• The Transactions of the Korea Information Processing Society
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• v.3 no.7
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• pp.1894-1905
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• 1996

Delauuany triangulation which is the dual of Dirichlet tessellation is not affine invariant. In other words, the triangulation is dependent upon the choice of the coordinate axes used to represent the vertices. In the same reason, Delahanty tetrahedrization does not have an affine iveariant transformation property. In this paper, we present a new type of tetrahedrization of spacial points sets which is unaffected by translations, scalings, shearings and rotations. An affine invariant tetrahedrization is discussed as a means of affine invariant 2 -D triangulation extended to three-dimensional tetrahedrization. A new associate norm between two points in 3-D space is defined. The visualization of the structure of tetrahedrization can discriminate between Delaunay tetrahedrization and affine invariant tetrahedrization.

• Communications of Mathematical Education
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• v.24 no.1
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• pp.145-158
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• 2010

In this paper we study tetrahedron's properties related with center of inscribed sphere using the center of mass. We show that the center of mass of four mass points (A,a), (B,b), (C,c), (D,d) coincide with center of tetrahedron's inscribed sphere, suggest equalities and inequalities related with center of inscribed sphere, and prove theses using the center of mass. Our results can be used in research and education programs, various types of gifted student education.

• Journal of Digital Contents Society
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• v.16 no.4
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• pp.575-581
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• 2015

This paper presents the development of certain highly efficient and accurate method for computing tangent curves for three-dimensional vector fields. Unlike conventional methods, such as Runge-Kutta method, for computing tangent curves which produce only approximations, the method developed herein produces exact values on the tangent curves based upon piecewise linear variation over a tetrahedral domain in 3D. This new method assumes that the vector field is piecewise linearly defined over a tetrahedron in 3D domain. It is also required to decompose the hexahedral cell into five or six tetrahedral cells for three-dimensional vector fields. The critical points can be easily found by solving a simple linear system for each tetrahedron. This method is to find exit points by producing a sequence of points on the curve with the computation of each subsequent point based on the previous. Because points on the tangent curves are calculated by the explicit solution for each tetrahedron, this new method provides correct topology in visualizing 3D vector fields.

• Journal of the Korea Computer Graphics Society
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• v.2 no.2
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• pp.11-20
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• 1996

The numerous application of scattered data include the modeling and visualization of physical phenomena. A tetrahedrization is one of pre-processing steps for 4-D surface interpolation. In this paper, various tetrahedrization methods are discussed including, Delaunay, least squares fitting, gradient difference, and jump in normal direction derivatives. This paper discriminates the characteristics of tetrahedrization through visualizing tetrahedral domain. This paper also, provides the tool that can compare and analyze the quality of 4-D space approximation over tetrahedral domain numerically, as well as graphically.

• Communications of Mathematical Education
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• v.19 no.3 s.23
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• pp.517-526
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• 2005

본 연구에서는 사면체의 부피를 구하는 두 가지 공식을 다룰 것이며, 이들은 외형적으로 또는 계산 방법상으로 삼각형의 넓이를 구하는 헤론의 공식과 유사하다. 이들 중에서 하나는 사면체의 모서리와 평면각들을 이용하여 사면체의 부피를 표현하며, 다른 하나는 사면체의 모서리들만 이용하여 부피를 표현한 것으로 2002년에 미해결 탐구 문제로 제시된 바 있다. 본 연구에서는 헤론 공식과 이들 두 공식의 유사점에 대해 논의하며, 모서리들만을 이용하여 부피를 구하는 공식에 대한 새로운 기초적인 증명 방법을 제시할 것이다.

• Journal of the Korea Computer Graphics Society
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• v.18 no.1
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• pp.29-34
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• 2012

High-quality tetrahedral meshes are crucial for FEM-based simulation of large elasto-plastic deformation and tetrahedral-mesh-based simulation of fluid flow. This paper proposes a volume meshing method that exploits an octree-based adaptive signed distance field to fill the inside of a polygonal object with tetrahedra, of which dihedral angles are good. The suggested method utilizes an octree structure to reduce the total number of tetrahedra by space-efficiently filling an object with graded tetrahedra. To obtain a high-quality mesh with good dihedral angles, we restrict the octree in such a way that any pair of neighboring cells only differs by one level. In octree-based tetrahedral meshing, the signed distance computation of a point to the surface of a given object is a very important and frequently-called operation. To accelerate this operation, we develop a method that computes a signed distance field directly on the vertices of the octree cells while constructing the octree using a top-down approach. This is the main focus of the paper. The suggested tetrahedral meshing method is fast, stable and easy to implement.

• Proceedings of the KIEE Conference
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• 2005.07d
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• pp.2864-2866
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• 2005

색역폭 사상은 디스플레이 장치간의 색재현성 차이를 보정하기 위한 기법이다. 본 논문에서는 사면체 보간에 의한 실시간 색역폭 사상을 제안하고자 한다. 기존의 제안된 육면체 보간 방식에 비해 이 논문에서 제안된 사면체 보간(tetrahedral interpolation) 방법은 색공간의 분할을 통해 분할된 각각의 사면체 색 공간에서 색역폭 사상이 수행됨으로서 왜곡이 감소되고 육면체 보간이 8개의 룩업테이블을 사용하는데 비해 4개의 룩업 테이블을 사용함으로서 실시간 처리속도의 향상과 하드웨어의 구현 시 비용절감을 기대할 수가 있다.

• Communications of Mathematical Education
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• v.21 no.3
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• pp.385-406
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• 2007

In this paper we study on various properties of triangle's escribed circle and tetrahedron's escribed sphere. In order to accomplish our study we extract some base problems related with investigating these properties. Using the base problems we are able to prove various properties of triangle's escribed circle, and to systemize these properties. And we succeed in drawing an analogy related with tetrahedron's escribed sphere.

• Journal of the Korea Computer Graphics Society
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• v.17 no.2
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• pp.45-53
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• 2011

This paper proposes a volume meshing method that fills the inside of an object with tetrahedra, of which dihedral angles are good. The suggested method is fast, stable and easy to implement It can also utilize an octree structure to space-efficiently fill an object with graded tetrahedra by reducing the total number of tetrahedra. To obtain a high-quality mesh with good dihedral angles, we restrict the octree such that any pair of neighboring cells only differs by one level. To efficiently construct a restricted-octree and generate a volume mesh from the octree, we utilize a signed distance field of an object on its bounded workspace. The suggested method can be employed in FEM-based simulation of large elasto-plastic deformation and tetrahedral-mesh-based simulation of fluid flow.

• The Transactions of the Korea Information Processing Society
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• v.3 no.6
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• pp.1553-1567
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• 1996

The numerous applications surface interpolation include the modeling and visualization phenomena. A tetrahedrization is one of pre-processing steps for 4-D space interpolation. The quality of a piecewise linear interpolation 4-D space depends not only on the distribution of the data points in $R^2$, but also on the data values. We show that the quality of approximation can be improved by data dependent tetraheadrization through visualization of 4-D space. This paper discusses Delaunary tetrahedrization method(sphere criterion) and one of the data dependent tetrahedrization methods(least squares fitting criterion). This paper also discusses new data dependent criteria:1) gradient difference, and 2) jump in normal direction derivative.