• International Journal of Precision Engineering and Manufacturing
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• v.9 no.2
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• pp.84-92
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• 2008

Free-form shapes which were once considered as an aesthetic feature are now an important functional requirement. CNC industries are looking for a compact solution for reproducing free-form shapes as conventional interpolation models are inadequate, The parametric curve interpolator developed in the last decade has clearly emerged as favorite among its contemporaries in recent years, At present intense research has been done on parametric curve interpolators and interesting developments are reported. Out of the various parametric representations for curves and surfaces, NURBS has been standardized and widely used in free-form shape design. This paper presents a review of various methods of parametric interpolation for NURBS and discusses the salient features, problems and solutions. Recent approaches on variable feedrate interpolation, parameter compensation are also reviewed and research trends are addressed finally.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2003.05a
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• pp.474-479
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• 2003

This paper addresses the problem of B-spline surface interpolation to serial contours, where the number of points varies from contour to contour. A traditional lofting approach creates a set of B-spline curves via B-spline curve interpolation to each contour, makes them compatible via degree elevation and knot insertion, and performs B-spline surface lofting to get a B-spline surface interpolating them. The approach tends to result in an astonishing number of control points in the resulting B-spline surface. This situation arises mainly from the inevitable process of progressively merging different knot vectors to make the B-spline curves compatible. This paper presents a new approach for avoiding this troublesome situation. The approach includes a novel process of getting a set of compatible B-spline curves from the given contours. The process is based on the universal parameterization [1,2] allowing the knots to be selected freely but leading to a more stable linear system for B-spline curve interpolation. Since the number of control points in each compatible B-spline curve is equal to the highest number of contour points, the proposed approach can realize efficient data reduction and provide a compact representation of a B-spline surface while keeping the desired surface shape. Some experimental results demonstrate its usefulness and quality.

• Bulletin of the Korean Mathematical Society
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• v.44 no.2
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• pp.351-358
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• 2007

For an entire function f whose Fourier transform has a compact support confined to $[-{\pi},\;{\pi}]$ and restriction to ${\mathbb{R}}$ belongs to $L^2{\mathbb{R}}$, we derive a nonuniform sampling theorem of Lagrange interpolation type with sampling points ${\lambda}_n{\in}{\mathbb{R}},\;n{\in}{\mathbb{Z}}$, under the condition that $$\frac{lim\;sup}{n{\rightarrow}{\infty}}|{\lambda}_n-n|<\frac {1}{4}$.

• Journal of Multimedia Information System
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• v.5 no.1
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• pp.63-66
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• 2018

In this work, the smoothing and the interpolation basis splines are analyzed. As well as the possibility of using the spectral properties of the basis splines for digital signal processing are shown. This takes into account the fact that basic splines represent finite, piecewise polynomial functions defined on compact media.

• 제어로봇시스템학회:학술대회논문집
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• 1986.10a
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• pp.586-591
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• 1986

In this paper, we designed simultaneous 2-axis control system using commercialized custom ICs for positioning and interpolation that is very compact and high reliable. This system is primarily designed for NC system, we verified it is more complete than the other hardware & software based system in its function, control accuracy and cost. Also, this system can be expanded for multi-axis control, it can be applied to the control of more complicated mechanism such as articulated robot.

• Journal of Advanced Navigation Technology
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• v.17 no.5
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• pp.475-483
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• 2013

In this paper, the performances of modeling methods for combining corrections from multiple reference stations for network user were compared and analyzed. The longer the distance between reference station and user is, the more the GPS errors are decorrelated. Based on this point, multiple corrections from reference stations which is constituting a network should be combined properly to be applied for user observation to eliminate GPS errors. There are many widely used conventional modeling methods and they are applied for Compact Network RTK users and user position accuracy is predicted by using residual errors in observation of user. Compact Network RTK is a technique of generating corrections which was developed by Seoul National University. As a result, the horizontal and vertical accuracies were within about 5 cm and 7 cm respectively with 95 % probability for all conventional modeling methods. In addition, we analyzed condition for reference station constellation for modeling method using height information.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.535-539
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• 2007

Given operators X and Y acting on a separable complex Hilbert space $\mathcal{H}$, an interpolating operator is a bounded operator A such that AX=Y. In this article, we show the following: Let $Alg\mathcal{L}$ be a tridiagonal algebra on a separable complex Hilbert space $\mathcal{H}$ and let $X=(x_{ij})\;and\;Y=(y_{ij})$ be operators in $\mathcal{H}$. Then the following are equivalent: (1) There exists a normal operator $A=(a_{ij})\;in\;Alg\mathcal{L}$ such that AX=Y. (2) There is a bounded sequence $\{\alpha_n\}\;in\;\mathbb{C}$ such that $y_{ij}=\alpha_jx_{ij}\;for\;i,\;j\;{\in}\;\mathbb{N}$. Given vectors x and y in a separable complex Hilbert space $\mathcal{H}$, an interpolating operator is a bounded operator A such that Ax=y. We show the following: Let $Alg\mathcal{L}$ be a tridiagonal algebra on a separable complex Hilbert space $\mathcal{H}$ and let $x=(x_i)\;and\;y=(y_i)$ be vectors in $\mathcal{H}$. Then the following are equivalent: (1) There exists a normal operator $A=(a_{ij})\;in\;Alg\mathcal{L}$ such that Ax=y. (2) There is a bounded sequence $\{\alpha_n\}$ in $\mathbb{C}$ such that $y_i=\alpha_ix_i\;for\;i{\in}\mathbb{N}$.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.44 no.2
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• pp.55-60
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• 2007

This paper presents a compact double resolution scheme for the optical angle sensor based on 1-dimensional CMOS photodiode pixel array. All the pixels are divided into the even pixel and the odd pixel groups. The winner take all circuit is provided for each group. The proposed interpolation scheme increases the resolution by 2 from the winner addresses and winner values. The interpolation scheme can be implemented without any additional pixels or winner take all circuits and require only a comparator and a XOR gate. The proposed pixel array chip that has 336 photodiode pixels with $5.6{\mu}m$ pitch was fabricated with $0.35{\mu}m$ CMOS process and was assembled with a $50{\mu}m$ slit to form an angle sensor. The measured resolution is $0.1{\circ}$ with the proposed interpolation. The chip consumes 35mW and provides 8k samples per second.

• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• 2004.04a
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• pp.359-364
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• 2004

A high-speed and intelligent CNC system has been developed by Turbotek Co., Ltd. This paper presents the study for commercialization of the developed CNC system. In order to acquire stability and reliability of the developed CNC system, its hardwares and softwares ate improved. The CNC main unit is revised to a compact box-type CNC controller. Moreover, the integrated CNC main unit that has built-in and expandable I/O modules is also developed. Remote monitoring, fault diagnosis End NURBS interpolation functions are realized on the CNC system as software modules. Through these efforts, the developed CNC system can be loaded on machine tools successfully.

• Proceedings of the KIEE Conference
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• 2005.05a
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• pp.170-172
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• 2005

The DSD(Direct Stream Digital) encoder, which is a standard for SACD(Super Audio Compact Disc) proposed by Sony and philips, use 1 bit representation with a sampling frequency of 2.8224 MHz (64 $\times$ 44.1 kHz). For multi-rate PCM (Pulse Code Modulation) input like as 48/96/192 kHz, a external sample-rate converter is necessary to the DSD encoder. This paper has been proposed a digital filter structure composed of sample-rate converter and interpolation filter for the DSD encoder with multi-rate (48/96/192 kHz) PCM input. without a external sample-rate converter.