• Bulletin of the Korean Mathematical Society
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• v.26 no.2
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• pp.175-177
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• 1989

The following is the basic problem about the stability in Riemannian Geometry; given a Riemannian manifold N, find all stable complete minimal submanifolds of N. As answers of this problem, do Carmo-Peng [1] and Fischer-Colbrie and Schoen [3] showed that the stable minimal surfaces in R$^{3}$ are planes and Schoen-Yau [5] and Fischer-Colbrie and Schoen [3] gave a solution for the case where the ambient space is a three dimensional manifold with nonnegative scalar curvature. In this paper we will remove the assumption of finite absolute total curvature in [3, Theorem 3].

• Korean Journal of Computational Design and Engineering
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• v.4 no.2
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• pp.79-86
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• 1999

A general approach to automatic generation of triangular meshes on three-dimensional surfaces is presented in this paper. The approach, developed with emphasis on program generality and interface with CAD/CAM systems, is based on the double mapping method and the looping method. The double mapping method is introduced and anew splitting scheme is proposed for the looping method employed for triangular mesh generation on the parametric domain. Several application examples are given.

• Journal of the Korean Institute of Landscape Architecture
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• v.17 no.3
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• pp.1-8
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• 1990

The digital terrain model (DTM) or digital elevation model (DEM) is commonly used in representing the continuous variation of relief over space. One of the most frequent applications is to display the three dimensional view of the landform concerned. In this paper, the altitude matrices-regular grid cell format of the elevation in Mt. Kyeryong National Park were used in developing the three dimensional view software for the first time in Korea. It required the removal of hidden lines or surfaces. To do this, it was necessary to identify those surfaces and line segments that are visible and those that are invisible. Then, only the visible portions of the landform were displayed. The assumption that line segments are used to approximate contour surfaces by polygons was used in developing the three dimensional orthographic view. In order to remove hidden lines, the visibility test and masking algorithms were used. The software was developed in the engineering workstation, SUN 3/280 at the Institute of Space Science and Astronomy using 'C' in UNIX operating system. The software developed in this paper can be used in various fields. Some of them are as follows : (1) Landscape design and planning for identifying viewshed area(line of sight maps) (2) For planning the route selection and the facility location (3) Flight simulation for pilot training (4) Other landscape planning or civil engineering purposes

• Korean Journal of Mathematics
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• v.25 no.4
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• pp.537-554
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• 2017

In this paper, we study the surfaces foliated by ellipses in three dimensional Euclidean space ${\mathbf{E}}^3$. We prove the following results: (1) The surface foliated by an ellipse have constant Gaussian curvature K if and only if the surface is flat, i.e. K = 0. (2) The surface foliated by an ellipse is a flat if and only if it is a part of generalized cylinder or part of generalized cone.

• Journal for History of Mathematics
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• v.20 no.4
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• pp.49-60
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• 2007

In this article, the concept of rigidity of smooth surfaces in the three dimensional Euclidean space which naturally arises in elementary geometry is introduced, and the natural process of the development of rigidity theory for compact surfaces and its generalizations are investigated.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.89.1-89
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• 2001

Measurement of complex surfaces without touching is desirable in several fields. This arises mainly for measurement of complex surfaces including those surfaces that deform during touch. Our research presented in this paper describes the use of a 3D digitizer for scanning 3D objects. The use of such a device, in addition to proper calibration, requires proper scaling in all three dimensions. We propose measurement techniques to measure various aspects of the surface circumference, area and volume. We also present experiments from using a 3D Minolta digitizer for measuring 3D human heads.

