• School Mathematics
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• v.7 no.4
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• pp.391-402
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• 2005

The purpose of this study is to resolve misunderstanding for centroid of a triangle and to clarify several logical problems in finding the centroid of a Polygon. The conclusions are the followings. For a triangle, the misunderstanding that the centroid of a figure is the intersection of two lines that divide the area of the figure into two equal part is more easily accepted caused by the misinterpretation of a median. Concerning the equilibrium of a triangle, the median of it has the meaning that it makes the torques of both regions it divides to be equal, not the areas. The errors in students' strategies aiming for finding the centroid of a polygon fundamentally lie in the lack of their understanding of the mathematical investigation of physical phenomena. To investigate physical phenomena mathematically, we should abstract some mathematical principals from the phenomena which can provide the appropriate explanations for then. This abstraction is crucial because the development of mathematical theories for physical phenomena begins with those principals. However, the students weren't conscious of this process. Generally, we use the law of lever, the reciprocal proportionality of mass and distance, to explain the equilibrium of an object. But some self-evident principles in symmetry may also be logically sufficient to fix the centroid of a polygon. One of the studies by Archimedes, the famous ancient Greek mathematician, gives a solution to this rather awkward situation. He had developed the general theory of a centroid from a few axioms which concerns symmetry. But it should be noticed that these axioms are achieved from the abstraction of physical phenomena as well.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.50 no.8
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• pp.551-557
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• 2022

LRU (Line Replacement Unit) modifications are often required for military aircraft due to aging. Recently, LRU modifications were proceeded for KA-O (Armed Airborne Controller) by replacing the ejection seat and adding avionic equipment, which made the aircraft's operational CG (Center of Gravity) on fuel consumption curve become out of the range of the specification requested. The off-ranged CG should be corrected by introducing an appropriate method. This study proposes a procedure for revising and verifying the empty weight CG altered due to LRU modification for small military aircraft (e.g., KA-O). In the proposed method, first, the change of empty weight CG of KA-O due to the LRU modifications is comprehensively examined. Then, several ballast masses are added to the engine mount strut to restore the empty weight CG on the fuel consumption curve to a safe operational range. The installations are verified via stress and fatigue analysis for various operating conditions. Considering that open information is not very available for the revision of empty weight CG, this study is valuable because it presents an established procedure for correcting and verifying empty weight CG during aircraft modification.

• Journal of Korea Game Society
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• v.10 no.2
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• pp.49-56
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• 2010

In this paper, we propose a control method of virtual hand by the recognition of a user's hand in the virtual reality game environment. We display virtual hand on the game screen after getting the information of the user's hand movement and the direction thru input images by camera. We can utilize the movement of a user's hand as an input interface for virtual hand to select and move the object. As a hand recognition method based on the vision technology, the proposed method transforms input image from RGB color space to HSV color space, then segments the hand area using double threshold of H, S value and connected component analysis. Next, The center of gravity of the hand area can be calculated by 0 and 1 moment implementation of the segmented area. Since the center of gravity is positioned onto the center of the hand, the further apart pixels from the center of the gravity among the pixels in the segmented image can be recognized as fingertips. Finally, the axis of the hand is obtained as the vector of the center of gravity and the fingertips. In order to increase recognition stability and performance the method using a history buffer and a bounding box is also shown. The experiments on various input images show that our hand recognition method provides high level of accuracy and relatively fast stable results.

• Journal of Educational Research in Mathematics
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• v.26 no.3
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• pp.421-442
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• 2016

This study analyzed characteristics which emerged while 38 secondary school teachers observed a video clip about a centroid of triangles instruction. The aim of this study based on the analysis was to deduce implications in terms of the various means which would enhance teachers' knowledge in teaching mathematics and assist in designing mathematics education programs for teachers and professional development initiatives. To achieve this goal, this research firstly reviewed previous studies relevant to the 'Knowledge Quartet' as a framework of analyzing teachers' knowledge in mathematics instructions. Secondly, this study probed the observation results from the teachers in the light of the KQ. Therefore, some issues in the teacher education program for teaching mathematics were thirdly identified in the categories of 'Foundation', 'Transformation', 'Connection', and 'Contingency' based on the analysis. This research inspires the elaboration of what features have with regard to effective teachers' knowledge in teaching mathematics through the analyzing process and additionally the elucidation of essential matters related to mathematics education on the basis of the analyzed results.

