable adjustment not including exercise and education (odds ratio, 95% confidence interval, P: 1.42, 1.21 to 1.66, &lt;0.001), and tall stature was associated with a reduced risk (0.77, 0.64 to 0.92, 0.003).ConclusionsOur findings indicate short stature was a risk factor, yet tall stature was a protective factor for CMD in Chinese. Notably, the prediction of short and tall stature for CMD may be mediate in part by exercise.

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