• Restorative Dentistry and Endodontics
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• v.22 no.2
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• pp.680-692
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• 1997

New bonding agent systems have been supplied which operators can simply apply to conditioned tooth surfaces. The purpose of this study was to evaluate the shear bond strengths and the microleakages of three bonding agents and composite resins to dentin. Seventy-five extracted human maxillary and mandibular molar teeth were used in this study. For the shear bond strength test, the entire occlusal dentin surfaces of thirty teeth were exposed with Diamond Wheel Saw and smoothed with Lapping and Polishing Machine (South Bay Technology Co., U.S.A). For the microleakage test, Class V cavities were prepared in the buccal surfaces of fourtyfive teeth. They were randomly assigned into 3 groups according to dentin bonding agents ($Scotchbond^{TM}$ Multi-Purpose plus, ONE-$STEP^{TM}$ and Prime & $Bond^{TM}$)and composite resins (Z-100, $Aelitefil^{TM}$ and TPH $Spectrum^{TM}$) to be used. Bonding agents and composite resins were bonded to exposed dentin surfaces of the tooth crown and to Class V cavities on the buccal surfaces respectively according to manufacturer's directions. The shear bond strengths were measured by universal testing machine($U^{TM}$ AGS-100, Japan). In addition, the degree of micro leakage at the occlusal and gingival margin was examined by 2 % methylene blue and stereomicroscope(Olymous SZH 10, Japan). The results were as follows: 1. The shear bond strength to dentin was the highest value in SBMP-Plus group($16.68{\pm}7.38$ MPa) and the lowest value in Prime & Bond group($11.61{\pm}5.82$ MPa), but there was no significant difference of shear bond strength among three groups. 2. The degree of microleakage at both occlusal and gingival margin was showed the lowest in SBMP-Plus group and the highest in ONE-STEP group. 3. At both occlusal and gingival margin, there was significant difference of microleakage between SBMP-Plus and ONE-STEP/ Prime & Bond groups(p<0.05), but no significant difference of microleakage between ONE-STEP and Prime & Bond group(p>0.05).

• Bulletin of the Korean Mathematical Society
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• v.52 no.2
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• pp.377-394
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• 2015

In this paper, we generalize some results about Bertrand curves and Razzaboni surfaces in Euclidean 3-space to the case that the ambient space is Minkowski 3-space. Our discussion is divided into three different cases, i.e., the parent Bertrand curve being timelike, spacelike with timelike principal normal, and spacelike with spacelike principal normal. For each case, first we show that Razzaboni surfaces and their mates are related by a reciprocal transformation; then we give B$\ddot{a}$cklund transformations for Bertrand curves and for Razzaboni surfaces; finally we prove that the reciprocal and B$\ddot{a}$cklund transformations on Razzaboni surfaces commute.

• Korean Journal of Computational Design and Engineering
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• v.7 no.3
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• pp.190-201
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• 2002

Surfaces of many engineering structures, specially, those of ships and airplanes are commonly fabricated as doubly curved shapes as well as singly curved surfaces to fulfill functional requirements. Given a three dimensional design surface, the first step in the fabrication process is unfolding or planar development of this surfaces into a planar shape so that the manufacturer can determine the initial shape of the flat plate. Also a good planar development enables the manufacturer to estimate the strain distribution required to form the design shape. In this paper, an algorithm for optimal approximated development of a general curved surface, including both singly and doubly curved surface is developed in the sense that the strain energy from its planar development to the design surface is minimized, subjected to some constraints. The development process is formulated into a constrained nonlinear programming problem, which is on basis of deformation theory and finite element. Constraints are subjected to characteristics of the fabrication method. Some examples on typical surfaces and the practical ship surfaces show the effectiveness of this algorithm.

• Journal of the Korean Society for Precision Engineering
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• v.26 no.9
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• pp.135-142
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• 2009

In the present study replication of microstructured surfaces by microinjection molding was carried out. For a fabrication of mold inserts, nickel microstructures having various characteristic dimensions were fabricated by nickel electroforming onto Si mother microstructures. In addition, reverse nickel microstructures based on the electroformed nickel microstructures were successfully realized by electroforming with passivation process. The fabricated nickel microstructures were used as mold inserts for a replication of microstructured surfaces by microinjection molding. Microinjection molding experiment was carried out under three different processing conditions, which revealed effects of a packing stage and mold wall temperature. The microinjection-molded microstructured surfaces were characterized by using an atomic force microscope (AFM). It was found that mold wall temperature could enhance replication quality resulting in the precise microstructured surfaces.