• Bulletin of the Korean Mathematical Society
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• v.54 no.3
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• pp.953-965
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• 2017

In this paper, we classify translation surfaces of Type 2 in the three dimensional simply isotropic space ${\mathbb{I}}_3^1$ satisfying some algebraic equations in terms of the coordinate functions and the Laplacian operators with respect to the first, the second and the third fundamental form of the surface. We also give explicit forms of these surfaces.

• Journal of the Korea Society of Computer and Information
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• v.17 no.7
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• pp.87-95
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• 2012

In this paper, PTAS three-dimensional Steiner minimum tree connecting numerous input nodes rapidly in 3D space is proposed. Steiner minimum tree problem belongs to NP problem domain, and when properly devised heuristic introduces, it is generally superior to other algorithms as minimum spanning tree affiliated with P problem domain. But when the number of input nodes is very large, the problem requires excessive execution time. In this paper, a method using PTAS is proposed to solve the difficulty. In experiments for 70,000 input nodes in 3D space, the tree produced by the proposed 8 space partitioned PTAS method reduced 86.88% execution time, compared with the tree by naive 3D steiner minimum tree method, though increased 0.81% tree length. This affirms the proposed method can work well for applications that many nodes of three dimensions are need to connect swifty, enduring slight increase of tree length.

• Journal of Astronomy and Space Sciences
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• v.16 no.2
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• pp.139-148
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• 1999

Bow shock formation, in case the supersonic solar wind flow is hindered by the atmosphere of Mars, is investigated. The atoms newly ionized from the extensive neutral atmosphere of Mars are loaded to the solar wind. By the conservation of momentum, the solar wind velocity is decreased. Then the supersonic flow velocity drops to the subsonic flow velocity in front of Mars at certain region, which is called the bow shock. The location of Mars subsolar bow shock is highly varying in the range of 1.3 to 2.5 Rm. Martian bow shock location is estimated by one-dimensional flux tube equations reduced from full three-dimensional MHD equations. The variability of Mars bow shock location effected by the solar wind conditions is studied. It is evident that the solar wind dynamic pressure change is able to make the Mars bow shock location variable.

• Nonlinear Functional Analysis and Applications
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• v.27 no.3
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• pp.569-585
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• 2022

A brief comparative survey of some generalizations of a metric space with three dimensional metric structures and different forms of the triangle inequality is done along with their topological properties. Then a common fixed point is obtained for reciprocally continuous and compatible self-maps in a G-metric space. Further, a common fixed point theorem is proved for a pair of weakly compatible self-maps on a G-metric space with the common limit range property.

• Journal of the korean academy of Pediatric Dentistry
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• v.35 no.2
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• pp.297-304
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• 2008

The purpose of this study was to evaluate a 3-Dimensional laser scanner for the space analysis after loss of a primary first molar. Six children with premature loss of a primary first molar were examined using study models taken before and after the extraction. The results were as follows: 1. There was no change in primary molar space after the extraction of a maxillary primary first molar However, 2 out of 3 children experienced primary molar space loss in extraction side of a mandibular primary first molar. 2. Arch width and arch perimeter showed no difference between initial and final model. 3. All primary canines did not show any changes in inclination. Maxillary primary second molars had similar changes in both extraction and control side. However, 2 out of 3 mandibular primary second molars in extraction side showed more lingual tipping compared to control side. Mandibular permanent first molars tipped more lingually in extraction side. 4. In angulation, primary canines showed nothing of significance. Mandibular primary second molars tipped more mesially in extraction side than in control side. Maxillary permanent first molars have increased distal angulation after extraction of primary first molars in both side.

• Journal of the Korea Society of Computer and Information
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• v.19 no.11
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• pp.53-61
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• 2014

In this paper, we propose a method using an image received by the depth camera in order to separate the wall in a three-dimensional space indoor environment. Results of the paper may be used to provide valuable information on the three-dimensional space. For example, they may be used to recognize the indoor space, to detect adjacent objects, or to project a projector on the wall. The proposed method first detects a normal vector at each point by using the three dimensional coordinates of points. The normal vectors are then clustered into several groups according to similarity. The RANSAC algorithm is applied to separate out planes. The domain knowledge helps to determine the wall among planes in an indoor environment. This paper concludes with experimental results that show performance of the proposed method in various experimental environment.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.41 no.4
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• pp.123-130
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• 2018

Triangulation is one of the fundamental problems in computational geometry and computer graphics community, and it has huge application areas such as 3D printing, computer-aided engineering, surface reconstruction, surface visualization, and so on. The Delaunay refinement algorithm is a well-known method to generate quality triangular meshes when point cloud and/or constrained edges are given in two- or three-dimensional space. In this paper, we propose a simple but efficient algorithm to triangulate Voronoi surfaces of Voronoi diagram of spheres in 3-dimensional Euclidean space. The proposed algorithm is based on the Ruppert's Delaunay refinement algorithm, and we modified the algorithm to be applied to the triangulation of Voronoi surfaces in two ways. First, a new method to deciding the location of a newly added vertex on the surface in 3-dimensional space is proposed. Second, a new efficient but effective way of estimating approximation error between Voronoi surface and triangulation. Because the proposed algorithm generates a triangular mesh for Voronoi surfaces with guaranteed quality, users can control the level of quality of the resulting triangulation that their application problems require. We have implemented and tested the proposed algorithm for random non-intersecting spheres, and the experimental result shows the proposed algorithm produces quality triangulations on Voronoi surfaces satisfying the quality criterion.

• Journal of the Korean Mathematical Society
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• v.45 no.2
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• pp.393-404
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• 2008

Biharmonic Legendre curves in a Sasakian space form are studied. A non-existence result in a 7-dimensional 3-Sasakian manifold is obtained. Explicit formulas for some biharmonic Legendre curves in the 7-sphere are given.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.4
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• pp.665-673
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• 2011

In this paper, we derive a set of the partial differential equations that characterize an inelastic flow of a curve in a 3-dimensional Galilean space. Also, we give necessary and sufficient condition for an inelastic flow.

• Journal of the Korean Mathematical Society
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• v.38 no.6
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• pp.1167-1177
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• 2001

The groups generated by reflections in faces of Coxeter polyhedra in three-dimensional Thurstons spaces are considered. We develop a method for finding of finite index subgroups of Coxeter groups which uniformize three-dimensional manifolds obtained as two-fold branched coverings of manifolds of Heegaard genus one, that are lens spaces L(p, q) and the space S$^2$$\times$S$^1$.