• Title/Summary/Keyword: cubic B-spline

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EIGENVALUE ANALYSIS USING PIECEWISE CUBIC B-SPLINE (CUBIC B-SPLINE을 이용한 고유치 해석)

  • Kim Young-Moon
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • 2000.10a
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    • pp.355-360
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    • 2000
  • This paper presents properties of piecewise cubic B-spline function and Rayleigh-Ritz method to compute the smallest eigenvales. In order to compute the smallest eigenvalues, Rayleigh quotient approach is used and four different types of finite element approximating functions corresponding to the statical deflection curve, spanned by the linearly independent set of piecewise cubic B-spline functions with equally spaced 5 knots from a partion of [0, 1], each satisfying homogeneous boundary conditions with constraining effects are used to compute the smallest eigenvalues for a Sturm-Lionville boundary equations of u"+ λ²u=0, u(0.0)=u(0.0)=0, 0≤x≤1.0.

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Analysis for computing heat conduction and fluid problems using cubic B-spline function (3차 B-spline 함수를 이용한 열전도 및 유체문제의 해석)

  • Kim, Eun-Pil
    • Journal of computational fluids engineering
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    • v.3 no.2
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    • pp.1-8
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    • 1998
  • We make use of cubic B-spline interpolation function in two cases: heat conduction and fluid flow problems. Cubic B-spline test function is employed because it is superior to approximation of linear and non-linear problems. We investigated the accuracy of the numerical formulation and focused on the position of the breakpoints within the computational domain. When the domain is divided by partitions of equal space, the results show poor accuracy. For the case of a heat conduction problem this partition can not reflect the temperature gradient which is rapidly changed near the wall. To correct the problem, we have more grid points near the wall or the region which has a rapid change of variables. When we applied the unequally spaced breakpoints, the results show high accuracy. Based on the comparison of the linear problem, we extended to the highly non-linear fluid flow problems.

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EXPLICIT ERROR BOUND FOR QUADRATIC SPLINE APPROXIMATION OF CUBIC SPLINE

  • Kim, Yeon-Soo;Ahn, Young-Joon
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.13 no.4
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    • pp.257-265
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    • 2009
  • In this paper we find an explicit form of upper bound of Hausdorff distance between given cubic spline curve and its quadratic spline approximation. As an application the approximation of offset curve of cubic spline curve is presented using our explicit error analysis. The offset curve of quadratic spline curve is exact rational spline curve of degree six, which is also an approximation of the offset curve of cubic spline curve.

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ON THE CONSTRUCTION AND THE EXISTENCE OF PARAMETRIC CUBIC$g^2$ B-SPLINE

  • Kimn, Ha-Jine
    • Communications of the Korean Mathematical Society
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    • v.10 no.2
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    • pp.483-490
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    • 1995
  • A parametric cubic spline interpolating at fixed number of nodes is constructed by formulating a parametric cubic $g^2$ B-splines $S_3(t)$ with not equally spaced parametric knots. Since the fact that each component is in $C^2$ class is not enough to provide the geometric smoothness of parametric curves, the existence of $S_3(t)$ oriented toward the modified second-order geometric continuity is focalized in our work.

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A Study on the Pit Excavation Volume Using Cubic B-Spline

  • Mun, Du-Yeoul
    • International Journal of Ocean Engineering and Technology Speciallssue:Selected Papers
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    • v.5 no.1
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    • pp.40-45
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    • 2002
  • The calculation of earthwork plays a major role in the planning and design phases of many civil engineering projects, such as seashore reclamation; thus, improving the accuracy of earthwork calculation has become very important. In this paper, we propose an algorithm for finding a cubic spline surface with the free boundary conditions, which interpolates the given three-dimensional data, by using B-spline and an accurate method to estimate pit-excavation volume. The proposed method should be of interest to surveyors, especially those concerned with accuracy of volume computations. The mathematical models of the conventional methods have a common drawback: the modeling curves form peak points at the joints. To avoid this drawback, the cubic spline polynomial is chosen as the mathematical model of the new method. In this paper, we propose an algorithm of finding a spline surface, which interpolates the given data, and an appropriate method to calculate the earthwork. We present some computational results that show the proposed method, of the Maple program, provides better accuracy than the method presented by Chen and Lin.

