• Journal of Positioning, Navigation, and Timing
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• v.9 no.2
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• pp.79-88
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• 2020

We determined Global Positioning System (GPS) satellite visibilities in signal-blockage simulations and then analyzed Position Dilution of Precision (PDOP) fluctuations obtained from those simulated satellite geometries. PDOP values under harsh signal-blockage simulation conditions become very high compared to those calculated with real observations. Especially when the number of observed satellites is four, which is the minimum requirement for GPS positioning, PDOP values instantaneously reached several hundreds or even several tens of thousands. It was also found that the volume of the tetrahedron composed with four satellites decreases significantly. When the correlation of the tetrahedron volume and PDOP was analyzed, we reached the following conclusions: PDOP values less than 4 can be acquired when the volume is larger than 103.2 × 10¹⁹ ㎥, and PDOP values increase beyond 50 when the volume is less than 6.0 × 10¹⁹ ㎥.

• Bulletin of the Korean Chemical Society
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• v.25 no.5
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• pp.673-675
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• 2004

The tetranuclear copper(II) cluster compound $[Cu_4OCl_6(C_{14}H_{12}N_2)_4]$ has been synthesized by hydrothermal reaction and studied by X-ray diffraction. The four copper(II) atoms locate four capsheaves of a tetrahedral skeletal structure and a oxygen atom as interstitial atom occupies the center position of the same tetrahedron, and each edge of the Cu-Cu tetrahedron is bridged by one ${\mu}_2$-Cl anion. The copper atom possesses slightly distorted trigonal bipyramidal geometry with three ${\mu}_2$-Cl atoms in equatorial position and the interstitial O atom and one N atom from 3-benzyl-benzimidazole ligand occupying axial position. The Cu-Cu distances are in the range of 3.0986-3.1162 ${\AA}$. The EPR spectrum suggested that the copper(II) ground state $d_{x2-y2}$ and the coordination geometry was trigonal bipyramidal.

• Journal of the Korean Ceramic Society
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• v.23 no.5
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• pp.25-34
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• 1986

This study was to refined the crystal structure of solid solution to determine the position and amount of Al in diopside and to relate crystal structure changes and properties of solid solution. Single crystals of the solid solution in the system CaO.MgO.$2 SiO_2-Al_2O_3$ were made from the melt with slow cooling and used to refine the structure. The following were obtained. 1. Tetrahedra rotated around axis parallel to the direction which the angle 03-03-03 became small. 2. Tetrahedron became large and regular. Average T-O bond distance increased 0.53 percent. 3. M1 octahedron became small and average M1-O bond distance decreased 1.1 percent. 4, M2 polyhedron became small and average M2-O bond distance decreased 0.37 percent Polythedron was affected not so much compared with any cation site. 5. Distance between metal ions distances between T and oxygens which were coordinated with M2 and meighboring tetrahedron distances between M2 and oxygens which coordinated with M1 and M2 were not changed almost. 6. $Al^{3+}$ substituted 4Mg^{2+}$ and $Si^{4+}$

• School Mathematics
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• v.12 no.4
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• pp.563-584
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• 2010

This study is aimed at analysing the mathematical thinking processes based on image by the mathematically gifted. For this, the 'Splitting a Tetrahedron' Task was used and mathematical thinking of the two middle school students were investigated. One of them deduced how many tetrahedral and octahedral were there when a tetrahedra was splitted by the surfaces which were parallel to each face of the tetrahedra without using any physical material. The other one solved the task using physical material and invented new images. A concrete image, indexical image and symbolic image were founded and the various roles of images could be confirmed.

• Journal of Institute of Control, Robotics and Systems
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• v.6 no.7
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• pp.559-567
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• 2000

This paper proposes simple and practical methods in order to overcome complex formulation and heavy computational burden of the forward kinematics of 6 앨 3-6 type parallel manipulators. Three ap-proaches for the forward kinematics are presented : one extra sensor a modified structure and novel numerical method. The proposed methods are applied to the forward kinematics of a new 6 앨 parallel manipulator with special geometry that has three internal links three external links and a moving platform of a cone shape. The proposed methods use three tetrahedrons for finding the position and orientation vector of the moving platform. The main advantages of the appraches using tetrahedrons are to abbreviate the formulation to easily find so-lutions of the forward kinematics and to be able to practically control of the manipulator in real time.

• Proceedings of the Korean Information Science Society Conference
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• 1999.10b
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• pp.562-564
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• 1999

래디오시티 렌더링 시스템에 적합한 모델링을 하는데 있어서 수작업을 비롯한 기존의 여러 방법을 적용해 본 결과, 제작하고자 하는 환경 설정에 많은 어려움을 겪었다. 본 논문은 이러한 문제를 해결하기 위해, 인크리먼털 컨벡스 헐 모델링 기법을 응용하여 시스템을 개발하였다. 이 시스템은 기본 데이터 정보를 입력하면 자동적으로 패치와 엘리먼트가 생성되는 프로그램으로, 물체가 많은 환경이나 곡면을 비교적 쉽고, 고속으로 표현할 수 있었다. 그리고 인크리먼털 컨벡스 헐 알고리즘으로 생성된 환경에, 폼 팩터의 대표적인 세 가지 알고리즘들을 비교.평가 해본 결과 Cubic-Tetrahedron 알고리즘이 가장 효율적이었음을 알 수 있었다.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2006.10a
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• pp.213-214
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• 2006

• Journal for History of Mathematics
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• v.14 no.2
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• pp.115-124
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• 2001

In this paper, we developed a Web application program that could show the shape, the number of the vertices, the edges, the faces and development figures of polygons(regular tetrahedron, regular hexahedron, etc). The program was implemented using GSP(Geometer's SketchPad) and then converted to JAVA to display the results of GSP on the Web. The results of this paper are applicable to geometry of a junior high school course.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.83.2-83
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• 2001

This paper presents a new formulation approach to reduce computational burden of the direct kinematics of 6-dof haptic devices with three sets of a parallel-serial linkage. Their direct kinematics has been formulated through employing the Denavit-Hartenberg notation, which results in complicated formulation procedures and heavy computational burden. For reducing these problems, this paper reconfigures the haptic devices into an equivalent kinematic model of the 3-6 Stewart-Gough Platform that has three connecting joints on the moving platform. Moreover, the direct kinematics of the 3-6 Platform can be effectively formulated by using the proposed Tetrahedron Approach.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.44 no.5
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• pp.55-61
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• 2007

In this paper, we propose a three-dimensional(3D) active shape models for medical image segmentation. In order to build a 3D shape model, we need to generate a point distribution model(PDM) and select corresponding landmarks in all the training shapes. The manual determination method, two-dimensional(2D) method, and limited 3D method of landmark correspondences are time-consuming, tedious, and error-prone. In this paper, we generate a 3D statistical shape model using the 3D model generation method of a distance transform and a tetrahedron method for landmarking. After generating the 3D model, we extend the shape model training and gray-level model training of 2D active shape models(ASMs) and we use the integrated modeling process with scale and gray-level models for the appearance profile to represent the local structure. Experimental results are comparable to those of region-based, contour-based methods, and 2D ASMs.