• Journal of Information Processing Systems
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• v.4 no.4
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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.

• Journal of the Korean Society for Precision Engineering
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• v.16 no.4 s.97
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• pp.129-137
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• 1999

A parametric curve interpolator has been proposed for machining curves instead of a linear interpolator in which curves are approximated by a set of line segment. The parametric curve interpolator is superior to linear interpolator in machining time and contour error and generate exact position commands directly from curve equations. In this paper, a new toolpath generation method is proposed based on the parametric curve interpolator. This method retains all the benefits of parametric curve interpolator and can bound the scallop height within a specified value. By interpolating curves and surfaces directly from the mathematical equations, the amount of data from CAD/CAM system to CNC controller can be significantly reduced. The proposed method was implemented on a CNC controller and was confirmed to give a better result than the other existing method.

• International Journal of Precision Engineering and Manufacturing
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• v.9 no.2
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• pp.84-92
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• 2008

Free-form shapes which were once considered as an aesthetic feature are now an important functional requirement. CNC industries are looking for a compact solution for reproducing free-form shapes as conventional interpolation models are inadequate, The parametric curve interpolator developed in the last decade has clearly emerged as favorite among its contemporaries in recent years, At present intense research has been done on parametric curve interpolators and interesting developments are reported. Out of the various parametric representations for curves and surfaces, NURBS has been standardized and widely used in free-form shape design. This paper presents a review of various methods of parametric interpolation for NURBS and discusses the salient features, problems and solutions. Recent approaches on variable feedrate interpolation, parameter compensation are also reviewed and research trends are addressed finally.

• Communications of the Korean Mathematical Society
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• v.10 no.2
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• pp.483-490
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• 1995

A parametric cubic spline interpolating at fixed number of nodes is constructed by formulating a parametric cubic $g^2$ B-splines $S_3(t)$ with not equally spaced parametric knots. Since the fact that each component is in $C^2$ class is not enough to provide the geometric smoothness of parametric curves, the existence of $S_3(t)$ oriented toward the modified second-order geometric continuity is focalized in our work.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.5 no.4
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• pp.47-52
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• 1996

The interpolator is very important in CNC machines. This study proposed a parametric curve interpolator(PCI) which can be used for machining any sculptured surface represented in a parametric form and generates commands for tool motion between CAD data points according to given accuracy demands. The proposed interpolator is superior to the existing linear interpolator in accuracy, feed rate and acceleration continuity. Moreover in comparison to the recently developed cubic spline interpolator, the PCI has the capability of handling higher order parametric curves and also ensures precise tracking in the velocity domain. Results from real time simulations and experiments on open architecture CNC machines equipped with the proposed interpolator are presented to show its practical capagility. It is believed that the combination of the proposed interpolator and the open architecture machine controller further advances the area of command generation which is an important aspect of CAD/CAM.

• Journal of Korea Multimedia Society
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• v.19 no.11
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• pp.1900-1908
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• 2016

Recent times have seen the introduction of modeling technologies using implicit surface and marching cubes algorithm in the field of computer graphics. Implicit surface modeling is used to express characters or fluid. This study presents a calculation method for the density of curve skeletal primitives using parametric curve and implements an implicit surface modeling tool by utilizing Maya API. Skeletal primitives can be assembled and utilized in character modeling using the implemented modeling tool. Results could be obtained more effectively compared to existing particle-based methods.

• Journal of Ship and Ocean Technology
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• v.10 no.2
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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.

• Communications for Statistical Applications and Methods
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• v.13 no.2
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• pp.273-283
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• 2006

In bioassay, the response curve is usually assumed monotone increasing, but its exact form is unknown, so it is very difficult to select the proper functional form for the parametric model. Therefore, we should probably use the nonparametric regression model rather than the parametric model unless we have at least the partial information about the true response curve. However, it is well known that the nonparametric regression estimate is not necessarily monotone. Therefore the monotonizing transformation technique is of course required. In this paper, we compare the finite sample properties of the monotone transformation methods which can be applied to the local linear quasi-likelihood response curve estimate.

• International Journal of CAD/CAM
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• v.6 no.1
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• pp.59-64
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• 2006

A new method to obtain explicit re-parameterization that preserves the curve degree and parametric domain is presented in this paper. The re-parameterization brings a curve very close to the arc length parameterization under $L_2$ norm but with less segmentation. The re-parameterization functions we used are $C^1$ continuous piecewise rational linear functions, which provide more flexibility and can be easily identified by solving a quadratic equation. Based on the outstanding performance of Mobius transformation on modifying pieces with monotonic parametric speed, we first create a partition of the original curve, in which the parametric speed of each segment is of monotonic variation. The values of new parameters corresponding to the subdivision points are specified a priori as the ratio of its cumulative arc length and its total arc length. $C^1$ continuity conditions are imposed to each segment, thus, with respect to the new parameters, the objective function is linear and admits a closed-form optimization. Illustrative examples are also given to assess the performance of our new method.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10b
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• pp.896-899
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• 1996

A new algorithm for planning a collision free path is developed based on linear parametric curve. A collision-free path is viewed as a connected space curve in which the path consists of two straight curve connecting start to target point. A single intermediate connection point is considered in this paper and is used to manipulate the shape of path by organizing the control point in polar coordinate (.theta.,.rho.). The algorithm checks interference with obstacles, defined as GM (Geometry Mapping), and maps obstacles in Euclidean Space into images in CPS (Connection Point Space). The GM for all obstacles produces overlapping images of obstacle in CPS. The clear area of CPS that is not occupied by obstacle images represents collision-free paths in Euclidean Space. Any points from the clear area of CPS is a candidate for a collision-free path. A simulation of GM for number of cases are carried out and results are presented including mapped images of GM and performances of algorithm.