• International Journal of Precision Engineering and Manufacturing
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• 제9권2호
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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.

• 한국경영과학회:학술대회논문집
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• 한국경영과학회/대한산업공학회 2003년도 춘계공동학술대회
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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.

• 대한수학회보
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• 제44권2호
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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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• 제5권1호
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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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• 제어로봇시스템학회 1986년도 한국자동제어학술회의논문집; 한국과학기술대학, 충남; 17-18 Oct. 1986
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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.

• 한국항행학회논문지
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• 제17권5호
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• pp.475-483
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• 2013

본 논문에서는 Network RTK 보정정보를 사용자에 적용 시, 다중 기준국 보정정보 모델링 방식에 따른 사용자 성능 비교를 수행하였다. 기준국과 사용자 거리가 멀어질수록 사용자와 기준국의 GPS 오차요소 상관성이 감소하므로, 이와 같은 GPS 오차요소의 공간적 특성에 입각하여 다수의 네트워크 보정정보를 적절히 조합하여 사용자에 적용해주어야 한다. 기존에 기준국간 수평 거리 및 고도를 활용한 다양한 보정정보 모델링 방식을 활용하여, MAC 방식의 Compact Network RTK에 적용 가능한지 이론적으로 분석하였다. 한국 내 설치된 상시 기준국에서 습득한 실측 GPS 데이터를 활용하여, 서울대학교에서 제안한 Compact RTK와 기존의 Network RTK가 결합된 방식인 Compact Network RTK 사용자에 대해 각 모델링 방식 별 사용자 성능을 측정치 잔여오차 및 위치 정확도 예측치 관점에서 비교 및 분석을 수행하였다. 그 결과, 각 보정정보 모델링 방식에 대해 사용자 수평 위치 정확도 예측치의 경우 모두 2DRMS 5 cm 이내의 정확도를 보였고, 수직 위치 정확도 예측치의 경우 모두 95 % 신뢰도로 7 cm 이내의 정확도를 나타내었다. 또한, 기존 보정정보 모델 방식 중, 기준국간 고도 차이를 사용한 모델링 방법의 적용 가능 기준국 배치 조건에 대해 분석하였다.

• Journal of applied mathematics & informatics
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• 제24권1_2호
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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 $y_i=\alpha_ix_i\;for\;i{\in}\mathbb{N}$.

• 대한전자공학회논문지SD
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• 제44권2호
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• pp.55-60
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• 2007

본 논문에서는 1차원 CMOS 포토다이오드 픽셀 어레이를 이용한 광학 각도 센서에서, 해상도를 2배 향상시키는 인터폴레이션 방법을 제안한다. 제안된 구조는 인터폴레이션을 위하여 모든 픽셀을 짝수 픽셀 그룹과 홀수 픽셀 그룹으로 나누어, 각 그룹에서 가장 밝은 빛이 들어오는 픽셀(winner)을 winner take all 회로를 이용하여 찾아 이로부터 인터폴레이션을 수행하여 각도 센서의 해상도를 2배 향상시킨다. 제안된 인터폴레이션 방법은 픽셀이나 WTA 회로의 추가없이 간단히 하나의 XOR 게이트와 전압 비교기 회로를 이용하여 구현할 수 있다. $5.6{\mu}m$의 픽셀 피치를 가진 336개의 포토다이오드 픽셀 어레이를 $0.35{\mu}m$ CMOS 공정으로 구현한 후, 그 위에 $50{\mu}m$ 폭의 슬릿을 붙여서 광학 센서를 구성하여 실험하였다. 측정된 각도 해상도는 $0.1{\circ}$이며 35mW의 전력을 소모하고 최대 초당 8000번 각도를 측정할 수 있다.

• 한국공작기계학회:학술대회논문집
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• 한국공작기계학회 2004년도 춘계학술대회 논문집
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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.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2005년도 심포지엄 논문집 정보 및 제어부문
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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.