• 대한수학회지
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• 제58권5호
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• pp.1211-1226
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• 2021

The study of reducible Hilbert curves of conic fibrations over a smooth surface is carried on in this paper and the question of when the main component is itself the Hilbert curve of some ℚ-polarized surface is dealt with. Special attention is paid to the polynomial defining the canonical equation of the Hilbert curve.

• Journal of Ship and Ocean Technology
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• 제10권2호
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• pp.24-36
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• 2006

Ship hullform is usually designed with a curve network, and smooth hullform surfaces are supposed to be generated by filling in (or interpolating) the curve network with appropriate surface patches. Tensor-product surfaces such as B-spline and $B\'{e}zier$ patches are typical representations to this interpolating problem. However, they have difficulties in representing the surfaces of irregular topological type which are frequently appeared in the fore- and after-body of ship hullform curve network. In this paper, we proposed a method that can automatically generate discrete $G^1$ continuous B-spline surfaces interpolating given curve network of ship hullform. This method consists of three steps. In the first step, given curve network is reorganized to be of two types: boundary curves and reference curves of surface patches. Especially, the boundary curves are specified for their surface patches to be rectangular or triangular topological type that can be represented with tensor-product (or degenerate) B-spline surface patches. In the second step, surface fitting points and cross boundary derivatives are estimated by constructing virtual iso-parametric curves at discrete parameters. In the last step, discrete $G^1$ continuous B-spline surfaces are generated by surface fitting algorithm. Finally, several examples of resulting smooth hullform surfaces generated from the curve network data of actual ship hullform are included to demonstrate the quality of the proposed method.

• 충청수학회지
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• 제27권4호
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• pp.563-569
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• 2014

We investigate a minimal set of generators of a homogeneous ideal of a curve of degree d on a linearly normal smooth surface scroll W in $P^r$ whose arithmetic genus is maximal among curves of degree d on W.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제10권2호
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• pp.113-118
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• 2010

This paper proposed an ECAM (Electronic cam) control system which has simple and general structure. The proposed cam controller adopted the linear and polynomial curve-fitting method to generates a smooth cam profile curve function. Smooth motion trajectory of master actuator guarantees the good performance of slave motion and has an important effect on the interpolation quality of ECAM. The auto-tuning PID velocity controller was applied to overcome the uncertainties in ECAM, and the gains of the controller are updated continuously to ensure the consistency of system performance under varying working conditions. The robustness of system against the varying load torque disturbances and noises is guaranteed by using the load torque disturbance observer to suppress the disturbance on master actuator. The velocity compensator was applied to compensate the degradation of performance of slave motion caused from the varying driving speed of master motion. The stability and validity of the proposed ECAM control system was verified by simulation results.

• 대한수학회지
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• 제56권5호
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• pp.1355-1370
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• 2019

A curve $X{\subset}\mathbb{P}^r$ has maximal rank if for each $t{\in}\mathbb{N}$ the restriction map $H^0(\mathcal{O}_{\mathbb{P}r}(t)){\rightarrow}H^0(\mathcal{O}_X(t))$ is either injective or surjective. We show that for all integers $d{\geq}r+1$ there are maximal rank, but not arithmetically Cohen-Macaulay, smooth curves $X{\subset}\mathbb{P}^r$ with degree d and genus roughly $d^2/2r$, contrary to the case r = 3, where it was proved that their genus growths at most like $d^{3/2}$ (A. Dolcetti). Nevertheless there is a sector of large genera g, roughly between $d^2/(2r+2)$ and $d^2/2r$, where we prove the existence of smooth curves (even aCM ones) with degree d and genus g, but the only integral and non-degenerate maximal rank curves with degree d and arithmetic genus g are the aCM ones. For some (d, g, r) with high g we prove the existence of reducible non-degenerate maximal rank and non aCM curves $X{\subset}\mathbb{P}^r$ with degree d and arithmetic genus g, while (d, g, r) is not realized by non-degenerate maximal rank and non aCM integral curves.

