• 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.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.

• 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.

• 한국CDE학회논문집
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• 제2권2호
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• pp.122-129
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• 1997

Ball rolling blending is a popular technique for blending between parametric surfaces. The ball rolling blend surface is conceptually a trajectory of a ball rolling between two base sufaces. It is constructed by sweeping a circular arc along a ball contact curve pair. Since a ball rolling blend surfaces does not have a polynomial form like a Bezier surface patch, it is impossible to apply this method directly to a commercial CAD/CAM system. In this paper an algorithm is developed to approximate a ball rolling blend surface into Bezier surface patches. Least square method is applied to obtain proper Bezier surface patches under a given tolerance. The Bezier surface patches have degree three or more and guarantee VC1-continuity.

• 제어로봇시스템학회논문지
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• 제19권12호
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• pp.1152-1159
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• 2013

This paper proposes an effective walking system for a hexapod robot on uneven terrain. To overcome the deficiencies of two-pair walking systems, which are effective on even terrain, the use of only three legs changes the steps required for movement. The proposed system receives feedback data from switches attached to the bottom of the legs and gyro sensor to carry out stable walking using the Bezier curve algorithm. From the coordinates of the Bezier curve, which guarantees the circular motion of legs, the motor's angle value can be obtained using inverse kinematics. The angle values are sent to each motor though RS-485 communication. If a switch is pushed by the surface during navigation in the Bezier curve pattern, the robot is designed to change its circular course. Through the changed course, each leg can be located on an optimal surface and the wobble phenomenon is reduced by using a normal vector algorithm. The simulation and experiment results show the efficiency of the proposed algorithm.

• 한국전산유체공학회지
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• 제10권3호
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• pp.27-35
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• 2005

A design optimization of hypersonic flight vehicle has been studied by using upwind Navier-Stokes method and numerical optimization method. CFD method is linked to numerical optimization method by using a Bezier curve and a design optimization of blunt nose hypersonic flight vehicle has been studied. Heat transfer coefficient and drag coefficient are selected as objective functions or design constraints. The Bezier curve-based shape function was applied to blunt body shape.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2004년도 추계 학술대회논문집
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• pp.197-201
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• 2004

A design optimization of Sphere-Cone blunt nose hypersonic flight vehicle has been studied by using upwind Navier-Stokes method and numerical optimization method. Heat transfer coefficient and drag coefficient are selected as objective function or design constraint. Control points of Bezier curve are considered as design variable.

• 한국CDE학회논문집
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• 제7권4호
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• pp.269-279
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• 2002

Geometric shape morphing is an interesting geometric operation that interpolates two geometric shapes to generate in-betweens. It is well known that Minkowski operations can be used to test and build collision-free motion paths and to modify shapes in digital image processing. In this paper, we present a new geometric modeling technique to control the morphing on geometric shapes based on Minkowski sum. The basic idea develops from the linear interpolation on two geometric shapes where the traditional algebraic sum is replaced by Minkowski sum. We extend this scheme into a Bezier-like control structure with multiple control shapes, which enables the interactive control over the intermediate shapes during the morphing sequence as in the traditional CAGD curve/surface editing. Moreover, we apply the theory of blossoming to our control structure, whereby our control structure becomes even more flexible and general. In this paper, we present mathematical models of control structure, their properties, and computational issues with examples.

• 대한산업공학회지
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• 제20권2호
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• pp.77-90
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• 1994

Curve-net interpolation surface is one of the most popular method in engineering design. Therefore it is supported with many commercial CAD/CAM system. However, construction algorithm of curve-net interpolation surfaces is rarely opened to the public because of its copy-right. In this paper we establish a construction algorithm of curve-net interpolation surface so called sweeping surface which especially concentrates on trajectory of cross-section curve. We also show the method which can construct sweeping surfaces as NURB or Bezier mathematical models. Surfaces having the form of standard mathematical models are very useful for the application of joining, trimming, blending etc. The proposed surface interpolation scheme consists of four steps; (1) preparation of guide curves and section curves, (2) remeshing guide curves and section curves, (3) blending section curves after deformation, and (4) determination of control points for sweeping surface using gordon method. The proposed method guarantee $G^1$-continuety, and construct the surface salifying given section curves and trajectory of section curves.

• 한국공작기계학회:학술대회논문집
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• 한국공작기계학회 2005년도 춘계학술대회 논문집
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• pp.115-124
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• 2005

This paper analyzes the problems that occurred in the magnification process for a fine input image and investigates a method to improve the problems. This paper applies a curve interpolation algorithm in CAD/CAM for the same test images with the existing image algorithm in order to improve the problems. As a result. the nearest neighbor interpolation. which is the most frequently applied algorithm for the existing image interpolation algorithm. shows that the identification of a magnified image is not possible. Therefore. this study examines an interpolation of gray-level data by applying a low-pass spatial filter and verifies that a bilinear interpolation presents a lack of property that accentuates the boundary of the image where the image is largely changed. The periodic B-spline interpolation algorithm used for curve interpolation in CAD/CAM can remove the blurring but shows a problem of obscuration, and the Ferguson's curve interpolation algorithm shows a more sharpened image than that of the periodic B-spline algorithm. For the future study, hereafter. this study will develop an interpolation algorithm that has an excel lent improvement for the boundary of the image and continuous and flexible property by using the NURBS. Ferguson's complex surface. and Bezier surface used in CAD/CAM engineering based on. the results of this study.