• 한국지능시스템학회:학술대회논문집
• /
• 한국퍼지및지능시스템학회 2003년도 ISIS 2003
• /
• pp.90-93
• /
• 2003

The function, which represents the closed curve, is found from the sampling data by S-System in this study. Two methods are proposed. One is the extension of S-System. The data x and y are regarded as input data, and the data z=0 as output data. To avoid the trap into the invalid function, the judgment points (x$\_$j/, y/sug j/) are introduced. They are arranged in the inside and the outside of the closed curve. By introducing this concept, the functions representing closed curve are found by S-System. This method is simple because of a little extension of S-System. It is, however, difficult for the method to find the complex function like a hand-written curve. Then another method is also proposed. It uses the system incorporating the argument function. The closed curve can be expressed by the argument function. The relatively complex function, which represents the closed curve like a hand-written curve, is found by utilizing argument function.

• 대한전기학회:학술대회논문집
• /
• 대한전기학회 2003년도 학술회의 논문집 정보 및 제어부문 B
• /
• pp.1022-1030
• /
• 2003

In this paper we propose a efficient offset curve construction algorithm for $C^0$-continuous Open and Closed 2D sequence curve with line segment in the plane. One of the most difficult problems of offset construction is the loop problem caused by the interference of offset curve segments. Prior work[1-10] eliminates the formation of local self-intersection loop before constructing a intermediate(or raw) offset curve, whereas the global self-intersection loop are detected and removed explicitly(such as a sweep algorithm[13]) after constructing a intermediate offset curve. we propose an algorithm which removes global as well as local intersection loop without making a intermediate offset curve by forward tracing of tangential circle. Offset of both open and closed poly-line segment sequence curve in the plane constructs using the proposed approach.

• Kyungpook Mathematical Journal
• /
• 제55권3호
• /
• pp.741-752
• /
• 2015

We introduce the warping crossing polynomial of an oriented knot diagram by using the warping degrees of crossing points of the diagram. Given a closed transversely intersected plane curve, we consider oriented knot diagrams obtained from the plane curve as states to take the sum of the warping crossing polynomials for all the states for the plane curve. As an application, we show that every closed transversely intersected plane curve with even crossing points has two independent canonical orientations and every based closed transversely intersected plane curve with odd crossing points has two independent canonical orientations.

• 호남수학학술지
• /
• 제22권1호
• /
• pp.83-90
• /
• 2000

We establish a sufficient condition for a simple closed curve in the Euclidean plain $\mathbb{R}^2$, the unit sphere $S^2$ or the hyperbolic plane $H^2$ to be the boundary of a metric ball.

• 충청수학회지
• /
• 제18권2호
• /
• pp.195-203
• /
• 2005

In this paper, we introduced the tiling, for closed plane curves ${\alpha}(s)$, and we discussed the properties of tiling. Also if ${\alpha}(s)$ was arbitrary plane closed curve equipped by tiling ${\Im}$ then we studied the effect of retraction and tiling retraction on it.

• Korean Journal of Mathematics
• /
• 제5권2호
• /
• pp.113-118
• /
• 1997

According to the Bernoulli-Euler theory of elastic rods the bending energy of the wire is proportional to the total squared curvature of ${\gamma}$, which we will denote by $F({\gamma})=\int_{\gamma}k^2ds$. If the result of J.Langer and D.Singer [3] extend to knotted elastic curve, then we obtain the following. Let {${\gamma},M$} be a closed knotted elastic curve. If the curvature of ${\gamma}$ is nonzero for everywhere, then ${\gamma}$ lies on torus.

• 한국CDE학회논문집
• /
• 제3권2호
• /
• pp.135-139
• /
• 1998

The hodograph, which are usually defined as the derivative of parametric curve or surface, is useful far various geometric operations. It is known that the hodographs of Bezier curves and surfaces can be represented in the closed form. However, the counterparts of rational Bezier curves and surface have not been discussed yet. In this paper, the equations are derived, which are the closed form of rational Bezier curves and surfaces. The hodograph of rational Bezier curves of degree n can be represented in another rational Bezier curve of degree 2n. The hodograph of a rational Hazier surface of degree m×n with respect to a parameter can be also represented in rational Bezier surface of degree 2m×2n. The control points and corresponding weight of the hodographs are directly computed using the control points and weights of the given rational curves or surfaces.

• 한국CDE학회논문집
• /
• 제1권2호
• /
• pp.158-162
• /
• 1996

Algorithms to find the Bezier control points of the image of a Bezier domain curve on a Bezier surface are described. The diagonal image curve is analysed and the general linear case is transformed to the diagonal case. This proposed algorithm gives the closed form solution to find the control points of the image curve of a linear domain curve. If the domain curve is not linear, the image curve can be obtained by solving the system of linear equations.

• 한국수학교육학회지시리즈A:수학교육
• /
• 제38권1호
• /
• pp.87-94
• /
• 1999

A multimedia CD title is developed for learning simple closed curve and Mobius band which are one of mathematics contents in the first grade of middle school. This title visualizes various figures through graphics and animations so that students can easily understand the relevant concepts and learn them with fun. It is shown that 88.6% of 30 sampled teachers are positive for the title and that 86.7% want to use it as a teaching tool in their classes.

• 한국지반공학회논문집
• /
• 제18권6호
• /
• pp.33-42
• /
• 2002

지반 굴착시 지반의 변위특성과 지보재의 설치시기에 대한 중요한 정보를 제공하는 지반반응곡선(Ground reaction curve)을 구하는 방법은 일반적으로 원형단면이고 측압계수 K＝1.0인 상태를 가정한 closed from solution을 통해서 구해지지만, 실제 현장에서는 주로 마제형 굴착단면이 사용되며 $K\neq$1.0인 경우 대부분이다. 지반 굴착시 측압계수와 굴착 형상에 따라 측벽에서의 초기탄성변위 및 임계지보압이 변화하는 경향을 알아보기 위하여 측압계수 값을 0.5～3.0 사이에서 변화시키고, 각 측압계수마다 초기연직응력을 5～30MPa 사이에서 변화시켜가면서 원형단면과 마제형 단면인 경우를 구분하여 수치해석을 통해 지반반응곡선을 얻었다. Closed form solution에 의해 얻어진 지반반응곡선은 측압계수와 굴착단면의 형상을 고려하지 못하기 때문에 $K\neq$1.0인 실제 지반에 대한 변위거동과 지반의 자립성을 평가하는 데 큰 오차를 유발할 수 있는 것으로 나타났다. 따라서, Closed from solution에 의해 지보재의 설치시기를 예측하는 것은 많은 오차를 수반하는 과정이므로, 수치해석을 통한 지보설치 시기와 자립성에 대한 검토를 수행하는 것이 바람직 할 것으로 판단된다.