• 제어로봇시스템학회논문지
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• 제12권10호
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• pp.1012-1017
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• 2006

By breaking the symmetry of the velocity profile in the S-curve, we developed a fast starting and smooth ending motion profile, named asymmetric S-curve(AS-curve). The problem for generating motion profile is formulated, and the algorithm for the AS-curve is derived and the flow chart of the AS-curve is illustrated. By various simulations, the derived algorithm is tested and shows the validity. This AS-curve can be applied to the high precision machines where fast and vibrationless motion is required in the near future.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제23권3호
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• pp.309-317
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• 2016

As a generalization of an inflection point, we consider a point P on a smooth plane curve C of degree m at which another curve C' of degree n meets C with high intersection multiplicity. Especially, we deal with the existence of two curves of degree m and n meeting at the unique point.

• 전자공학회논문지
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• 제53권6호
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• pp.137-145
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• 2016

본 논문에서는 새로운 방법의 3차원 컴퓨터단층영상에서 혈관을 추적하는 알고리즘을 소개하고자 한다. 해당 방법은 먼저 빠르게 다수의 2차 혹은 3차의 정칙곡선들로 대표되는 혈관의 지역적 모델들을 생성한다. 혈관의 특징을 고려한 비용함수로부터 각 곡선들은 영상데이터를 기반으로 생성된 비용을 부여 받는다. 추적 과정에서 매 단계 다음 혈관을 추정하기 위한 곡선들은 특정 기준에 의하여 여과되어 결국 혈관의 내부에 위치한 곡선들만 걸러낸다. 그 후 이들을 기반으로 혈관의 중심 선에 해당하는 최적의 정칙곡선 하나를 선정하게 된다. 지역적으로 최적인 정칙곡선이 순차적으로 검출되며 이들을 연결하여 하나의 혈관을 대표하는 구분적으로 부드러운 곡선을 만들어낸다. 짧은 정칙곡선은 제어 점들만으로 빠르게 기하학적 변환이 가능하며, 정의역 모든 구간에 대하여 미분이 가능하므로 곡률과 비틀림과 같은 기하학적 정보를 얻기 용이한 장점이 있다. 해당 방법에서 사용되는 정칙곡선모델이 혈관을 분류하고 추적함에 있어서 그 적합성을 증명하였고, 공공 데이터를 이용한 실험을 통하여 정확성과 수행 시간에 대해 최신기법들과 비교할만한 결과를 얻었다.

• 한국재료학회지
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• 제26권11호
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• pp.644-648
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• 2016

In order to examine how the solid-liquid interface responds to temperature variation depending on the materials characteristics, i.e. faceted phase or nonfaceted phase, the moving solid-liquid interface of transparent organic material, as a model substance for metallic materials (pivalic acid, camphene, salol, and camphor-50wt% naphthalene) was observed in-situ. Plots of the interface movement distance against time were obtained. The solid-liquid interface of the nonfaceted phase is atomically rough; it migrates in continuous mode, giving smooth curves of the distance-time plot. This is the case for pivalic acid and camphene. It was expected that the faceted phases would show different types of curves of the distance-time plot because of the atomically smooth solid-liquid interface. However, salol (faceted phase) shows a curve of the distance-time plot as smooth as that of the nonfaceted phases. This indicates that the solid-liquid interface of salol migrates as continuously as that of the nonfaceted phases. This is in contrast with the case of naphthalene, one of the faceted phases, for which the solid-liquid interface migrates in "stop and go" mode, giving a stepwise curve of the distance-time plot.

• 대한기계학회논문집
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• 제7권1호
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• pp.28-35
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• 1983

Quantitative analysis have been carried out on the micro-cracks on the surface and into the depth of unnotched smooth mild steel specimen under cyclic stains by rotating bending fatigue tests. Some of the results are; (1) Cracks initiate at the early stage of fatigue life N$_{I}$/ N$_{f}$=10 to 20%, and propagate during the rest of fatigue life. (2) Coalescence of highly crowded small fatigue cracks of random distribution seems to induce the final fracture at higher stress level. (3) The curves of crack initiation and the equal crack length on the graph of stress versus number of cycles are parallel to the S-N curve. (3) The curves of crack initiation and the equal crack length on the graph of stress versus number of cycles are parallel to the S-N curve. (4) The distributions of micro-surface crack length and depth show the composite Weibull distributions which are approximated to two straight lines separated by the value of transient region between stage I and stage II crack.k.k.