• Journal for History of Mathematics
• /
• v.19 no.4
• /
• pp.107-116
• /
• 2006

This article reviews the exciting developments in Morse theory by S.Smale, Freedmann and others, including a proof of the generalized Poincare' Conjecture in the handle body theory. We study its relations with handle body theory _and geodesic theory.

• Journal of the Korea Institute of Information and Communication Engineering
• /
• v.15 no.2
• /
• pp.364-370
• /
• 2011

This paper propose a novel method for tracking moving object based on covariance matrix and Riemannian Manifolds. With image backgrounds continuously changed, we use the covariance matrices to extract features for tracking nonrigid object undergoing transformation and deformation. The covariance matrix can make fusion of different types of features and has its small dimension, therefore we enable to handle the spatial and statistical properties as well as the component correlation. The proposed method can estimate the position of the moving object by employing the covariance matrix of object region as a feature vector and comparing the candidate regions. Rimannian Geometry is efficiently adapted to object deformation and change of shape and improve the accuracy by using geodesic distance to predict the estimated position with the minimum distance. The experimental results have shown that the proposed method correctly tracked the moving object.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
• /
• v.1 no.2
• /
• pp.42-59
• /
• 1983

This article investigates the situation of the Plane Rectangular Coordinate derived from the Gauss Double Projection whereby the positioning of triangulation point in Korea has been represented on. Analyzing and assessing it have been performed by means of new computational method such as computer programing. On the basis of the results brought about, it is found that a new Plane Rectangular Coordinate as well as map projection and scale factor of geodetic length may be adapted to improve the distortion along the geodetic line on a certain zone of map projection in order to enhance the accuracy and the utility of the practical surveying works. The proposals for this study are as follows; (1) projection: Gauss-Kruger's projection (2) Coordinate system: Plane Rectangular coordinate with 8 origin system (3) Scale factor of geodetic length in origin; $m_0=0.9999$

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
• /
• v.32 no.spc4_2
• /
• pp.401-412
• /
• 2014

This study is purposed on showing an effective process for coordinate transformation of cadastral maps, based on the local datum, in the World Geodetic System (WGS) for Cadastral Reform Project (CRP). The process follows three steps: coordinate adjustment, datum transformation and distortion modeling. The first procedure is that point coordinates on local datum has to be adjusted by those GPS observed point-to-point distances, using trilateration. Secondly, the adjusted coordinates need to be transformed to WGS by applying the Affine model, while the verification of the methodology is implemented under numerical experiments. To conduct this procedure, 195 points in the same coordinate origins in Seoul and 61 points in several different origins in Incheon are used in the estimation. As a result, there are less than 2cm coordinate differences between transformed coordinates and measured ones at everywhere. Also, it is remarkable that the transformation does not depend on either of the particular common points or the sizes of computed region. Therefore, this suggested methodology is expected to easily provide identifications and corrections for points-deviations for improved quality of the cadastral map by distortion modeling through CRP.

• Proceedings of the Earthquake Engineering Society of Korea Conference
• /
• 1997.04a
• /
• pp.49-61
• /
• 1997

본 연구에서는 한국에서 구삼각강(1910-1915)과 정밀1차측지망(1975-1994)을 사용하여 지각변동량을 계산하고, 지체구조의 일반적인 변형패턴을 기하학적으로 조사하였다. 본 연구에서는 변형량을 계산하기 위하여 2차원의 무한소 변형모델을 설정하였으며, 수평변형량은 구좌표와 정밀1차측지망의 정밀동시강조정을 자유강조정법에 의하여 최초로 실시하여 일괄성있는 신좌표를 사용하여 계산된 측지선의 변화량으로 추정하였다. 변형설계결과로부터 1910년부터 1994년까지 누적된 변형량은 평균(1.07$\pm$0.5)$\times$10-5이고, 이로부터 년변형속도는 (0.13$\pm$0.063)$\mu$/yr 임을 알 수 있었으며, 변형의 경향을 보면 변형량이 10$\mu$ 보다 큰 값이 한반도의 동해안 지역에 분포하고 있으며, 서부쪽에는 10$\mu$이하의 값이 분포하고 있는 것으로 나타나 한반도의 동해안에서 지진의 발생빈도가 높은 것을 고려한다면 본 연구로부터 계산된 결과는 장래의 연구를 위해 중요한 데이터가 될 것이다. 본 연구에서 얻은 주변형축의 방향은 전국적으로 $77.6^{\circ}$$\pm$$13.5^{\circ}$방향임을 보여주고 있어 한반도의 지각은 ENE~WSW방향으로 압축상태에 있음을 알 수 있었으며, 이 결과는 지질학자나 지진학자들의 연구로부터 얻은 결과와 P-축의 방향이 일치하고 있고, 최대전단변형 이론과 일치하고 있는 것으로 나타났다.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 2006.04a
• /
• pp.325-332
• /
• 2006

