• The Transactions of the Korea Information Processing Society
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• v.7 no.9
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• pp.3019-3028
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• 2000

One of the most frequently used spline scheme in CAD and graphics package is Bezier curve. Although simple and easy to implement, it supports diverse kinds of curves and surfaces. In view of the design convenience, the main advantage of the Bezier curves is that they observe user-specified slope conditions at both endpoints while maintaining smoothness. This paper expands the advantage by deriving equations for generalized Bezier curves, and applying the equation to observe additional slope condition at midpoint. This is possible by decomposing and analyzing the user-specified midpoint slope, and reflecting the result back into the Bezier basis matrix in parametric form. Consequently, users can control the curve shapes not only by the endpoint slope handles but also at the midpoint slope handle, which helps them to be able to apply more accurate control over the conventional Bezier curve shapes.

• Communications for Statistical Applications and Methods
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• v.21 no.1
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• pp.105-114
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• 2014

In this paper we suggest an efficient method to estimate the distribution function using the Bezier curve, and compare it with existing methods by simulation studies. In addition, we suggest a robust version of cross-validation criterion to estimate the number of Bezier points, and showed that the proposed method is better than the existing methods based on simulation studies.

• The Korean Journal of Applied Statistics
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• v.25 no.6
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• pp.1049-1058
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• 2012

Nonparametric methods are often used as an alternative to parametric methods to estimate density function and regression function. In this paper we consider improved methods to select the Bezier points in Bezier curve smoothing that is shown to have the same asymptotic properties as the kernel methods. We show that the proposed methods are better than the existing methods through numerical studies.

• Transactions of the Korean Society of Machine Tool Engineers
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• v.13 no.3
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• pp.113-118
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• 2004

In this paper, we propose a new weaving trajectory algorithm for the arc welding of a articulated manipulator. The algorithm uses the theory of Bezier spline. We make a comparison between the conventional algorithms using Catmull-Rom curve and the new algorithms using Bezier spline. The proposed algorithm has been evaluated based on the MATLAB environment in order to illustrate its good performance. Through simulations, the proposed algorithm can result in high-speed and flexible weaving trajectory planning so that it's trajectory cannot penetrate into a base metal compared to the conventional algorithm using Catmull-Rom curve.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2003.06a
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• pp.1760-1763
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• 2003

In this paper, we propose a new weaving trajectory algorithm for the are welding of a articulated manipulator. The algorithm uses the theory of Bezier spline. We make a comparison between the conventional algorithms using Catmull-Rom curve and the new algorithms rising Bezier spline. The proposed algorithm has been evaluated based on the MATLAB environment in order to illustrate its good performance. The algorithm has been implemented on to the industrial manipulator of DR6 so as to show its real possibility. Through simulations and real implementations, the proposed algorithm can result in high-speed and flexible weaving trajectory planning and can reduce the processing time because it needs one-half calculation compared to the conventional algorithm using Catmull-Rom curve.

• Proceedings of the KIEE Conference
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• 2002.07d
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• pp.2472-2474
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• 2002

This paper describe a trajectory generation method for a two-wheeled mobile robot using cubic Bezier curve. It is proposed that the method to determine the location of control points which mainly affect the shape of curve, and constrains for two-wheeled mobile are examined. Simulation results show its traceability of the trajectory of mobile robot.

• Proceedings of the Optical Society of Korea Conference
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• 2007.02a
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• pp.265-266
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• 2007

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2010.11a
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• pp.39-40
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• 2010

• The Journal of Korean Institute of Communications and Information Sciences
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• v.21 no.8
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• pp.1861-1873
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• 1996

This paper describes the content-based image retrieval system that is implemented to retrieve images using constituent rate of lines and Bezier curves. We proposed the line and Bezier curve extraction algorithm which extracts lines and curve that are fitted on the contour information of images. For this extration, it was necessary to remove internal area of the proprocessed object within images and to approximate its contour to polygon, and proposed retrevial algorithm which gets the simularity using the consitituent rate of lines and curves and perform the simularity matching.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.31B no.5
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• pp.1-11
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• 1994

In computer graphics since objects atre constructed by lines and curves, the high-speed curve generator is indispensible for computer aided design and simulatation. Since the functions of graphic generation can be represented as a series of matrix operations, in this paper, two kind of the high-speed Bezier curve generator that uses matrix equation and a recursive relation for Bezier polynomials are designed. And B-spline curve generator is designed using interdependence of B-spline blending functions. As the result of the comparison of designed curve generator and reference [5], [6] in the operation time and number of operators, the curve generator with 1-dimensional systolic array processor for matrix vector operation that uses matrix equation for Bezier curve is more effective.