• Journal of applied mathematics & informatics
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• 제18권1_2호
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• pp.159-169
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• 2005

An algorithmic approach to degree reduction of rational Bezier curves is presented. The algorithms are based on the degree reduction of polynomial Bezier curves. The method is introduced with the following steps: (a) convert the rational Bezier curve to polynomial Bezier curve by using homogenous coordinates, (b) reduce the degree of polynomial Bezier curve, (c) determine weights of degree reduced curve, (d) convert the Bezier curve obtained through step (b) to rational Bezier curve with weights in step (c).

• 한국CDE학회논문집
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• 제1권2호
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• pp.158-162
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• 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.

• 한국CDE학회논문집
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• 제3권2호
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• pp.113-120
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• 1998

Calculation of intersection points by two curves is fundamental to computer aided geometric design. Bezier clipping is one of the well-known curve intersection algorithms. However, this algorithm is only applicable to Bezier curve representation. Therefore, the NURBS curves that can represent free from curves and conics must be decomposed into constituent Bezier curves to find the intersections using Bezier clipping. And the respective pairs of decomposed Bezier curves are considered to find the intersection points so that the computational overhead increases very sharply. In this study, extended Bezier clipping which uses the linear precision of B-spline curve and Grevill's abscissa can find the intersection points of two NURBS curves without initial decomposition. Especially the extended algorithm is more efficient than Bezier clipping when the number of intersection points is small and the curves are composed of many Bezier curve segments.

• 정보학연구
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• 제5권1호
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• pp.99-111
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• 2002

원 영상에 근접한 색채 재현을 위한 선형 변환을 이용한 영상의 컬러 보정은 컬러 공간의 비 선형성으로 인해 색의 왜곡 현상이라는 문제가 발생하게 된다. 이러한 문제를 극복하기 위해 선형 이론인 임의의 평면상에 주어진 자료점들로 구성되는 베지어 곡선이 사용되어 왔다. 그러나, 이 베지어 곡선은 자료점의 개수에 따라 차수가 증가하게 되므로 수치적 계산상의 많은 제약을 받게 된다. 본 논문에서는 각 구간에서나 전체 구간에서의 차수가 3차이면서 베지어 곡선의 특성을 갖는 "3중첩 구간적 베지어 3차 곡선"(TPBC Curve; Triplicated Piecewise Bezier Cubic Curve)를 이용하였다. 이에 따른, TPBC-곡선과 20차 베지어 곡선을 이용하였을 때와 비교하여 컬러 보정 시 발생하는 왜곡 현상, 그리고 좁은 영역의 컬러 보정으로 인한 작업량의 증가를 감소시킨 결과를 보여주고자 한다. 보여주고자 한다.

• 한국생산제조학회지
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• 제24권6호
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• pp.696-702
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• 2015

This paper suggests a new method for making a navigation path by using Bezier curve in order to improve the navigation performance used to avoid obstacles during a robot soccer game. We analyzed the advantages and disadvantages of both vector-field and limit-cycle navigation methods, which are the mostly widely used navigation methods for avoiding obstacles. To improve the disadvantages of these methods, we propose a new design technique for generating a more proper path using Bezier curve and describe its advantages. Using computer simulations and experiments, we compare the performance of vector-field navigation with that of Bezier curve navigation. The results prove that the navigation performance using Bezier curve is relatively superior to the other method.

• 한국CDE학회논문집
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• 제3권2호
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• pp.135-139
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• 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.

• 대한공간정보학회지
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• 제7권1호
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• pp.29-40
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• 1999

벡터 GIS에서 자연선형체는 통상 일련의 직선분(line segments)에 의해 표시되나 그 대안으로 곡선분(curve segments) 역시 사용될 수 있다. 곡선분은 스플라인보간법에 의해 생성가능하며 이를 위해 Bezier방법과 신보간법(유기윤, 1998)이 사용될 수 있는데 본 연구에서는 신보간법의 퍼포먼스를 테스트해 보았다. 테스트는 두 가지에 촛점을 두었는데 (1) 새보간법에 의해 생성된 선형분이 직선분 보다 정확하게 자연선형체를 표현할 수 있는지 여부와 (2) 새보간법에 의해 생성된 선형분이 Bezier방법에 의해 생성된 선형분 보다 자연선형체를 정확하게 표현할 수 있는지 여부에 대한 검정이다. 이를 위해 t-테스트에 의한 가설검정법이 이용되었으며 자료로는 미 지질조사국의 7.5분 지형도가 이용되었다. 테스트결과 새보간법과 Bezier방법에 의해 생성된 선형분이 직선분 보다 자연선 형체를 정확하게 표현하였으며 새보간법에 의해 생성된 선형분이 Bezier방법에 의해 생성된 선형분보다 정확하게 표현하였다.

• 한국CDE학회논문집
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• 제4권4호
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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.

• 대한조선학회논문집
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• 제34권4호
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• pp.127-138
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• 1997

본 연구에서는 선박의 기본설계 단계에서 정의된 선도를 입력 정보로 하여 순정도 높은 선형을 표현할 수 있는 기법을 개발하였다. 곡선모델링의 경우, de Casteljau (드 카스텔죠)알고리듬과 Bezier 조정점을 이용하여 자유곡선을 표현하였고, 이를 토대로 Non-Uniform B-Spline(NUB) 곡선, Spline곡선 등으로 서로 변환(Conversion)할 수 있는 Unified curve modeling( 곡선모델링 단일화) 기법을 정립하였다. 곡면모델링의 경우, 곡면정의를 위하여 입력되는 그물망 곡선(Mesh curve net)을 먼저 Unified curve modeling 기법에 의하여 Interpolation(보간)한 후, "Remeshing" (그물망 곡선의 재생성)기법에 의하여 Gregory surface patch(그레고리 곡면 patch)의 Mesh curve segment(경계 세그멘트 곡선)를 생성하고 이를 접속하여 순정도 높은 Composite surface(합성곡면)를 만드는 기법을 개발하였다.

• 한국산업정보학회:학술대회논문집
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• 한국산업정보학회 2002년도 춘계학술대회 논문집
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• pp.161-165
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• 2002

This paper describe a trajectory generation method for a soccer robot using cubic Bezier curve. It is proposed that the method to determine the location of control points. The control points are determined by the distance and the velocity parameters of start and target positions. Simulation results show its traceability of the trajectory of mobile robot.