• Bulletin of the Korean Mathematical Society
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• v.49 no.1
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• pp.175-195
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• 2012

Representing planar Pythagorean hodograph (PH) curves by the complex roots of their hodographs, we standardize Farouki's double cubic method to become the undetermined junction point (UJP) method, and then prove the generic existence of solutions for general $C^1$ Hermite interpolation problems. We also extend the UJP method to solve $C^2$ Hermite interpolation problems with multiple PH cubics, and also prove the generic existence of solutions which consist of triple PH cubics with $C^1$ junction points. Further generalizing the UJP method, we go on to solve $C^2$ Hermite interpolation problems using two PH quintics with a $C^1$ junction point, and we also show the possibility of applying the modi e UJP method to $G^2[C^1]$ Hermite interpolation.

• Journal of Electrical Engineering and Technology
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• v.10 no.2
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• pp.676-687
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• 2015

Path planning algorithms are used to allow mobile robots to avoid obstacles and find ways from a start point to a target point. The general path planning algorithm focused on constructing of collision free path. However, a high continuous path can make smooth and efficiently movements. To improve the continuity of the path, the searched waypoints are connected by the proposed polynomial interpolation. The existing polynomial interpolation methods connect two points. In this paper, point groups are created with three points. The point groups have each polynomial. Polynomials are made by matching the differential values and simple matrix calculation. Membership functions are used to distribute the weight of each polynomial at overlapped sections. As a result, the path has $G^2$ continuity. In addition, the proposed method can analyze path numerically to obtain curvature and heading angle. Moreover, it does not require complex calculation and databases to save the created path.

• Structural Engineering and Mechanics
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• v.11 no.2
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• pp.221-236
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• 2001

A local point interpolation method (LPIM) is presented for the stress analysis of two-dimensional solids. A local weak form is developed using the weighted residual method locally in two-dimensional solids. The polynomial interpolation, which is based only on a group of arbitrarily distributed nodes, is used to obtain shape functions. The LPIM equations are derived, based on the local weak form and point interpolation. Since the shape functions possess the Kronecker delta function property, the essential boundary condition can be implemented with ease as in the conventional finite element method (FEM). The presented LPIM method is a truly meshless method, as it does not need any element or mesh for both field interpolation and background integration. The implementation procedure is as simple as strong form formulation methods. The LPIM has been coded in FORTRAN. The validity and efficiency of the present LPIM formulation are demonstrated through example problems. It is found that the present LPIM is very easy to implement, and very robust for obtaining displacements and stresses of desired accuracy in solids.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2002.10a
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• pp.570-575
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• 2002

This paper presents a new circular curve fitting approach of articulated manipulators, based on pseudoinverses. The paper aims at gaining the interpolation of circle from n data points, under the condition that the fitted circle should pass both a start point and an end point. In this paper, two algorithms of circular interpolation are presented. Prior to circular interpolation, are a spherical fitting should be performed, using least squares. In the first algorithm, the relationship between point data and normal vector on the sphere is used. In the second algorithm. the equation of plane which can be obtained from 3 points, i.e., a start point, an end point, and center of a sphere. The proposed algorithms are show to be efficient by using MATLAB-based simulation.

• Proceedings of the KSRS Conference
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• 2008.10a
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• pp.297-300
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• 2008

High-resolution mesoscale meteorological modeling requires more accurate and higher resolution digital elevation model (DEM) data. Shuttle Radar Topographic Mission (SRTM) has created 90 m DEM for entire globe and that is freely available for meteorological modeling and environmental applications. In this research, the effects of the topographic interpolation methods on high-resolution wind field simulation in the coastal regions were quantitatively analyzed using Weather Research and Forecasting (WRF) model with SRTM data. Sensitivity experiments with three different interpolation schemes (four-point bilinear, sixteen-point overlapping parabolic and nearest neighbor interpolation methods) were preformed using SRTM. In WRF modeling with sixteen-point overlapping parabolic interpolation, the coastal line and some small islands show more clearly than other cases. The maximum height of inland is around 140 meters higher, while the minimum of sea height is about 80 meter lower. As it concerns the results of each scheme it seems that the sixteen-point overlapping parabolic scheme indicates the well agreement with observed surface wind data. Consequently, topographic changes due to interpolation methods can lead to the significant influence on mesoscale wind field simulation of WRF modeling.

