• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2010.05a
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• pp.389-392
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• 2010

In this paper, it presents to detect location using structural information of hand from the input color images on Webcam and to recognize hand gestures. In this system, based on the skin color, the image changes a binary number and labels. Within each labeled area, we can find the Maximum Inscribed Circle using Voronoi Diagram. This circle can find the center of hand. And the circle extracts hand region from analyzing the ellipse elements to relate Maximum Inscribed Circle. We use the Maximum Inscribed Circle and the ellipse elements as characteristic of hand gesture recognition. In various environments, we cannot recognize the object that have similar colors like the background colors. But the proposed algorithm has the advantage that can be effectively eliminated about it.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2010.10a
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• pp.281-284
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• 2010

In this paper, we present Hand-gesture recognition for actual computing into color images from camera. Color images are binarization and labeling by using the YCbCr Color model. Respectively label area seeks the center point of the hand from to search Maximum Inscribed Circle which applies Voronoi-Diagram. This time, searched maximum circle and will analyze the elliptic ingredient which is contiguous so a hand territory will be able to extract. we present the presentation contral system using elliptic element and Maximum Inscribed Circle. This algorithm is to recognize the various environmental problems in the hand gesture recognition in the background objects with similar colors has the advantage that can be effectively eliminated.

• Honam Mathematical Journal
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• v.34 no.1
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• pp.103-111
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• 2012

Wetzel[5] proved if ${\Gamma}$ is a closed curve of length L in $E^n$, then ${\Gamma}$ lies in some ball of radius [L/4]. In this paper, we generalize Wetzel's result to the non-Euclidean plane with much stronger version. That is to develop a lower bound of length of a triangle inscribed in a circle in non-Euclidean plane in terms of a chord of the circle.

• Journal for History of Mathematics
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• v.27 no.6
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• pp.395-402
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• 2014

When the circle inscribed in a square is projected to a picture plane, one sees, in general, an ellipse in a convex quadrilateral. This ellipse is poorly described in the works of Alberti and Durer. There are one parameter family of ellipses inscribed in a convex quadrilateral. Among them only one ellipse is the perspective image of the circle inscribed in the square. We call this ellipse "the projected ellipse." One can easily find the four tangential points of the projected ellipse and the quadrilateral. Then we show how to find the center of the projected ellipse. Finally, we describe a pair of conjugate vectors for the projected ellipse, which finishes the construction of the desired ellipse. Using this algorithm, one can draw the perspective image of the squared-circle tiling.

• Journal of Institute of Control, Robotics and Systems
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• v.20 no.10
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• pp.1057-1062
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• 2014

This paper proposes a tip-over detection method for a mobile robot using a support inscribed circle defined as an inscribed circle of a support polygon. A support polygon defined by the contact points between the robot and the terrain is often used to analyze the tip-over. For a robot moving on uneven terrain, if the intersection between the extended line of gravity from the robot's COG and the terrain is inside the support polygon, tip-over will not occur. On the contrary, if the intersection is outside, tip-over will occur. The terrain is detected by using an RGB-D sensor. The terrain is locally modeled as a plane, and thus the normal vector can be obtained at each point on the terrain. The support polygon and the terrain's normal vector are used to detect tip-over. However, tip-over cannot be detected in advance since the support polygon is determined depending on the orientation of the robot. Thus, the support polygon is approximated as its inscribed circle to detect the tip-over regardless of the robot's orientation. To verify the effectiveness of the proposed method, the experiments are carried out using a 4-wheeled robot, ERP-42, with the Xtion RGB-D sensor.

• 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.

• 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.

• Honam Mathematical Journal
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• v.40 no.1
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• pp.83-91
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• 2018

We consider the existence problem of inscribed n-gons ($n{\geq}5$) in a circle and find a necessary condition on exterior angles $a_1,\;{\cdots},\;a_n$ of an inscribed n-gon. Conversely, we show that this condition is sufficient for an inscribed polygon with exterior angles $a_1,\;{\cdots},\;a_n$ in this cyclic order to exist.

• Journal of the Korean School Mathematics Society
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• v.20 no.4
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• pp.445-464
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• 2017

This study targeting 10 high school 3rd grade students who have studied space figures in natural sciences track analyzes the process of analogical discovery from the construction of inscribed and circumscribed circles of a triangle to that of inscribed and circumscribed spheres of a tetrahedron through the analytical method using Geogebra. The subjects are divided into two groups of five, the experimental group consisting of those who have experienced analytical method and the comparative group consisting of those who haven't. This research analyzing the process of constructing inscribed and circumscribed spheres of a tetrahedron. Although students of both groups all have an accurate preliminary knowledge of inscribed and circumscribed circles of a triangle, they have difficulty in constructing inscribed and circumscribed spheres of a tetrahedron. However, the students of experimental group who have studied the constructing process of inscribed and circumscribed circles of a triangle in reverse using analytical method and Geogebra can perform analogical discovery finding out the way to construct inscribed and circumscribed spheres of a tetrahedron using analogy by themselves. They can control and explore space figures by visualization. Also, they can immediately examine and provide feedback on the analogizing process of their own. In addition, the process affects the attitude of students toward mathematics positively as well as gives validity to the result of analogy.

• Journal of Korean Society of Transportation
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• v.35 no.5
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• pp.385-395
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• 2017

This study deals with the small-scale roundabout. The purpose of this study is to analyze the average delay of vehicle in roundabout, and suggest the efficient planning and design standard. In pursuing the above, this study gives particular attentions to analyzing the average delay time according to the inscribed circle diameter, speed of circulatory roadway lane and traffic volume. The operational efficiencies of 96 scenarios (3 sizes of inscribed circle diameter ${\times}$ 4 types of circulatory roadway speed ${\times}$ traffic volume) are analyzed using VISSIM (Verkehr In $St{\ddot{a}}dten$-SIMulationsmodell). The main results are as follows. First, the optimal design speed of small-scale roundabout are derived from the above scenario analysis. Second, the traffic volume of LOS D is estimated to be 2,180-2,740pcph. Third, the traffic volume of LOS F that is required to improve is above 2.780pcph. The results might be expected to give some implications to providing the countermeasures for the operational efficiency of roundabout.