• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.20 no.2
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• pp.151-161
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• 2016

In this paper, we present a $C^3$ quartic B-spline approximation of circular arcs. The Hausdorff distance between the $C^3$ quartic B-spline curve and the circular arc is obtained in closed form. Using this error analysis, we show that the approximation order of our approximation method is six. For a given circular arc and error tolerance we find the $C^3$ quartic B-spline curve having the minimum number of control points within the tolerance. The algorithm yielding the $C^3$ quartic B-spline approximation of a circular arc is also presented.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.17 no.3
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• pp.171-179
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• 2013

In this paper we present a method of circular arc approximation by quartic B$\acute{e}$zier curve. Our quartic approximation method has a smaller error than previous quartic approximation methods due to the alternation of the error function of our quartic approximation. Our method yields a closed form of error so that subdivision algorithm is available, and curvature-continuous quartic spline under the subdivision of circular arc with equal-length until error is less than tolerance. We illustrate our method by some numerical examples.

• Journal of KIISE:Software and Applications
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• v.32 no.9
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• pp.868-877
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• 2005

Arcs are usually treated as significant features in the field of pattern recognition. This paper presents a method to detect arcs from digital planar curves and estimate their arc centers and radii by using geometric analysis. The deviation of distance between the original curve and the detected arc by the proposed method does not exceed a tolerant error. The experimental results show that the proposed method is available for the detection of arcs iron not only smooth but also heavily noisy curves.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2001.04a
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• pp.975-978
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• 2001

For machining auto-mobile cam, the developed biarcs-fitting method eliminates the ridge problems in conventional straight-line fitting approximation or single-arc fitting of curve tool path where it leaves ridges of tool marks on the machined surface of the workpiece. The powerful advantage of this biarc method is demonstrated by applying it to the numerically controlled machining of a curved cam profile, also verified by using a CNC simulating program for auto-mobile cam profile. As a result, this algorithm may be used in CNC milling and turning for cam profile machining with short block line.

• Journal of Power System Engineering
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• v.5 no.2
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• pp.43-49
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• 2001

For machining auto-mobile cam, the developed biarcs-fitting method eliminates the ridge problems in conventional straight-line fitting approximation or single-arc fitting of curve tool path where it leaves ridges of tool marks on the machined surface of the workpiece. The powerful advantage of this biarc method is demonstrated by applying it to the numerically controlled machining of a curved cam profile, also verified by using a CNC simulating program for auto-mobile cam profile. As a result, this algorithm may be used in CNC milling and turning for cam profile machining with short block line.

• Korean Journal of Computational Design and Engineering
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• v.2 no.2
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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.