• Korean Journal of Computational Design and Engineering
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• v.12 no.1
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• pp.58-73
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• 2007

This paper described a method for the construction of a surface through a set of nonuniform scattered points. When the shift vectors of some points as constraints on the original surface are given, those of the other points should be computed to make the new surface. To keep up the look-see and smoothness with the original surfaces, the proper relationship should be formulated between the shifts of the constraint points and those of the other points. Vector fields for 3 dimensional shift of a point on the surface are made based in the constraint shifts. Vector fields for 3 dimensional shift of a point on the surface are made based on the constraint shifts. Multilevel B-spline approximation technique was used to construct the vector field. The technique uses coarse-to-fine hierarchy of control lattices. The developed method was applied to shoe sole design system especially for grading. Using this system, a shoe sole can be modified effectively.

• International Journal of Control, Automation, and Systems
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• v.5 no.5
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• pp.479-491
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• 2007

This paper presents a new adaptive observer design method for a class of uncertain nonlinear systems by using spline approximation. This scheme leads to a simplified observer structure which requires only fixed number of integrations, regardless of the number of parameters to be estimated. This benefit can reduce the number of integrations of the observer filter dramatically. Moreover, the proposed adaptive observer automatically generates the required spline elements according to the varying output value and, as a result, does not requires the pre-knowledge of upper and lower bounds of the output. This is another benefit of our approach since the requirement for known output bounds have been one of the main drawbacks of practical universal approximation problems. Both of the benefits stem from the local support property, which is specific to splines.

• Journal of the Korea Computer Graphics Society
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• v.22 no.3
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• pp.1-9
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• 2016

Linear interpolation is a basic sampling method for volume visualization. This method generates good images but sometimes it is inferior to our high expectation because it is encouraged to produce high quality images in the medical applications. In this paper, B spline based tri-cubic interpolation is used for the re-sampling step. The conventional B spline is an approximation method which does not cross control points so that we moved the control points and the curve crosses the original control points. In the rendering step, the empty space leaping is applicable to increase rendering speed. We have to calculate the maximum and minimum values for each block to detect empty space. The convex hull property of B spline enables the values of control points to be used as the maximum and minimum values. As a result, tri-cubic interpolated volume rendering is possible in interactive speed.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2002.05a
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• pp.287-292
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• 2002

This paper presents a reverse engineering method for compound surfaces using vision system. A CNC machining center is used as a measuring station, which is equipped with slit beam generator and vision probe. Since obtained data using slit beam or laser scanner may have much data loss along the edge of compound surfaces, an algorithm is presented in this study to recover missing geometric data at such region. First, b-spline interpolation is applied to extract edge information of the surface, and as a next step, b-spline approximation is applied to recover the missing geometric data. Finally, b-spline skinning method is applied to regenerate the surface information. Appropriate simulation and experimental works are preformed to very the effectiveness of the proposed methods.

• Journal of computational fluids engineering
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• v.12 no.3
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• pp.20-28
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• 2007

A fast and robust method of grid generation to multiple functions has been developed for flow analysis in three dimensional space. It is based on the Non-Uniform Rational B-Spline(NURBS) of an approximation method. Many of NURBS intrinsic properties are introduced and much more easily understood. The grid generation method, details of numerical implementation. examples of application, and potential extensions of the current method are illustrated in this paper. The object of this study is to develop the surface grid generation and the grid cluster techniques capable of resolving complex flows with shock waves, expansion waves, shear layers. The knot insert method of Non-Uniform Rational B-Spline seems well worked. In addition, NURBS has been widely utilized to generate grids in the computational fluid dynamics community. Computational examples associated with practical configurations have shown the utilization of the algorithm.

• Nonlinear Functional Analysis and Applications
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• v.27 no.2
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• pp.363-379
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• 2022

In this paper, we carried out a new numerical approach for solving integral algebraic equations with weakly singular kernels. The novel method is based on the construction of B-spline tight framelets using the unitary and oblique extension principles. Some numerical examples are given to provide further explanation and validation of our method. The result of this study introduces a new technique for solving weakly singular integral algebraic equation and thus in turn will contribute to providing new insight into approximation solutions for integral algebraic equation (IAE).

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.10 no.1
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• pp.31-45
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• 2006

Recently advanced device and sophisticated manufacture process by high-density, high-integration require critical inspection criteria in SMT(surface mounting technologies). Especially for solder paste which come out over 60% of inferior goods of all product, 3-dimensional inspection replaces 2-D inspection as a effectiveness substitute of this trend. Therefore this paper proposes a fast 3-D inspection system and measurement algorithm automatically inspecting 3-D solder paste of PCB in SMT assembly line. The proposed method generates 3-D surface of data using B-spline algorithm and then extracts to inspect the pad.

• Structural Engineering and Mechanics
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• v.38 no.2
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• pp.211-229
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• 2011

In this paper, we present a new explicit procedure using periodic cubic B-spline interpolation polynomials to solve linear and nonlinear dynamic equation of motion governing single degree of freedom (SDOF) systems. In the proposed approach, a straightforward formulation was derived from the approximation of displacement with B-spline basis in a fluent manner. In this way, there is no need to use a special pre-starting procedure to commence solving the problem. Actually, this method lies in the case of conditionally stable methods. A simple step-by-step algorithm is implemented and presented to calculate dynamic response of SDOF systems. The validity and effectiveness of the proposed method is demonstrated with four examples. The results were compared with those from the numerical methods such as Duhamel integration, Linear Acceleration and also Exact method. The comparison shows that the proposed method is a fast and simple procedure with trivial computational effort and acceptable accuracy exactly like the Linear Acceleration method. But its power point is that its time consumption is notably less than the Linear Acceleration method especially in the nonlinear analysis.

• Journal of information and communication convergence engineering
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• v.9 no.4
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• pp.424-427
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• 2011

The paper is devoted to problem of spline approximation. A new method of nodes location for curves and surfaces computer construction by means of B-splines, of Reyabenko's splines and results of simulink-modeling is presented. The advantages of this paper is that we comprise the basic spline with classical polynomials both on accuracy, as well as degree of paralleling calculations are also show's.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.33 no.2
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• pp.127-134
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• 2009

T-splines are recently proposed geometric modeling tools. A T-spline surface is a NURBS surface with T-junctions and is defined by a control grid called T-mesh. Local refinement can be performed very easily for T-splines while it is limited for B-splines or NURBS. Using T-splines, patches with unmatched boundaries can be combined easily without special technique. In this study, the analysis methodology using T-splines is proposed. In this methodology, T-splines are used both for description of geometries and for approximation of solution spaces. Two-dimensional linear elastic and dynamic problems will be solved by employing the proposed T-spline finite element method, and the effectiveness of the current analysis methodology will be verified.