• Journal of Welding and Joining
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• v.18 no.5
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• pp.90-97
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• 2000

Effect of alloy elements on joinability of insert metal for liquid phase diffusion bonding of heat resistant alloys was investigated in this study. Also, optimum chemical composition of insert metal was explained using interpolation method. The insert metals utilized was commercial Ni-base amorphous foils and newly developed Ni-base filler metals with B, Si and Cr in this study. Melting point and critical interlayer width(CIW) decreased with increasing additional amount of B, Si and Cr, melting point lowering element of the insert metal. Optimized chemical composition of insert metals could be estimated by interpolation method. The optimum amount of B, Si, Cr addition into the insert metal were found to be about 3%, 4% and 3%, respectively. The measured characteristic values, melting point, microhardness in the bonded interlayer and CIW of the insert metals were the almost identical to ones of the calculated results by interpolation method.

• Structural Engineering and Mechanics
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• v.14 no.6
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• pp.713-732
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• 2002

A local radial point interpolation method (LRPIM) based on local residual formulation is presented and applied to solid mechanics in this paper. In LRPIM, the trial function is constructed by the radial point interpolation method (PIM) and establishes discrete equations through a local residual formulation, which can be carried out nodes by nodes. Therefore, element connectivity for trial function and background mesh for integration is not necessary. Radial PIM is used for interpolation so that singularity in polynomial PIM may be avoided. Essential boundary conditions can be imposed by a straightforward and effective manner due to its Delta properties. Moreover, the approximation quality of the radial PIM is evaluated by the surface fitting of given functions. Numerical performance for this LRPIM method is further studied through several numerical examples of solid mechanics.

• Transactions of the Korean Society of Machine Tool Engineers
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• v.18 no.2
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• pp.154-161
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• 2009

In order to implement continuous-path motion on a robot, it is necessary to blend one joint motion to another joint motion near a via point in a trapezoidal form of joint velocity. First, the velocity superposition using parametric interpolation is proposed. Hybrid motion blending is defined as the blending of different two type's motions such as blending of joint motion with linear motion, in the neighborhood of a via point. Second, hybrid motion blending algorithm is proposed based on velocity superposition using parametric interpolation. By using a 3-axis SCARA (Selective Compliance Assembly Robot Arm) robot with $LabVIEW^{(R)}$ $controller^{(1)}$, the velocity superposition algorithm using parametric interpolation is shown to result in less vibration, compared with PTP(Point- To-Point) motion and Kim's algorithm. Moreover, the hybrid motion $algorithm^{(2)}$ is implemented on the robot using $LabVIEW^{(R)(1)}$ programming, which is confirmed by showing the end-effector path of joint-linear hybrid motion.

• Honam Mathematical Journal
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• v.39 no.4
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• pp.617-635
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• 2017

By applying a classical approach for scalar rational interpolation problem, certain type of minimal interpolation problem for rational matrix functions is solved. It is shown that an appropriately defined matrix plays a key role in solving the minimal problem.

• Journal of the Korean association of regional geographers
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• v.10 no.2
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• pp.389-406
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• 2004

with the increasing popularity of regional studies, the importance of regional data has been recognized dramatically in recent years. However, due to potential problems from the intrinsic characteristics of aggregate regional data for the research, and incompatible regional units between source and target regional data units, the method for reorganizing the regional data units for a given research analysis should be required. In this regard, the purpose of this research is to review the significant interpolation methods for reorganizing the data units and, based on it, to propose the population weighted interpolation method. For the first purpose, areal weighted interpolation method, pycnophylactic method, dasymetric method, area-to-point method were reviewed. The proposed population-weighted interpolation method was applied to the case study of population census regional data in Erie County, NY, compared with areal weighted interpolation method, pycnophylactic method in terms of several statistical characteristics.