Relevant bibliographies by topics / Bi-cubic Splines

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Academic literature on the topic 'Bi-cubic Splines'

Author: Grafiati
Published: 4 June 2021
Last updated: 9 February 2022

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Journal articles on the topic "Bi-cubic Splines"

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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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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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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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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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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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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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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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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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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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Dissertations / Theses on the topic "Bi-cubic Splines"

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Enge, Leo. "Periodic and Non-Periodic Filter Structures in Lasers." Thesis, KTH, Matematik (Avd.), 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-288181.

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Communication using fiber optics is an integral part of modern societies and one of the most important parts of this is the grating filter of a laser. In this report we introduce both the periodic and the non-periodic grating filter and discuss how there can be resonance in these structures. We then provide an exact method for calculating the spectrum of these grating filters and study three different methods to calculate this approximately. The first one is the \emph{Fourier approximation} which is very simple. For the studied filters the fundamental form of the results for this method is correct, even though the details are not. The second method consists of calculating the spectrum exactly for some values and then use interpolation by splines. This method gives satisfactory results for the types of gratings analysed. Finally a method of perturbation is provided for the periodic grating filter as well as an outline for how this can be extended to the non-periodic grating filter. For the studied filters the results of this method are very promising. The method of perturbations may also give a deeper understanding of how a filter works and we therefore conclude that it would be of interest to study the method of perturbations further, while all the studied methods can be useful for computation of the spectrum depending on the required precision.<br>Fiberoptisk kommunikation utgör en viktig del i moderna samhällen och en av de grudläggande delarna av detta är Bragg-filter i lasrar. I den här rapporten introducerar vi både det periodiska och det icke-periodiska Bragg-filtret och diskuterar hur resonans kan uppstå i dessa. Vi presenterar sedan en exakt metod för att beräkna spektrumet av dessa filter samt studerar tre approximativa metoder för att beräkna spektrumet. Den första metoden är \emph{Fourier-approximationen} som är väldigt enkel. För de studerade filtrena blir de grundläggande formerna korrekta med Fourier-approximationen, medan detaljerna är fel. Den andra metoden består av att räkna ut spektrumet exakt för några punkter och sedan interpolera med hjälp av splines. Den här metoden ger mycket bra resultat för de studerade filtrena. Till sist presenteras en metod baserad på störningsteori för det periodiska filtret, samt en översikt över hur det här kan utökas till det icke-periodiska filtret. Denna metod ger mycket lovande resulat och den kan även ge djupare insikt i hur ett filter fungerar. Vi sluter oss därför till att det vore intressant att vidare studera metoder med störningar, men även att alla studerade metoder kan vara användabara för beräkningen av spektra beroende på vilken precision som krävs.
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Conference papers on the topic "Bi-cubic Splines"

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Vetter, C. "High-voltage field computation using bi-cubic surface splines." In 11th International Symposium on High-Voltage Engineering (ISH 99). IEE, 1999. http://dx.doi.org/10.1049/cp:19990600.

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Park, F. C., and I. G. Kang. "A Cubic Spline Algorithm on the Rotation Group Using Cayley Parameters." In ASME 1996 Design Engineering Technical Conferences and Computers in Engineering Conference. American Society of Mechanical Engineers, 1996. http://dx.doi.org/10.1115/96-detc/dac-1060.

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Abstract This article presents a cubic spline algorithm for interpolation on the rotation group SO(3). Given an ordered set of rotation matrices and knot times, the algorithm generates a twice-differentiable curve on SO(3) that interpolates the given rotation matrices at their specified times. In our approach SO(3) is locally parametrized by the Cayley parameters, and the generated curve is cubic in the sense that the Cayley parameter representation is a cubic polynomial. The resulting algorithm is a computationally efficient way of generating bi-invariant (i.e., invariant with respect to choice of both inertial and body-fixed frames) trajectories on the rotation group that does not require the evaluation of transcendental functions, and can also be viewed as an approximation to a minimum angular acceleration trajectory. Because the Cayley parameters provide a one-to-one correspondence between R3 and a dense set of SO(3), the resulting trajectories do not have the “multiple winding” effect that occurs in several existing methods.
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Zhang, Z. Q., X. Jin, and Z. J. Zhang. "Study on modeling method of the precision machined surface geometry form error based on Bi-cubic B-spline." In 2015 International Conference on Power Electronics and Energy Engineering. Atlantis Press, 2015. http://dx.doi.org/10.2991/peee-15.2015.26.

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Chen, Yih-Jen D. "Smooth Surface Fitting and Finite Element Mesh Generation for Irregularly Distributed Data Points." In ASME 1993 Design Technical Conferences. American Society of Mechanical Engineers, 1993. http://dx.doi.org/10.1115/detc1993-0372.

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Abstract This paper presents two computational methods for geometric modeling of curved surfaces represented by irregularly distributed data points. The study emphasizes irregularly distributed data points since this represents the most general case in geometric data interpretation. The first method is a direct mesh mapping procedure, which projects an relatively regular mesh to the complicated real surface. The second method is a surface fitting technique that reconstructs the mathematical surface model using piecewise bi-cubic parametric functions or B-spline functions. This data reconstruction method uses a normal-distance least-squares concept to generate the best fit. Recursive subdivision algorithm and quad tree data structure are applied to optimize the number of patches needed within the desired precision and thus minimize the computing time in the further processing of the surface model. A computer program based on the two computational methods in surface modeling has been developed and demonstrated by its engineering application. Its development provides an automated tool for design engineers and structure analysts to interpret and model complex surfaces derived from data points.
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