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A Study of Geometric Modeling for Ship Hull Forms Using Open Uniform B-spline Surface (Open 균일 B-spline 곡면을 이용한 선체 곡면 표현에 관한 연구)

  • H.K. Shin;K.W. Park
    • Journal of the Society of Naval Architects of Korea
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    • v.28 no.2
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    • pp.21-27
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    • 1991
  • This paper outlines the method of formulating the bi-cubic B-spline surface of ship hull, employing the open uniform knot vector as well as the periodic uniform knot vector. An appropriate set of B-spline control vertices to generate the B-spline surface is determined by obtaining the pseudoinverse matrix of basis functions. The comparison between the given offsets and the resulting coordinates from the generated ship hull surface shows a good agreement. To check the fairness of the surface Gaussian curvature is calculated on many small subpatches and displayed on the black-and-white plot of the isoparametric net of the surface.

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Interpolator Design for Cubic Parallel Manipulator (육면형 병렬공작기계의 보간기 설계)

  • Kim, H.;Hong, D.;Choi, W. C.;Song, J.-B.
    • Proceedings of the Korean Society of Precision Engineering Conference
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    • 2001.04a
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    • pp.492-495
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    • 2001
  • In order to utilize a parallel machine tool for CAM system, the development of adequate interpolator is necessary. This paper presents a quintic B-spline interpolator with algorithm of limiting maximum interpolation error. The favored property of near arc-length parametrization in the curve representation is used in the implementation of the reference command generation. Then, this interpolator is applied to cubic parallel manipulator to show its validity.

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CUBIC B-SPLINE FINITE ELEMENT METHOD FOR THE ROSENAU-BURGERS EQUATION

  • Xu, Ge-Xing;Li, Chun-Hua;Piao, Guang-Ri
    • East Asian mathematical journal
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    • v.33 no.1
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    • pp.53-65
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    • 2017
  • Numerical solutions of the Rosenau-Burgers equation based on the cubic B-spline finite element method are introduced. The backward Euler method is used for discretization in time, and the obtained nonlinear algebraic system is changed to a linear system by the Newton's method. We show that those methods are unconditionally stable. Two test problems are studied to demonstrate the accuracy of the proposed method. The computational results indicate that numerical solutions are in good agreement with exact solutions.

A Study on Development of an Algorithm for Vertex Creation to Define Ship Hull Forms (선체형상 정의를 위한 버텍스 산출 알고리즘 개발에 관한 연구)

  • Hyun-Kyoung Shin;Sang-Sung Shin;Kyu-Won Park
    • Journal of the Society of Naval Architects of Korea
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    • v.31 no.3
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    • pp.31-37
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    • 1994
  • When a lot of input data are not distributed uniformly n a chord-span direction or when the given shape is complicated, it is very difficult to obtain an inverse matrix which represents the smooth Bi-cubic B-spline surface of the initial shape. To overcome this problem, we suggest image Surface Expansion Method(ISE Method) which is suggested for vertex creation of B-spline curves and surfaces. Its basic concept, convergency and verification are shown. Also B-spline curves and Surfaces represented by ISE Method were compared with those represented by the existing method which is based on the inverse matrix method, the pseudoinverse matrix method and the chord length approximation method for vertex yielding. Ship Hull Forms which have Knuckle, Bulbous Bow, Transom and Stern frame were represented by the ISE Method.

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Comparison of Channel Estimation Schemes for Digital Broadcasting System in a Mobile Environment (이동 환경에서 디지털 방송 시스템을 위한 채널 추정 기법의 성능 비교)

  • Kim, Ki-Nam;Kim, Jin-Ho;Cho, Sung-Joon
    • Journal of Advanced Navigation Technology
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    • v.9 no.1
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    • pp.41-47
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    • 2005
  • In this paper, the performances of various channel estimation schemes for DVB-H system are investigated. The linear interpolation, the second order interpolation, the cubic spline interpolation, and the time-domain interpolation, which are used in frequency domain, are chosen as the channel estimation schemes. We derived the performances of Mean Square Error (MSE), Bit Error Rate (BER), and the complexity of calculation in Rayleigh and Rician fading channel through computer simulations. From the simulation results, the cubic spline interpolation shows the best performance under high $E_b/N_0$ environments.

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