• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.7 no.5
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• pp.15-28
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• 1998

Recently may investigations have been studied on the high-speed machining by using machine tools. A CNC machine tool makes some tool path errors caused by software acceleration/deceleration. The faster a cutting feedrate is, the bigger the tool path errors are. Some known methods reduce these kinds of errors, but they make the total cutting time increased. This paper presents a feed-forward algorithm that can be generated by distorting the original tool path, and reduces the tool path errors and the total cutting time. The algorithm to generate a new tool path is represented as following; 1)calculating each distance of software acceleration/deceleration between two adjacent blocks, 2) estimating the distorted distance which is the adjacent-ratio-constant(k1, k2) multiply the distance of software acceleration/deceleration, 3) generating a 3-degree Bezier curve approximating the distorted tool path, 4) symmetrically transforming the Bezier curve about the intersection point between two blocks, and 5) connecting the transformed Bezier curve with the original tool path. The algorithm is applied to FANUC 0M. The study is to promote the high-precision machining and to reduce the total cutting time.

• Communications of the Korean Mathematical Society
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• v.22 no.4
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• pp.641-648
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• 2007

In this paper, we present the exact Hausdorff distance between the offset curve of quadratic $B\'{e}zier$ curve and its quadratic $GC^1$ approximation. To illustrate the formula for the Hausdorff distance, we give an example of the quadratic $GC^1$ approximation of the offset curve of a quadratic $B\'{e}zier$ curve.

• Communications of the Korean Mathematical Society
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• v.9 no.1
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• pp.253-259
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• 1994

• Korean Journal of Computational Design and Engineering
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• v.3 no.3
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• pp.183-191
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• 1998

There are many available algorithms based on the different approaches to solve the intersection problems between two curves. Among them, the implicitization method is frequently used since it computes precise solutions fast and is robust in lower degrees. However, once the degrees of curves to be intersected are higher than cubics, its computation time increases rapidly and the numerical stability gets worse. From this observation, it is natural to transform the original problem into a set of easier ones. Therefore, curves are subdivided appropriately depending on their geometric behavior and approximated by a set of rational quadratic Bezier cures. Then, the implicitization method is applied to compute the intersections between approximated ones. Since the solutions of the implicitization method are intersections between approximated curves, a numerical process such as Newton-Raphson iteration should be employed to find true intersection points. As the seeds of numerical process are close to a true solution through the mix-and-match process, the experimental results illustrates that the proposed algorithm is superior to other algorithms.

• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• 2005.05a
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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.

• Journal of applied mathematics & informatics
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• v.3 no.2
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• pp.245-252
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• 1996

We described a relationship of the $L_2$ norm of the $L_2$norm of a Bzier curve and l2 norm of its confrol points. The use of Bezier curves finds much application in the general description of curves and surfaces and provided the mathematical basis for many computer graphics system. We define the $L_2$ norm for Bezier curves and find a upper and lower bound for many computer graphics system. We define the $L_2$ norm for Bezier curves and find a upper and lower bound for the $L_2$ norm with respect to the $L_2$ norm for its control points for easy computation.

• Proceedings of the IEEK Conference
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• 2002.06c
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• pp.17-20
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• 2002

This paper proposes a new 75 fuzzy model approximation method which reduces error in nonlinear fuzzy model approximation over the V-type decision rules. Employing rational Bezier curves used in computer graphics to represent curves or surfaces, the proposed method approximates the decision rule by constructing a tractable linear equation in the highly non-linear fuzzy rule interval. This algorithm is applied to the self-adjusting air cushion for spinal cord injury patients to automatically distribute the patient's weight evenly and balanced to prevent decubitus. The simulation results indicate that the performance of the proposed method is bettor than that of the conventional TS Fuzzy model in terms of error and stability.

• Kyungpook Mathematical Journal
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• v.58 no.2
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• pp.333-346
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• 2018

An approximation scheme utilizing Bezier curves is considered for solving time-delayed optimal control problems with terminal inequality constraints. First, the problem is transformed, using a $P{\acute{a}}de$ approximation, to one without a time-delayed argument. Terminal inequality constraints, if they exist, are converted to equality constraints. A computational method based on Bezier curves in the time domain is then proposed for solving the obtained non-delay optimal control problem. Numerical examples are introduced to verify the efficiency and accuracy of the proposed technique. The findings demonstrate that the proposed method is accurate and easy to implement.

• 제어로봇시스템학회:학술대회논문집
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• 1991.10b
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• pp.1601-1606
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• 1991

We present an algorithm to approximate the Voronoi diagrams of 2D objects bounded by algebraic curves. Since the bisector curve for two algebraic curves of degree d can have a very high algebraic degree of 2 * d$^{4}$, it is very difficult to compute the exact algebraic curve equation of Voronoi edge. Thus, we suggest a simple polygonal approximation method. We first approximate each object by a simple polygon and compute a simplified polygonal Voronoi diagram for the approximating polygons. Finally, we approximate each monotone polygonal chain of Voronoi edges with Bezier cubic curve segments using least-square curve fitting.

• Korean Journal of Computational Design and Engineering
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• v.4 no.4
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• pp.350-354
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• 1999

The problem of the computation of derivatives arises in various applications of rational Bezier curves. These applications sometimes require the computation of derivative on numerous points. Therefore, many researches have dealt with the representation for the computation of derivatives with the small computation error. This paper compares the performances of the representations for the derivative of rational Bezier curves in the performances. The performance is measured as computation requirements at the pre-processing stage and at the computation stage based on the theoretical derivation of computational bound as well as the experimental verification. Based on this measurement, this paper discusses which representation is preferable in different situations.