• 호남수학학술지
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• 제35권1호
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• pp.17-27
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• 2013

We survey and study several volume formulas of a Euclidean tetrahedron.

• 대한수학회지
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• 제50권6호
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• pp.1223-1256
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• 2013

We give a geometric proof of the analyticity of the volume of a tetrahedron in extended hyperbolic space, when vertices of the tetrahedron move continuously from inside to outside of a hyperbolic space keeping every face of the tetrahedron intersecting the hyperbolic space. Then we find a geometric and analytic interpretation of a truncated orthoscheme and Lambert cube in the hyperbolic space from the viewpoint of a tetrahedron in the extended hyperbolic space.

• 대한수학회지
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• 제49권4호
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• pp.765-778
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• 2012

We construct a symmetric finite volume element (SFVE) scheme for a self-adjoint elliptic problem on tetrahedron grids and prove that our new scheme has optimal convergent order for the solution and has superconvergent order for the flux when grids are quasi-uniform and regular. The symmetry of our scheme is helpful to solve efficiently the corresponding discrete system. Numerical experiments are carried out to confirm the theoretical results.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제4권1호
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• pp.1-6
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• 1997

We will construct the generalized law of cosines in a tetrahedron, in a natural way, which gives three dimensional Pythagoras' theorem and enables us to calculate the volume of an arbitrary tetrahedron.

• 대한의용생체공학회:학술대회논문집
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• 대한의용생체공학회 1998년도 추계학술대회
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• pp.273-274
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• 1998

We construct a volume whose boundary is a tetrahedron with triangular faces intersecting the cutting planes along the given contours. This volume is obtained by calculating the Delaunay triangulation slice by slice, mapping 2D to 3D as tetrahedron. Also, eliminate extra-voronoi skeleton and non-solid tetrahedron. In this paper, we propose new method to eliminate non-solid tetrahedron based on the modified extra-voronoi skeleton path. This method enable us to do a compact tetrahedrisation and to reconstruct complex shapes.

• 대한수학교육학회지:학교수학
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• 제8권1호
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• pp.27-43
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• 2006

이 연구의 목적은 예비중등교사들의 실제적인 수학화 능력을 신장할 수 있도록 n-단체의 n-부피를 탐구하는 교수단원 를 설계하는 것이다. 이 교수단원에서는 2차원 도형인 삼각형의 넓이와 3차원 도형인 사면체의 부피를 n-단체의 n-부피로 일반화하는 것에 초점을 맞추고 있다. 이 일반화 과정에는 형식불역의 원리와 카발리에리의 원리가 적용된다. n-단체의 n-부피를 구하기 위해 n-직교삼각기둥을 정의하고, 그것의 n-부피를 공리적으로 탐색한다. 그리고 n-단체의 n-부피를 벡터와 행렬식을 이용하여 구한다. 이 교수단원을 통해 예비 중등교사들은 삼각형과 사면체의 일반화된 도형인 n-단체, 그리고 삼각형의 넓이와 사면체의 부피의 일반화된 n-단체의 부피를 이해하고 탐구할 수 있고, 학교수학과 학문수학의 자연스런 연결을 도모할 수 있다.

• Journal of Positioning, Navigation, and Timing
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• 제9권2호
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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 ㎥.

• 한국CDE학회논문집
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• 제22권1호
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• pp.59-69
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• 2017

Internal capacity of a refrigerator is an important indicator for design and purchasing criteria. The components facing the internal space may have holes or gaps between parts. In traditional way, design engineers manually remodeled the parts to fill the holes and the gaps for enclosed boundary of the internal space. Then they calculated internal volume by subtracting the assembly of parts from its enclosing volume. However, filling holes and gaps is not an automated process requiring a plenty of labor and time. In this research, we have developed a voxel-based method to estimate the internal volume of a refrigerator automatically. It starts transforming all components facing the interior space into voxels and fills all holes and gaps automatically by the developed hole-filling algorithm to form a completely closed boundary of the assembly. Then, it identifies the boundary voxels that are facing to the internal voxels with any part of the component. After getting the intersection points between the boundary voxels and the surfaces of components, it generates the boundary surface of triangular facets with the intersection points. Finally, it estimates the internal volume by adding volume of each tetrahedron composed of a triangle of boundary surface and an arbitrary point.

• 대한전기학회논문지
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• 제37권12호
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• pp.847-853
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• 1988

A method of three-demensional finite element mesh generation is presented in this paper. This method is based on the Delaunay's triangulation whose dual is Voronoi's diagram. A set of points is given on the boundary surface of the concerning domain and the initial tetrahedra are generated by the given set of points. Then, the quality of every tetrahedron is investigated and the interior points are generated near the tetrahedra which are inferior in quality and the tetrahedra of good quality can be controlled by the density of the initial boundary points. Regions with different material constant can be refined in tetrahedra respectively. To confirm the effectiveness of this algorithm,the total volume of tetrahedra was compared to the true volume and this mesh generator was applied to a three-dimensional electostatic problem.

• 제어로봇시스템학회논문지
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• 제4권2호
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• pp.220-225
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• 1998

In GPS (Global Positioning System) positioning, various measures can be used to select satellites or to evaluate the positioning results. Among these, GDOP (Geometric Dilution of Precision) and RGDOP (Relative GDOP) are the most frequently used. Although these measures are frequently used, the relationship between them is not clearly known. Moreover, the condition number is used as a traditional measure of numerical stability in solving linear equations. Sometimes, the volume of a tetrahedon made by the line of sight vector is used for simplicity. All of these measures share some common properties as well as differences. The relationships between these measures are analyzed in this paper.