• Journal of applied mathematics & informatics
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• v.7 no.2
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• pp.517-525
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• 2000

A constrained rational cubic spline with linear denominator was constructed in [1]. In the present paper, the sufficient condition for convex interpolation and some properties in error estimation are given.

• Journal of the Korea Society of Computer and Information
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• v.18 no.11
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• pp.59-68
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• 2013

In this paper, an effective scheme was proposed to estimate simple convex surface and simple concave surface which exist in image. This scheme is applied to input image to estimate simple convex surface or simple concave surface. When simple convex surface or simple concave surface exists, another proposed efficient interpolation scheme is used for the interpolated pixel to have the characteristics of simple convex surface or simple concave surface. The magnified image using the proposed schemes is more similar to the real image than the magnified image using the previous schemes. The PSNR values of the magnified images using the proposed schemes are greater than those of the magnified images using the previous interpolation schemes.

• Bulletin of the Korean Mathematical Society
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• v.29 no.2
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• pp.193-200
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• 1992

This paper uses a piecewise ratonal cubic interpolant to solve the problem of shape preserving interpolation for plane curves; scalar curves are also considered as a special case. The results derived here are actually the extensions of the convexity preserving results of Delbourgo and Gregory [Delbourgo and Gregory'85] who developed a $C^{1}$ shape preserving interpolation scheme for scalar curves using the same piecewise rational function. They derived the ocnstraints, on the shape parameters occuring in the rational function under discussion, to make the interpolant preserve the convex shape of the data. This paper begins with some preliminaries about the rational cubic interpolant. The constraints consistent with convex data, are derived in Sections 3. These constraints are dependent on the tangent vectors. The description of the tangent vectors, which are consistent and dependent on the given data, is made in Section 4. the convexity preserving results are explained with examples in Section 5.

• Journal of Broadcast Engineering
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• v.16 no.4
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• pp.669-679
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• 2011

In this paper, we propose a POCS based irregularly sampled image interpolation method exploiting non-local block-based wavelet shrinkage denoising algorithm. The method provides convex sets to improve the performance. The Delaunay triangulation interpolation is first applied to interpolate the missing pixels of the irregularly sampled image into the regular grids. Then, the non-local block-based wavelet shrinkage denoising algorithm is applied, and the originally observed pixels are enforced. After iteration is performed, the denoising algorithm for non-edge areas is applied to acquire the final result. The experimental results show that the proposed method outperforms the conventional methods.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.1
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• pp.166-174
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• 1994

A critical evaluation is made of the spectral bias which occurs in the use of a laser doppler velocimeter(LDV). Two processing algorithms are considered for spectral estimates: the sample and hold interpolation method(SH) and the nonuniform Shannon reconstruction technique(SR). Assessment is made of these for varying data densities $(0.05{\le}d.d.{\le}5)$ and turbulence levels(t.i.=30%, 100%). As an improved version of the spectral estimator, the utility of POCS (the projection onto convex sets) has been tested in the present study. This algorithm is found useful to be in the region when $d.d.{\gep}3.$

• Journal of the Korea Society of Computer and Information
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• v.18 no.2
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• pp.49-57
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• 2013

To improve the quality of magnified image, two schemes were proposed. The one is used to estimate simple convex surface and simple concave surface using the information of adjacent pixel values, and the other scheme is used to produce magnified image using the characteristics of simple convex surface and simple concave surface. The magnified image using the proposed scheme is more similar to real image than the magnified image using the previous schemes. The PSNR values of the magnified images using the proposed scheme are greater than those of the magnified images using the previous interpolation schemes.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.397-410
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• 2007

Visualization of 2D and 3D data, which arises from some scientific phenomena, physical model or mathematical formula, in the form of curve or surface view is one of the important topics in Computer Graphics. The problem gets critically important when data possesses some inherent shape feature. For example, it may have positive feature in one instance and monotone in the other. This paper is concerned with the solution of similar problems when data has convex shape and its visualization is required to have similar inherent features to that of data. A rational cubic function [5] has been used for the review of visualization of 2D data. After that it has been generalized for the visualization of 3D data. Moreover, simple sufficient constraints are made on the free parameters in the description of rational bicubic functions to visualize the 3D convex data in the view of convex surfaces.

• Journal of the Korean Society for Precision Engineering
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• v.16 no.10
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• pp.126-131
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• 1999

Up until now, it is said that no satisfactory computer solutions have been found for synthesizing four-bar linkage based on the prescribed coupler link curve. In our study, an algorithm has been developed to improve the design synthesis of four-bar linkage automatically generating prescribed path by using B-spline interpolation. The suggested algorithm generates the desired coupler curve by using B-spline interpolation, and hence the generated curve approximates as closely as to the desired curve representing coupler link trajectory. Also, when comparing each generated polygon with the control polygon, rapid comparison by applying convex hull concept. finally, optimization process using ADS is incorporated into the algorithm based on the 5 precision point method to reduce the total optimization process time. As for examples, three different four-bar linkages were tested and the results showed the effectiveness of the algorithm.

• Journal of Institute of Control, Robotics and Systems
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• v.19 no.6
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• pp.489-494
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• 2013

This paper tackles the problem of designing a dynamic output-feedback control for linear discrete-time norm-bounded uncertain systems with input saturation. By employing a LPV (Linear Parameter Varying) instead of LTI (Linear Time-Invariant) control, the useful information on interpolation parameters appearing in the procedure of representing saturation nonlinearity as a convex polytope is additionally applied in the control design procedure. By solving the addressed problem that can be recast into a convex optimization problem characterized by LMIs (Linear Matrix Inequalities) with one prescribed scalar, the vertices of convex set containing an LPV output-feedback control gain and the associated maximal invariant set of initial states are simultaneously obtained.

• Journal of the Society of Naval Architects of Korea
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• v.31 no.4
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• pp.32-40
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• 1994

This paper describes a smooth surface interpolating method of ship hull using a three-dimensional currie net that comes from the mesh curve fairing process. Geometric continuity(($GC^1$) is preserved across the boundary curve between patches. The three-dimensional curve net can have nonrectangular topologies, such as triangular and pentagonal topology. Among the boundary curve interpolation methods, Hermite blended Coons patch, Convex combination, and Gregory patch interpolation method are used to generate the ship hull surface. To check the fairness of the surface, the numerical method of surface/surface intersection problem is adopted. An application to an actual ship hull is given as an example.