• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제13권4호
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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.

• 한국기계가공학회지
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• 제10권3호
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• pp.33-38
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• 2011

A cubic spline trajectory planner with arc-length parameter is formulated with estimation by summing up to the 3rd order in Taylor's expansion. The PVAJT motion planning is presented to reduce trajectory calculation time at every cycle time of servo control loop so that it is able to generate cubic spline trajectory in real time. This method can be used to more complex spline trajectory. Several case studies are executed with different values of cycle time and sampling time, and showed the advantages of the PVAJT motion planner. A DSP-based motion controller is designed to implement the PVAJT motion planning.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2000년도 가을 학술발표회논문집
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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.

• 대한수학회논문집
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• 제10권2호
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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.

• 대한기계학회논문집
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• 제19권5호
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• pp.1168-1175
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• 1995

The application of cubic spline is presented for basic curve (DRD motion) of cam motion. The purpose of this paper is to achieve better dynamic characteristics than general cam curves. A cubic spline is a piecewise function that is continuous in displacement, velocity and acceleration. The best cam curve is obtained by changing the weights of the object function. So the method can be used to any machine system case by case. For the proposed object function, the result has improved all characteristics such as velocity, acceleration and jerk compared with that of the modified sine curve.

• 한국전산유체공학회지
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• 제3권2호
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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.

• International Journal of Ocean Engineering and Technology Speciallssue:Selected Papers
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• 제5권1호
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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.

• 대한조선학회지
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• 제27권1호
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• pp.3-10
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• 1990

선체형상의 수치적 표현방법에는 선형을 구성하고 있는 일련의 곡선들을 이용하여 선형을 표현하는 curve approach와 선형을 직접 surface로 수식 처리하여 선형을 정의하는 surface approach가 있다. 본 논문에서는 2차원 곡선인 transverse section curve와 3차원 곡선인 longitudinal curve로 구성되는 곡선군들에 의해 형성되는 곡면요소를 수학적으로 처리하여 선체형상을 정의하는 curve approach방법에 대해 기술하였다. 형상 표면에 사용된 곡선 형태는 일반적인 parametric cubic spline을 보완한 modified cubic spline으로서 이 spline형태는 곡선 segment의 양 끝점에서의 접선 각도가 클 경우에도 아주 부드러운 곡률 분포를 얻을 수 있게 하기 때문에 선박 계산뿐만 아니라 유체동역학적 계산을 위한 선형 정의용으로 사용 가능할 정도의 정확성을 가진 기본 설계용 선형정의 결과를 얻을 수 있었다. 응용 예로서 SWATH 선형과 해양 조사선 선형을 표현한 결과를 보였으며, 본 선형 정의 방법을 선형 변환 기법과 연결하여 설계 요구 조건에 적합한 선형을 얻기 위한 선형 변환 예도 보였다.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2004년도 학술대회 논문집 정보 및 제어부문
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• pp.169-171
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• 2004

This paper propose a new detection method of curve lane using Catmull-Rom spline for recognition various shape of the curve lane. To improve the accracy of lane detection, binarization and thinning process are firstly performed on the input image. Next, features on the curve lane such as curvature and orientation are extracted, and the control points of Catmull-Rom spline are detected to recognize the curve lane. Finally, Computer simulation results are given using a natural test image to show the efficiency of the proposed scheme.

• Industrial Engineering and Management Systems
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• 제9권4호
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• pp.323-338
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• 2010

In this paper, we introduce the implied volatility from Black-Scholes model and suggest a model for constructing implied volatility surfaces by using the two-dimensional cubic (bi-cubic) spline. In order to utilize a spline method, we acquire grid (knot) points. To this end, we first extract implied volatility curves weighted by trading contracts from market option data and calculate grid points from the extracted curves. At this time, we consider several conditions to avoid arbitrage opportunity. Then, we establish an implied volatility surface, making use of the two-dimensional cubic spline method with previously estimated grid points. The method is shown to satisfy several properties of the implied volatility surface (smile, skew, and flattening) as well as avoid the arbitrage opportunity caused by simple match with market data. To show the merits of our proposed method, we conduct simulations on market data of S&P500 index European options with reasonable and acceptable results.