• Communications of the Korean Mathematical Society
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• v.37 no.4
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• pp.1259-1267
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• 2022

In this paper we present a full circle approximation method using parametric polynomial curves with algebraic coefficients which are curvature continuous at both endpoints. Our method yields the n-th degree parametric polynomial curves which have a total number of 2n contacts with the full circle at both endpoints and the midpoint. The parametric polynomial approximants have algebraic coefficients involving rational numbers and radicals for degree higher than four. We obtain the exact Hausdorff distances between the circle and the approximation curves.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.9 no.1
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• pp.68-74
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• 2000

The STL file format is an approximation of 3-D model with triangular facets. STL is a standard input file format of Rapid Prototyping(RP) equipment In computer graphics a circle has been approximated with an inscribed polygon which causes an error between the real and approximated circles. In this study an intersecting polygon has been used to approximate the circle and applied to produce more accurate RP part. The newly proposed method shows it's excellence in part accuracy.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.18 no.12
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• pp.2953-2960
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• 2014

In the field of image recognition, circle detection is one of the most widely used techniques. Conventional algorithms are mainly based on Hough transform, which is the most straightforward algorithm for detecting circles and for providing enough robust algorithm. However, it suffers from large memory requirements and high computational loads, and sometimes tends to detect incorrect circles. This paper proposes an optimal circle detection and approximation method which is applicable for inspecting fiber optic connector endface. The proposed method finds initial center coordinates and radius based on the initial edge lines. Then, by introducing the simplified K-means algorithm, the proposed method investigates a substitute-circle by minimizing the area of non-overlapped regions. Through extensive simulations, it is shown that the proposed method can improve the error rate by as much as 67% and also can reduce the computing time by as much as 80%, compared to the Hough transform provided by the OpenCV library.

• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• 1999.05a
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• pp.81-86
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• 1999

The STL file format is an approximation of 3-D model with triangular facets. STL is a standard input file format of Rapid Prototyping(RP) equipment. In computer graphics, a circle has been approximated with an inscribed polygon, which causes an error between the real and approximated circles. In this study, an intersecting polygon has been used to approximate the circle and applied to produce more accurate RP part. The newly proposed method shows it's excellence in part accuracy.

• School Mathematics
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• v.16 no.4
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• pp.763-782
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• 2014

The purpose of this study is to investigate mathematics content knowledge(MCK) of pre-service teachers about the area of a circle. 53 pre-service teachers were asked to perform four tasks based on the central ideas of measurement for the area of a circle. The results of this study are as follows. First, pre-service teachers had some difficulty in describing the meaning of the area of a circle. Quite a few of them didn't recognize the necessity of counting the number of area units. Secondly, pre-service teachers had insufficient content knowledge about the central ideas of measurement for the area of a circle such as partitioning, unit iteration, rearranging, structuring an array and approximation. Lastly, few pre-service teachers understood the concept of actual infinity. Most students regarded the rectangle as the figure having the approximation error instead of the limitation from rearranging the parts of a circle.

• Journal of Integrative Natural Science
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• v.9 no.1
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• pp.10-15
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• 2016

In this paper the approximation methods of offset curve of conic with explicit error bound are considered. The quadratic approximation of conic(QAC) method, the method based on quadratic circle approximation(BQC) and the Pythagorean hodograph cubic(PHC) approximation have the explicit error bound for approximation of offset curve of conic. We present the explicit upper bound of the Hausdorff distance between the offset curve of conic and its PHC approximation. Also we show that the PHC approximation of any symmetric conic is closer to the line passing through both endpoints of the conic than the QAC.

• 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.

• Communications of Mathematical Education
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• v.26 no.1
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• pp.137-154
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• 2012

Approximation' is one of central conceptions in calculus. A basic conception for explaining 'approximation' is 'tangent', and 'tangent' is a 'line' with special condition. In this study, we will study pedagogically these mathematical knowledge on the ground of a viewpoint on the teaching of secondary geometry, and in connection with these we will suggest the teaching program and the chief end for the probable teaching. For this, we will examine point, line, circle, straight line, tangent line, approximation, and drive meaningfully mathematical knowledge for algebraic operation through the process translating from the above into analytic geometry. And we will construct the stream line of mathematical knowledge for approximation from a view of modern mathematics. This study help mathematics teachers to promote the pedagogical content knowledge, and to provide the basis for development of teaching model guiding the mathematical knowledge. Moreover, this study help students to recognize that mathematics is a systematic discipline and school mathematics are activities constructed under a fixed purpose.

• Journal of the Institute of Electronics Engineers of Korea TE
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• v.39 no.1
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• pp.37-45
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• 2002

This paper proposes new features for recognizing telltale bulb in a cluster. A typical feature employed in model-based pattern recognition is polygonal approximation points of object. But recognition using these dominant points has many mismatching counts in small model such as telltale bulb. To reduce mismatching counts, proposed features are the circle distribution of object pixel and the ratio of distance from center to boundary in object. This Paper also proposes new decision function using three features. In simulation result, we make a comparison mismatching counts between recognition using dominant points and the new recognition algorithm using three features.