• Honam Mathematical Journal
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• v.41 no.4
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• pp.683-695
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• 2019

In the present paper, we study curves in 𝔼³ with density $e^{ax^2+by^2}$, where a, b ∈ ℝ not all zero constants and give the parametric expressions of the curves with vanishing weighted curvature. Also, we create ruled surfaces whose base curves are the curve with vanishing weighted curvature and the ruling curves are Smarandache curves of this curve. Then, we give some characterizations about these ruled surfaces by obtaining the mean curvatures, Gaussian curvatures, distribution parameters and striction curves of them.

• ETRI Journal
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• v.23 no.2
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• pp.85-95
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• 2001

The surface modeling capability of CAD systems is widely used to design products bounded by free form surfaces and curves. However, the surfaces or curves generated by popular data fitting methods usually have shape imperfections such as wiggles. Thus, fairing operations are required to remove the wiggles, which makes the surfaces or curves smooth. This paper proposes a new method based on the wavelet transform for fairing the surfaces or curves while preserving the continuity with adjacent surfaces or curves. The wavelet transform gives a hierarchical perspective of the surfaces and the curves, which can be decomposed into the overall sweep and details, i.e., local deviations from sweep like the wiggles. The proposed fairing method provides a similar effect on the mathematical surface as that of the grinding operation using sandpaper on the physical surface.

• Journal of Environmental Impact Assessment
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• v.16 no.5
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• pp.341-350
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• 2007

Lake Youngrang is a lagoon whose effluent flows into the East Sea. Because two resort towns and two golf courses are situated at the lake basin, many tourists visit this area. Stormwater runoff surveys were carried out for the eight storm events from 2004 to 2005 in the eutrophic lake watershed to give a basic data for the diffuse pollution control of the lake. Dimensionless mass-volume curves indicating the distribution of pollutant mass vs. volume were used to analyze the first flush phenomenon. The mass-volume curves were fitted with a power function and polynomial equation curves. The regression analysis showed that the polynomial equation curves were better than the power function in representing the tendency of the first flush, and second degree polynomial equation curves indicated the strength of the first flush effectively.

• Journal of Korea Multimedia Society
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• v.20 no.7
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• pp.1004-1013
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• 2017

This paper presents a relationship between the number of curves and geometric parameters of a 3D object. Once the relationship is established, the number of closed curves that can reliably represent 3D object is derived. Inspired by Shannon-Nyquist Sampling Theorem, in this paper, approach for sampling rate (defined as the minimum number of curves) for 3D reconstruction is proposed. The relationship is straightforward, is suitable for application to 3D object overlaid with closed-continuous curves, and can achieve efficient 3D reconstruction system in practice. To substantiate the proposed approach, simulation results are provided and the results show that the number of curves can be decreased without loss of generality of characteristics of a target 3D object.

• Korean Journal of Computational Design and Engineering
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• v.4 no.4
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• pp.312-317
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• 1999

An inflection point on a curve is a point where the curvature vanishes. An inflection point is useful for various geometric operations such as the approximation of curves and intersection points between curves or curve approximations. An inflection point on planar Bezier curves can be easily detected using a hodograph and a derivative of hodograph, since the closed from of hodograph is known. In the case of rational Bezier curves, for the detection of inflection point, it is needed to use the first and the second derivatives have higher degree and are more complex than those of non-rational Bezier curvet. This paper presents three methods to detect inflection points of rational Bezier curves. Since the algorithms avoid explicit derivations of the first and the second derivatives of rational Bezier curve to generate polynomial of relatively lower degree, they turn out to be rather efficient. Presented also in this paper is the theoretical analysis of the performances of the algorithms as well as the experimental result.

• Journal of the Korean Mathematical Society
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• v.37 no.3
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• pp.437-454
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• 2000

Let C be a smooth k-gonal curve of genus g. We study the number of pencils of degree k on C. In case $g\geqk(k-a)/2$ we state a conjecture based on a discussion on plane models for C. From previous work it is known that if C possesses a large number of pencils then C has a special plane model. From this observation the conjectures are split up in two cases : the existence of some types of plane curves should imply the existence of curves C with a given number of pencils; the non-existence of plane curves should imply the non-existence of curves C with some given large number of pencils. The non-existence part only occurs in the range $k(k-1)/2\leqg\leqk(k-1)/2] if k\geq7$. In this range we prove the existence part of the conjecture and we also prove some non-existence statements. Those result imply the conjecture in that range for $k\leq10$. The cases $k\leq6$ are handled separately.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.11a
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• pp.1048-1052
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• 2003

This study aims to derive frequency weighting curves for the estimation of driver's discomfort by steering wheel vibration in the vertical and rotational direction with respect to a steering column. Subjective tests for the determination of equal sensation curves, inverse of frequency weighting curves, for the two kinds of vibrations were performed using the sinusoidal signals with reference amplitudes from 0.2m/s$^2$ to 0.4 m/s$^2$ in the frequency range from 5㎐ to 100㎐. Twelve subjects joined at the tests, and median values of the twelve judgments were used to determine the frequency weighting curves. Second experiment was followed to determine relative magnitude between the two frequency weighting curves by direct comparison of discomfort due to the two kinds of vibrations at 50㎐, which showed discomfort by the rotational vibration was 1.5 times of that by the vertical vibration.

• Journal for History of Mathematics
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• v.30 no.3
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• pp.185-199
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• 2017

In tropical geometry, the sum of two numbers is defined as the minimum, and the multiplication as the sum. As a way to build tropical plane curves, we could use Newton polygons or amoebas. We study one method to convert the representation of an algebraic variety from an image of a rational map to the zero set of some multivariate polynomials. Mikhalkin proved that complex curves can be replaced by tropical curves, and induced a combination formula which counts the number of tropical curves in complex projective plane. In this paper, we present close examinations of this particular combination formula.

• Transactions of the Korean Society of Automotive Engineers
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• v.11 no.4
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• pp.165-172
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• 2003

This study aims to find frequency weighting curves for the evaluation of drivers' discomfort by vertical and rotational steering wheel vibration. Equal sensation curves, inverse of frequency weighting curves, were determined for the two kinds of vibrations respectively by using the sinusoidal signals with reference amplitudes from 0.2 to 0.4 m/s2 in the frequency range from 5 to 100 ㎐. Twelve subjects joined at the tests, and median values of the twelve judgments were used to determine the equal sensation curves. An experiment was followed to compare the relative sensation magnitude between the two kinds of equal sensation curves, which showed discomfort by the rotational vibration was 1.5 times of that by the vertical vibration at 50 ㎐.

• Journal of the Korea institute for structural maintenance and inspection
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• v.6 no.1
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• pp.255-262
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• 2002

This paper presents a statistical analysis of empirical fragility curves for bridge. The empirical fragility curves are developed utilizing bridge damage data obtained from the 1995 Hyogoken Nanbu(Kobe) earthquake. Two-parameter lognormal distribution functions are used to represent the fragility curves with the parameters estimated by the maximum likelihood method. This paper also presents methods of testing the goodness of fit of the fragility curves and estimating the confidence intervals of the two parameters(median and log-standard deviation) of the distribution. An analytical interpretation of randomness and uncertainty associated with the median is provided.