• Journal of the Korean Society for Precision Engineering
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• v.16 no.9
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• pp.172-178
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• 1999

3D linear and circular interpolations are a basic part for the machining of complex shapes. Until now, because of the absence of appropriate algorithms for the generation of 3D lines and circles, a full accomplishment for available machine tool resolution is difficult. this paper presents new algorithms for 3D linear and circular interpolation in the reference pulse technique. In 3D space, the line or circle is not expressed as an implicit function, it is only defined as the intersection of two surfaces. A 3D line is defined as the intersection of two planes, and a 3D circle is defined as the intersection of a plane and the surface of a sphere. Based on these concepts, interpolation algorithms are designed to follow intersection curves in 3D space, and a real-time 3D linear and circular interpolator was developed in software using a PC. The algorithm implemented in a PC showed promising results in interpolation error and speed performance. It is expected that it can be applied to the next generation computerized numerical control systems for the machining of 3D lines, circles and some other complex shapes.

• Communications of the Korean Mathematical Society
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• v.22 no.3
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• pp.475-485
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• 2007

We construct high-degree interpolation rules using not only pointwise values of a function but also of its derivatives up to the p-th order at equally spaced nodes on a closed and bounded interval of interest by introducing a linear functional from which we produce systems of linear equations. The linear systems will lead to a conclusion that the rules are uniquely determined for the nodes. An example is provided to compare the rules with the classical interpolating polynomials.

• Communications of the Korean Mathematical Society
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• v.21 no.2
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• pp.397-407
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• 2006

We construct polynomial-fitting interpolation rules to agree with a function f and its first derivative f' at equally spaced nodes on the interval of interest by introducing a linear functional with which we produce systems of linear equations. We also introduce a matrix whose determinant is not zero. Such a property makes it possible to solve the linear systems and then leads to a conclusion that the rules are uniquely determined for the nodes. An example is investigated to compare the rules with Hermite interpolating polynomials.

• 한국전산유체공학회:학술대회논문집
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• 2010.05a
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• pp.397-403
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• 2010

The Immersed boundary method(IBM) is one of CFD techniques which can simulate flow field around complex objectives using simple Cartesian grid system. In the previous studies the IBM has mostly been implemented to fractional step method based Navier-Stokes solvers. In these cases, pressure buildup near IB was found to occur when linear interpolation and stadard mass conservation is used and the interpolation scheme became complicated when higher order of interpolation is adopted. In this study, we implement the IBM to an incompressible Navier-Stokes solver which uses SIMPLE algorithm. Bi-linear and quadratic interpolation equations were formulated by using only geometric information of boundary to reconstruct velocities near IB. Flow around 2D circular cylinder at Re=40 and 100 was solved by using these formulations. It was found that the pressure buildup was not observed even when the bi-linear interpolation was adopted. The use of quadratic interpolation made the predicted aerodynamic forces in good agreement with those of previous studies.

• Journal of the Korean Society for Precision Engineering
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• v.17 no.1
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• pp.192-197
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• 2000

In CNC machining, a free curve is cut into small linear segments using the linear interpolation(G01) method. Therefore, the interpolation error along the curve is not constant due to the changing curvature. This paper presents a NURBS (Non-Uniform Rational B-Spline) interpolation algorithm for machining free curves with high precision and high speed. The proposed NURBS interpolation defines the tool path with NURBS parameters and limits the interpolation error to any desired level by adjusting the feed rate considering the curvature of the shape and sampling time. Both linear and NURBS interpolations are compared to show the validity of the proposed algorithm.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.20 no.6
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• pp.778-784
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• 2011

This paper presents the study on orientations interpolation of 6-axis articulated robot using quaternion. In this paper, we propose a control algorithm between given two orientations of 6-axis articulated robot by using a quaternion with spherical linear interpolation. In order to study the quaternion interpolation, We created Inverse kinematics program and Interpolation program using LabVIE$^{(R)}$. The rotation angle of each axis were calculated using both euler orientations interpolation program and quaternion orientations interpolation program. The proposed control algorithm is shown to be effective in terms of motor angles and torques when compared to a conventional Euler angle interpolation, by using both LabVIEW$^{(R)}$ and RecurDyn$^{(R)}$.

• Journal of the Korean Data and Information Science Society
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• v.13 no.2
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• pp.365-379
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• 2002

We apply the techniques of interpolation and extrapolation to derive a new estimator based on centered modified systematic sampling for the mean of a population which has a linear trend. The efficiency of the proposed estimation method is compared with that of various existing methods. An illustrative numerical example is given.

• International Journal of CAD/CAM
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• v.3 no.1_2
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• pp.77-83
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• 2003

We propose two algorithms to generate (1) polygonal meshes and (2) developable surface patches far generalized cylinders defined by contours of discrete curves. To solve the contour blending problem of generalized cylinder, the presented algorithms have adopted the algorithm and related properties of LIDM (linear interpolation by direction map) that interpolate geometric shapes based on direction map merging and group scaling operations. Proposed methods are fast to compute and easy to implement.

• Korean Journal of Remote Sensing
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• v.18 no.5
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• pp.299-303
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• 2002

Many ocean color sensors are being operated at present and will be continued to operatein the coming years. However, these ocean color sensors have different spectral bands locations and higher level product algorithms. Thus the continuity of ocean color data from the satellite with different missions will be important for monitoring of oceanographic variation with long term research. In this study, CZCS band and algorithm are compared with OCTS and SeaWiFS algorithm for estimating chlorophyll. Missing bands of OCTS and CZCS for chlorophyll algorithm are estimated by linear-interpolation using SeaWiFS data. We were able to evaluate the effectiveness of the correction methods using linear interpolation method. Surprisingly, linear interpolation gave a better result than those of other bands.

• Transactions of the Korean Society of Mechanical Engineers
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• v.6 no.4
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• pp.341-345
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• 1982

The interpolator is usually built in hardware (logic circuitry), and the interpolator fabricated in a single LSI chip is recently made use of in most NC controllers, making the system more compact. However, the LSI interpolator not only has the technical difficulties but also requires high cost, in its fabrication. To solve these problems, we tried to find the method of interpolation by software, and succeeded in developing a program which, executed by INTEL's 8085 microprocessor, can distribute the input pulses of up to 4.0 [Kpps] for the linear interpolation and 3.0 [Kpps] for the circular interpolation. This paper presents the algorithm used to reduce the execution time and the flow chart of the interpolation program, and also shows the possibility of software interpolation. The interpolation program designed in assembly language is presented in the appendix.