• Smart Media Journal
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• v.5 no.3
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• pp.93-98
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• 2016

The literal meaning of loitering is "to lingering aimlessly or as if aimless in or about a place". And most criminals show this kind of act before they actually commit crime. Therefore, detecting this kind of loitering can effectively prevent a variety of crime. In this paper, we propose a loitering-detection algorithm using the Raspberry Pi. Proposed algorithm uses an adaptive difference image to detect moving objects and morphology opening operation to enhance the accuracy of detection. The loitering- behavior is being detected by using the center of gravity of the object to see the changes of angle; and pixel movement distance to determine the height of the object. When the loitering-behavior is detected, it outputs the alarm to tell the users by using the Raspberry Pi.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2001.12a
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• pp.173-176
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• 2001

본 논문은 영상 해석 알고리즘의 하나인 원형 패턴 벡터 알고리즘을 이용하여 손가락으로 커서를 제어하는 시스템을 구현하였다. 이 알고리즘을 적용하기 위하여 영상에서 손 영역에만 해당하는 최대 원을 여러 개 그린 후 가장 큰 원의 중심점을 무게 중심점으로 사용하였으며, 무게 중심점에서 손의 외곽까지의 거리를 구하여 가리키는 손가락을 찾도록 하였다. 화면상의 커서의 수평 방향은 가리키는 손가락 방향을 이용하여 평면 좌표로 해석하여 제어하였고, 수직 방향은 모니터 중앙 상단에 한대의 카메라를 사용하였기 때문에 손가락 길이를 이용하여 불연속적으로 상-중-하의 세 영역으로 제어하였다. 수직 방향의 커서이동이 불연속적이기 때문에, 구축한 인터페이스 화면의 범위를 축소한 후 축소된 범위를 전체 화면으로 확대해 나감으로써 사용자가 원하는 목표지점으로 커서를 이동시킬 수 있다.

• Journal of Educational Research in Mathematics
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• v.15 no.3
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• pp.335-352
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• 2005

In this paper, we consider a center of gravity of convex polygon which could be an enriched topic for the gifted in mathematics(7th grades) and suggested a case that the gifted experienced a center of gravity. Based on properties of Archimedes' center of mass, we define it as a point which make a polygon be in counterpoised with its area and explain how to find that point through using integral calculus or internal division. Then we consider that the gifted would experience various kinds of mathematical thinking and apply diverse ways of problem solving 3s searching for this topic. As this research, the teacher would be able to conduct the gifted with penetration into center of gravity and to let them participate in advanced learning courses which value ma-thematical thinking while they undergo similar experiences such as mathematicians.

• KIPS Transactions on Software and Data Engineering
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• v.11 no.12
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• pp.525-530
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• 2022

Although the iterative closest point (ICP) algorithm has been widely used to align two point clouds, ICP tends to fail when the initial orientation of the two point clouds are significantly different. In this paper, when two triangular meshes A and B have significantly different initial orientations, we present an algorithm to align them. After obtaining weighted centroids for meshes A and B, respectively, vertices that are likely to correspond to each other between meshes are set as feature points using the distance from the centroid to the vertices. After rotating mesh B so that the feature points of A and B to be close each other, RMSD (root mean square deviation) is measured for the vertices of A and B. Aligned meshes are obtained by repeating the same process while changing the feature points until the RMSD is less than the reference value. Through experiments, we show that the proposed algorithm aligns the mesh even when the ICP and Go-ICP algorithms fail.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.40 no.2
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• pp.1-9
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• 2003

We develop an experimental system to inspect a metal mask and, in this paper, introduce its inspection algorithm. This system is composed of an ASC(Area Scan Camera) and a belt type xy-table. The whole area of the metal mask is divided into several inspection blocks. The area of each block is equal to FOV(Field of View). For each block, the camera image is compared to the reference image. The reference image is made by gerber file. The rotation angle of the metal mask is calculated through the linear equation that is substituted two end points of horizontal boundary of a specific hole in a camera image. To calculate the position error caused by the belt type xy-table, HT(Hough-Transform) using distances among the holes in two images is used. The center of the reference image is moved as much as the calculated Position error to be coincided with the camera image. The information of holes in each image, such as centroid, size, width and height, are calculated through labeling. Whether a holes is mado correctly by laser machine or not, is judged by comparing the centroid and the size of hole in each image. Finally, we build the experimental system and apply this algorithm.

• Proceedings of the Korea Information Processing Society Conference
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• 2001.10a
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• pp.751-754
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• 2001

본 논문에서는 외형 정보 기반의 객체 정보 분할을 이용한 다중객체 추적을 다룬다. 일반적인 다중객체 추적 시스템은 움직임이 탐지된 다중 객체에 대한 외형(appearance) 정보를 이용하여 비강체를 정의하고, 객체의 일부 특징점이나 무게 중심점을 이용한 추적을 통해 객체간의 중첩(occlusion)이나 객체 분리(split) 등의 문제에 초점을 맞춘다. 무게 중심점 등을 이용한 추적은 장시간 추적하는 경우, 즉 움직임 방향 전환이 발생하는 경우에는 정확하고 매끄러운 추적이 불가능하다. 본 논문에서는 이러한 문제를 해결하기 위해 어파인 구조를 이용한 개별 객체 추적 기법을 적용하되, 객체에 대한 외형 정보를 바탕으로 객체 분리 및 객체별 어파인 구조 변환을 감지하여 정확하고 매끄럽게 다중 객체를 추적하는 알고리즘을 제안하고 성능을 분석한다.