• Journal of Information Processing Systems
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• 제4권4호
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• pp.153-158
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• 2008

This paper deals with the geometric fitting algorithms for parametric curves and surfaces in 2-D/3-D space, which estimate the curve/surface parameters by minimizing the square sum of the shortest distances between the curve/surface and the given points. We identify three algorithmic approaches for solving the nonlinear problem of geometric fitting. As their general implementation we describe a new algorithm for geometric fitting of parametric curves and surfaces. The curve/surface parameters are estimated in terms of form, position, and rotation parameters. We test and evaluate the performances of the algorithms with fitting examples.

• 한국CDE학회논문집
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• 제4권1호
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• pp.32-42
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• 1999

Approximate lofting or skinning is one of practical surface modeling techniques well used in CAD and reverse engineering applications. Presented in this paper is a method for approximately lofting a given set of curves wihin a specified tolereance. It is based on refitting input curves simultaneously on a common knot vector and interpolating them to get a resultant NURBS surface. A concept of reducing the number of interior knots of the common knot vector is well adopted to acquire more compact representation for the resultant surface. Energy minimization is newly introduced in curve refitting process to stabilize the solution of the fitting problem and get more fair curve. The proposed approximate lofting provides more smooth surface models and realizes more efficient data reduction expecially when the parameterization and compatibility of input curves are not good enough. The method has been successfully implemented in a new CAD/CAM product VX Vision? of Varimetrix Corporation.

• 정보처리학회논문지A
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• 제8A권1호
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• pp.42-47
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• 2001

In this paper, we present a curve fitting algorithm using a ball curve. Our algorithm is recursive method for fitting, which is not a traditional ball function but a continuous ball function. This algorithm consists of two steps. The first step, it is classified the composite corner points to joint points until selected from the given data set. The second step is the curve fitting. The basis function for curve fitting is use to ball function. Also, the weighted least square method, to insert knot, is an efficient method for piecewise ball curve and ball curve segments will be smoothly connected at all composit points. The proposed algorithm will be applied to represent image representation, like fonts, digital image and GIS.

• 한국공작기계학회:학술대회논문집
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• 한국공작기계학회 1997년도 추계학술대회 논문집
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• pp.230-234
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• 1997

Reverse engineering involves digitizing a three-dimensional model or part converting the data to a CAD database description and manufacturing by CNC. Currently, the digitization is done through measurements taken manually by a CMM or touch probe mounted on a CNC machinetool. Some reverse engineering techniques require close integration between the data collection method and the surface-fitting algorithms. Accurate surface data are collected by input to the surface fitting method. This study has been found that both the smoothness of surfaces and accuracy of surface fitting are related with the degree of the interpolated surfaces.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 2001년도 춘계학술대회 논문집
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• pp.426-429
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• 2001

Many various products are manufactured which have sculptured surfaces recently. Constructing surface of these models is required technique called reverse engineering. In reverse engineering, a product which has sculptured surfaces is measured and we create surface model to acquire complete model data of object. Measured point data needs preprocess and sampling. Next a set of point data in a plane fit section curve. At last, surface is generated by fitting to section curves. Here we uses sweep surface. Sweep surface is compatible fitting CAD model to drawing. This paper discusses converting approximation of NURBS surface as a standard surface.

• 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.

• Current Optics and Photonics
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• 제7권6호
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• pp.701-707
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• 2023

In laser imaging, accurate extraction of the laser's center is essential. Several methods exist to extract the laser's center in an image, such as the geometric mean, the parabolic curve fitting, and the Gaussian curve fitting, etc. The Gaussian curve fitting is the most suitable because it is based on the physical properties of the laser. The width of the Gaussian laser beam depends on the distance from the laser source to the target object. It is assumed in general that the distance remains constant at a laser spot resulting in a symmetric Gaussian model for the laser image. However, on a curved surface of the object, the distance is not constant; The laser beam is narrower on the side closer to the focal point of the laser light and wider on the side closer to the laser source, which causes the distribution of the laser beam to skew. This study presents a modified Gaussian model in the laser imaging to incorporate the slant angle of a curved object. The proposed method is verified with simulation and experiments.

• 공업화학
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• 제5권4호
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• pp.580-587
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• 1994

고정층 상압 유통식 반응기에서 메탄의 전화율 10% 미만의 범위에서 $Na^+(50wt%)/MgO$ 촉매를 사용하여 반응온도 710, 730, 750, 770, $790^{\circ}C$에서 메탄과 산소의 분압을 변화시켜 가면서 메탄의 oxidative coupling반응을 수행하여 이산화탄소와 에탄의 생성속도를 구하고 curve fitting으로 속도식을 증명하였다. Langmuir-Hinshelwood, Rideal-Redox, Eley-Rideal형 반응 메카니즘 중에서 Langmuir-Hinshelwood형 반응 메카니즘이 실험 결과와 가장 잘 일치하였으며, $CH_3{\cdot}$의 생성에 관여하는 산소종은 촉매 표면의 $O_2{^-}$ 또는 $O_2{^{2-}}$으로 제시할 수 있었고, 이때의 활성화 에너지는 약 39.3kcal/mol이었다. 또한, curve fitting결과 $CO_x$을 생성하는 산소의 화학 양론계수 x는 약 1.5이었으며, 이로부터 $CH_3{\cdot}$의 일부가 표면산소에 의해서 산화반응을 거쳐 $CH_3O_2{\cdot}*$ 형성을 추측할 수 있었다.

• 한국윤활학회:학술대회논문집
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• 한국윤활학회 1998년도 제28회 추계학술대회
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• pp.300-305
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• 1998

A method of calculating wear amount which is based on digitally measured surface profile was suggested. The original profile of worn out profile was estimated from its adjacent surface profile by using least squares curve fitting with Fourier series. The approximated curve was well fitted to original surface profile. With this approach, more accurate calculation of the wear amount will be possible.

• Advances in Energy Research
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• 제1권1호
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• pp.35-52
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• 2013

A model for DMFC anode performance is developed. The model takes into account potential--independent methanol adsorption on the catalyst surface, finite rate of proton transport through the anode catalyst layer (ACL), and a potential loss due to methanol transport in the anode backing layer. An approximate analytical half--cell polarization curve is derived and equations for the anode limiting current density are obtained. The polarization curve is fitted to the curves measured by Nordlund and Lindbergh and parameters resulted from the fitting are discussed.