• Journal of applied mathematics & informatics
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• v.6 no.1
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• pp.203-216
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• 1999

In this paper a rational cubic interpolant spline with linear denominator has been constructed and it is used to constrain interpolation curves to be bounded in the given region. Necessary and sufficient conditions for the interpolant to satisfy the constraint have been developed. The existence conditions are computationally efficient and easy to apply. Finally the approximation properties have been studied.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.34 no.2
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• pp.191-201
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• 2010

This paper presents a new global optimization algorithm based on the branch-and-bound principle using Bspline approximation techniques. It describes the algorithmic components and details on their implementation. The key components include the subdivision of a design space into mutually disjoint subspaces and the bound calculation of the subspaces, which are all established by a real-valued B-spline volume model. The proposed approach was demonstrated with various test problems to reveal computational performances such as the solution accuracy, number of function evaluations, running time, memory usage, and algorithm convergence. The results showed that the proposed algorithm is complete without using heuristics and has a good possibility for application in large-scale NP-hard optimization.

• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.713-719
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• 2011

The problem of approximation from a set of scattered data arises in a wide range of applied mathematics and scientific applications. In this study, we present a quasi-interpolatory approximation scheme for scattered data approximation problem, which reproduces a certain space of polynomials. The proposed scheme is local in the sense that for an evaluation point, the contribution of a data value to the approximating value is decreasing rapidly as the distance between two data points is increasing.

• Journal of Computational Design and Engineering
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• v.2 no.4
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• pp.218-232
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• 2015

Piecewise linear (G01-based) tool paths generated by CAM systems lack $G_1$ and $G_2$ continuity. The discontinuity causes vibration and unnecessary hesitation during machining. To ensure efficient high-speed machining, a method to improve the continuity of the tool paths is required, such as B-spline fitting that approximates G01 paths with B-spline curves. Conventional B-spline fitting approaches cannot be directly used for tool path B-spline fitting, because they have shortages such as numerical instability, lack of chord error constraint, and lack of assurance of a usable result. Progressive and Iterative Approximation for Least Squares (LSPIA) is an efficient method for data fitting that solves the numerical instability problem. However, it does not consider chord errors and needs more work to ensure ironclad results for commercial applications. In this paper, we use LSPIA method incorporating Energy term (ELSPIA) to avoid the numerical instability, and lower chord errors by using stretching energy term. We implement several algorithm improvements, including (1) an improved technique for initial control point determination over Dominant Point Method, (2) an algorithm that updates foot point parameters as needed, (3) analysis of the degrees of freedom of control points to insert new control points only when needed, (4) chord error refinement using a similar ELSPIA method with the above enhancements. The proposed approach can generate a shape-preserving B-spline curve. Experiments with data analysis and machining tests are presented for verification of quality and efficiency. Comparisons with other known solutions are included to evaluate the worthiness of the proposed solution.

• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• 2002.04a
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• pp.319-325
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• 2002

Reverse Engineering is to find CAD model through measured data of a physical model which is not available in CAD model. The measured data are obtained from measuring with Coordinate Measuring Machine or Laser Scanner. This paper introduces efficient methods of reconstruction through the applicating process of the Reverse Engineering with technical surfaces.

• Communications of the Korean Institute of Information Scientists and Engineers
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• v.1 no.1
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• pp.72-74
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• 1983

Traditionally, polynomials have been used to approximte functions with prescribed values at a number of points(called the knots) on a given interal on the real line. The method of splines recently developed is more flexible. It approximates a function in a piece-wise fashion, by means of a different polynomial in each subinterval. The cubic spline gas ets origins in beam theory. It possessed continuous first and second deriatives at the knots and is characterised by a minimum curvature property which es rdlated to the physical feature of minimum potential energy of the supported beam. Translated into mathematical terms, this means that between successive knots the approximation yields a third-order polynomial sith its first derivatives continuous at the knots. The minimum curvature property holds good for each subinterval as well as for the whole region of approximation This means that the integral of the square of the second derivative over the entire interval, and also over each subinterval, es to be minimized. Thus, the task of determining the spline lffers itself as a textbook problem in discrete computer programming, since the integral of ghe square of the second derivative can be obviously recognized as the criterion function whicg gas to be minimized. Starting with the initial value of the function and assuming an initial solpe of the curve, the minimum norm property of the curvature makes sequential decision of the slope at successive knots (points) feasible. It is the aim of this paper to derive the cubic spline by the methods of computer programming and show that the results which is computed the all the alues in each subinterval of the spline approximations.

• Proceedings of the Korean Society of Surveying, Geodesy, Photogrammetry, and Cartography Conference
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• 2002.04a
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• pp.229-238
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• 2002

The calculation of earthwork plays a major role in plan or design of many civil engineering projects, and thus it has become very important to improve the accuracy of earthwork calculation. In this paper, we propose an algorithm of 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 concerned with accuracy of volume computations. We present some computational results showing that our proposed method provides good accuracy.

• Journal of the Korean Society for Precision Engineering
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• v.20 no.10
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• pp.156-163
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• 2003

This research presents modeling of a functional surface which is a constructed free-formed surface. The modeling introduced in this paper adopts modified B-spline that is utilizing approximating technique. The modified B-Spline is constructed with altered control vertices. It is applied to measure points on a surface of an impeller blade. This research builds a surface-modeler accepting inputs of measured points. Generation of cutter-paths for NC machining employs the model of the constructed surfaces. The machined surfaces which is generated in several cases are compared in the aspect of machining accuracy.

• Korean Journal of Geomatics
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• v.2 no.1
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• pp.25-29
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• 2002

The calculation of earthwork plays a major role in plan or design of many civil engineering projects, and thus it has become very important to improve the accuracy of earthwork calculation. 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 concerned with accuracy of volume computations. We present some computational results showing that our proposed method provides good accuracy.

• International Journal of Precision Engineering and Manufacturing
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• v.6 no.1
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• pp.15-22
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• 2005

This research presents modeling of a functional surface that is constructed with a free-formed surface. The modeling of functional surfaces, being introduced in this paper, adopts a modified B-spline that utilizes an approximating technique. The modified B-Spline is constructed with altered control vertices. It is applied to measure the surface of an impeller blade. This research builds an algorithm accepting inputs of measured points. Generating the cutter-paths for NC machining employs the model of the constructed surfaces. The machined surfaces that are generated in several cases are compared with each other in the aspect of machining accuracy.