• Journal of Integrative Natural Science
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• v.9 no.1
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• pp.10-15
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• 2016

In this paper the approximation methods of offset curve of conic with explicit error bound are considered. The quadratic approximation of conic(QAC) method, the method based on quadratic circle approximation(BQC) and the Pythagorean hodograph cubic(PHC) approximation have the explicit error bound for approximation of offset curve of conic. We present the explicit upper bound of the Hausdorff distance between the offset curve of conic and its PHC approximation. Also we show that the PHC approximation of any symmetric conic is closer to the line passing through both endpoints of the conic than the QAC.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.13 no.4
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• pp.257-265
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• 2009

In this paper we find an explicit form of upper bound of Hausdorff distance between given cubic spline curve and its quadratic spline approximation. As an application the approximation of offset curve of cubic spline curve is presented using our explicit error analysis. The offset curve of quadratic spline curve is exact rational spline curve of degree six, which is also an approximation of the offset curve of cubic spline curve.

• Communications of the Korean Mathematical Society
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• v.22 no.4
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• pp.641-648
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• 2007

In this paper, we present the exact Hausdorff distance between the offset curve of quadratic $B\'{e}zier$ curve and its quadratic $GC^1$ approximation. To illustrate the formula for the Hausdorff distance, we give an example of the quadratic $GC^1$ approximation of the offset curve of a quadratic $B\'{e}zier$ curve.

• Communications of the Korean Mathematical Society
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• v.17 no.2
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• pp.331-347
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• 2002

We characterize the best geometric conic approximation to regular plane curve and verify its uniqueness. Our characterization for the best geometric conic approximation can be applied to degree reduction, offset curve approximation or convolution curve approximation which are very frequently occurred in CAGD (Computer Aided Geometric Design). We also present the numerical results for these applications.

• Journal of the Korean Society for Precision Engineering
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• v.22 no.8 s.173
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• pp.76-83
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• 2005

In this study a general method for computing offsets of free form curves is presented. In the method arbitrary free form curve is approximated with point series considering required tolerance. The point series are offset precisely using the normal vectors computed at each point and loop removal is carried out by the newly suggested algorithm. The resulting offset points are transformed to lines and arcs using the biarc approximation method. Tangent vectors for approximation of discrete points data are calculated by traditional local interpolation scheme. In order to show the validity and generality of the proposed method , various of offsettings are carried our for the base curves with complex shapes.

• Communications for Statistical Applications and Methods
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• v.19 no.4
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• pp.537-546
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• 2012

In this paper, for analyzing binary data, Poisson regression with offset and logistic regression are compared with respect to the power via simulations. Poisson distribution can be used as an approximation of binomial distribution when n is large and p is small; however, we investigate if the same conditions can be held for the power of significant tests between logistic regression and offset poisson regression. The result is that when offset size is large for rare events offset poisson regression has a similar power to logistic regression, but it has an acceptable power even with a moderate prevalence rate. However, with a small offset size (< 10), offset poisson regression should be used with caution for rare events or common events. These results would be good guidelines for users who want to use offset poisson regression models for binary data.

• Korean Journal of Computational Design and Engineering
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• v.5 no.2
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• pp.168-174
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• 2000

A biarc is a curve connecting two circular arcs with the constraints of tangent continuity so that it can represent the free form currie approximately connecting several biarcs with the tangent continuity. Since a biarc consists of circular arcs, the offset curve of the curve represented by biarcs can be easily obtained. Besides. if the tool path is represented by biarcs, the efficiency of machining is improved and the amount of data is decreased. When approximating a curve with biarcs, the location of the point where two circular arcs meet each other plays an important part in determining the shape of a biarc. In this thesis, the optimum point where two circular arcs meet is calculated using the tangent information of the curve to approximate so that it takes less calculation time to approximate due to the decrease of the number of iterations.

• Journal of the Korea Computer Graphics Society
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• v.25 no.3
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• pp.93-103
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• 2019

We introduce a geometric processing method for freeform surfaces based on high-precision torus patch approximation, a new spatial data structure for efficient geometric operations on freeform surfaces. A torus patch fits the freeform surface with flexibility: it can handle not only positive and negative curvature but also a zero curvature. It is possible to precisely approximate the surface regardless of the convexity/concavity of the surface. Unlike the traditional method, a torus patch easily bounds the surface normal, and the offset of the torus becomes a torus again, thus helps the acceleration of various geometric operations. We have shown that the torus patch's approximation accuracy of the freeform surface is high by measuring the upper bound of the two-sided Hausdorff distance between the freeform surface and set of torus patches. Using the method, it can be easily processed to detect an intersection curve between two freeform surfaces and find the offset surface of the freeform surface.

• The Journal of the Korea institute of electronic communication sciences
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• v.13 no.5
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• pp.917-922
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• 2018

In the conventional interchannel interference self-cancellation (ICI-SC) schemes, the length of sampling window is the same as the symbol length of orthogonal frequency division multiplexing (OFDM). Thus, the number of complex operations to compute the interference coefficient of each subchannel is significantly increased. To solve this problem, we present an approximated mathematical model for the coefficients of ICI-SC schemes. Based on the proposed approximation, we analyze mean squared error (MSE) and computational complexity of the ICI-SC schemes with the length of sampling window. As a result, the presented approximation has an error of less than 0.01% on the MSE compared to the original equation. When the number of subchannels is 1024, the number of complex computations for the interference coefficients is reduced by 98% or more. Since the computational complexity can be remarkably reduced without sacrificing the self-cancellation capability, it is considered that the proposed approximation is very useful to develop an algorithm for the ICI-SC scheme.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.43 no.5
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• pp.711-720
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• 1994

A distance relaying algorithm for detecting faults at power transmission line is presented in this paper. The algorithm is based on differential equation from relaton between voltage and current, which is composed of lumped resistance and inductance. During the fault transient state,the voltage and current signals are severely distorted due to the exponentially decaying DC offset and high frequency components, In spite of using small data, the presented integral method to evaluate R and L from voltage and current has high performance against these harmonics including DC offset. Therefore, the presented algorithm can be implemented with only a low order anti-aliasing analog filter and dosen't need any digital filter to remove specific components.