• 호남수학학술지
• /
• 제39권4호
• /
• pp.515-525
• /
• 2017

In this paper, we study planar normal section curves. We have interpreted curvatures of normal section curves. On the other hand we have investigated sufficient and necessary conditions for a normal section curve to be biharmonic.

• 한국CDE학회논문집
• /
• 제3권2호
• /
• pp.127-134
• /
• 1998

This paper presents d new algorithm to compute the offlet curve of a given planar parametric curve. We reduce the problem of computing an offset curve to that of intersecting a surface to a paraboloid. Given an input curve C(t)=(x(t), y(t))∈R², the corresponding surface D/sub c(t)/ is constructed symbolically as the envelope surface of a one-parameter family of tangent planes of the paraboloid Q:z=x²+y²along a lifted curve C(t)=(x(t), y(t), x(t)²+y(t)²∈Q. Given an offset distance d∈R, the offset curve C/sub d/(t) is obtained by the projection of the intersection curve of D/sub c(t)/ and a paraboloid Q:z=x²+y²-d² into the xy-plane.

• 한국방송∙미디어공학회:학술대회논문집
• /
• 한국방송공학회 2009년도 IWAIT
• /
• pp.482-486
• /
• 2009

Scale-invariant feature is an effective method for retrieving and classifying images. In this study, we analyze a scale-invariant planar curve features for developing 2D shapes. Scale-space filtering is used to determine contour structures on different scales. However, it is difficult to track significant points on different scales. In mathematics, curvature is considered to be fundamental feature of a planar curve. However, the curvature of a digitized planar curve depends on a scale. Therefore, automatic scale detection for curvature analysis is required for practical use. We propose a technique for achieving automatic scale detection based on difference of curvature. Once the curvature values are normalized with regard to the scale, we can calculate difference in the curvature values for different scales. Further, an appropriate scale and its position are detected simultaneously, thereby avoiding tracking problem. Appropriate scales and their positions can be detected with high accuracy. An advantage of the proposed method is that the detected significant points do not need to be located in the same contour. The validity of the proposed method is confirmed by experimental results.

• 한국CDE학회논문집
• /
• 제15권2호
• /
• pp.115-123
• /
• 2010

We present an efficient algorithm for computing the Hausdorff distance between two planar curves. The algorithm is based on an efficient trimming technique that eliminates the curve domains that make no contribution to the final Hausdorff distance. The input curves are first approximated with biarcs within a given error bound in a pre-processing step. Using the biarc approximation, the distance map of an input curve is then approximated and stored into the graphics hardware depth-buffer by rendering the distance maps (represented as circular cones) of the biarcs. We repeat the same procedure for the other input curve. By sampling points on each input curve and reading the distance from the other curve (stored in the hardware depth-buffer), we can easily estimate a lower bound of the Hausdorff distance. Based on the lower bound, the algorithm eliminates redundant curve segments where the exact Hausdorff distance can never be obtained. Finally, we employ a multivariate equation solver to compute the Hausdorff distance efficiently using the remaining curve segments only.

• International Journal of Ocean System Engineering
• /
• 제2권2호
• /
• pp.63-70
• /
• 2012

This paper presents a new curvature based kinematic displacement theory and a numerical method to calculate the planar displacement of structures from a geometrical viewpoint. The theory provides an opportunity to satisfy the kinematic equilibrium of a planar structure using a progressive numerical approach, in which the cross sections are assumed to remain plane, and the deflection curve was evaluated geometrically using the curvature values despite being solved using differential equations. The deflection curve is parameterized with the arc-length, and was taken as an assembly of the chains of circular arcs. Fast and accurate solutions of most complex deflections can be obtained with few inputs.

• 대한수학회지
• /
• 제14권2호
• /
• pp.153-158
• /
• 1978

• 제어로봇시스템학회:학술대회논문집
• /
• 제어로봇시스템학회 1991년도 한국자동제어학술회의논문집(국제학술편); KOEX, Seoul; 22-24 Oct. 1991
• /
• pp.1617-1622
• /
• 1991

Plane sweep is a general method in computational geometry. There are many efficient theoretical algorithms designed using plane sweep technique. However, their practical implementations are still suffering from the topological inconsistencies resulting from the numerical errors in geometric computations with finite-precision arithmetic. In this paper, we suggest new implementation techniques for the plane sweep algorithms to resolve the topological inconsistencies and construct the planar object boundaries from given input curve segments.

• 호남수학학술지
• /
• 제45권1호
• /
• pp.130-145
• /
• 2023

In this paper, we define some integral curves connected with a framed curve in Euclidean 3-space. These curves include framed generalized principal-direction curve, framed generalized binormal-direction curve, framed principal-donor curve and framed Darboux-direction curve. We obtain some relations between the framed curvatures of new defined framed curves and framed curvatures of given framed curve. By using the obtained relationships we give some characterizations for such curves. We also give methods for constructing framed helix and framed slant helix from planar curves.

• 한국CDE학회논문집
• /
• 제4권4호
• /
• pp.312-317
• /
• 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.

• 전기화학회지
• /
• 제7권2호
• /
• pp.69-79
• /
• 2004

전산모사를 이용하여 특성을 정확하게 모사하기 위해서는 전지 내부에서 발생하는 다양한 물리적, 화학적 현상을 고려하여야 한다. 이를 위해, 본 연구에서는 다양한 전지 내부 현상에 대한 변수를 고려할 수 있는 전산유체 상용코드인 CFD-ACE+를 이용하여 평판형 고체산화물 연료전지의 작동 특성을 분석하였다. 단위 스택에서 발생하는 물질전달과 열전달 및 전기화학 반응에 의한 전하이동을 복합적으로 고려하여, 작동조건 하에서 각 공정적, 구조적 변수 변화에 따른 전지특성을 예측하였다. 이러한 전산모사 방법을 통하여 확산과 유동에 의한 전지 내 반응물과 생성물의 mass fraction 분포와 단위 스택의 내부 온도분포 그리고 전지 특성을 나타내는 polarization curve에 의한 고체산화물 연료 전지의 분극 특성을 정성, 정량적으로 제시하였다. 본 연구를 통해 평판형 단위 스택 내에서의 다양한 변수 변화에 따른 전지의 작동 특성에 대한 효율적 예측이 가능하였고, 고체산화물 연료전지 작동 시 발생하는 현상에 대한 전산모사 접근법을 체계적으로 제시할 수 있었다.