Membrane structures, a kind of lightweight soft structural system, are used for spatial structures. The design procedure of membrane structures are needed to do shape finding, stress-deformation analysis and cutting pattern generation, because the material property has strong axial stiffness, but little bending stiffness. The problem of cutting pattern is highly varied in their size, curvature and material stiffness. So, the approximation inherent in cutting pattern generation methods is quite different. Therefore the ordinary computer software of structural analysis & design is not suitable for membrane structures. In this study, we develop the program for cutting pattern generation using geodesic line, and investigate the result of example's cutting pattern in detail.

• Proceeding of KASS Symposium
• /
• 2005.05a
• /
• pp.125-132
• /
• 2005

Membrane structures, a kind of lightweight soft structural system, are used for spatial structures. The material property of the membrane has strong axial stiffness, but little bending stiffness. The design procedure of membrane structures are needed to do shape finding, stress-deformation analysis and cutting pattern generation. In shape finding, membrane structures are unstable structures initially. These soft structures need to be introduced initial stresses because of its initial unstable state, and it happens large deformation phenomenon. And also there are highly varied in their size, curvature and material stiffness. So, the approximation inherent in cutting pattern generation methods is quite different. Therefore, in this study, to find the structural shape after large deformation caused by Initial stress, we need the shape analysis considering geometric nonlinear ten And the geodesic line on surface of initial equilibrium shape and the cutting pattern generation using the geodesic line is introduced.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
• /
• v.30 no.3
• /
• pp.241-247
• /
• 2012

The national geodetic reference frame of Korea switched to the International Terrestrial Reference Frame (ITRF) in 2003. In order to study the land area changes, we calculated the entire land area of Korea using the administrative boundaries of census data provided by Statistics Korea. The standard transformation procedure by the National Geographic Information Institute (NGII) was followed. The Transverse Mercator (TM) projected coordinates were transformed into the GRS80-based world geodetic reference frame, and the ellipsoidal and the projected areas were calculated. The provinces that range over two projection origins were divided into two polygons and projected using appropriate origins. After the transformation, all boundaries were shifted in the northwestern direction, resulting in a decreased area of $1.36km^2$ (about 0.0013%) on the projected plane. Moving the boundaries into a high latitude area cancels out the effect of the enlarged ellipsoid. In addition, the rate of change shows that a higher-latitude province is more sensitive to the shift of the boundaries. The data by Statistics Korea is significantly different from those of the Ministry of Land, Transport and Maritime Affairs (MLTM), thus it is urgently recommended that the data are integrated and unified.

• The Journal of the Acoustical Society of Korea
• /
• v.31 no.1
• /
• pp.51-61
• /
• 2012

In this research, we have analyzed the trend of radiation pattern variation in relation to the change of design variables such as source interval and source number for conformal array transducers arranged in equi-angle, equi-interval, and geodesic dome forms. Through statistical multiple regression analysis of the results, we derived functional forms of the side lobe level and the beamwidth in terms of the design variables. Futhermore, the structure of the array transducer was optimized to achieve the smallest side lobe level while satisfying the requirements on beam width by the GA (genetic algorithm) method. Based on the optimized results, we have determined the equi-interval form as the optimal array geometry among the three conformal array geometries.

• Bulletin of the Society of Naval Architects of Korea
• /
• v.2 no.1
• /
• pp.24-28
• /
• 1965

불규칙(不規則)한 곡면(曲面)으로 이루어진 선체외판(船體外板)의 전개(展開)는 근사전개법(近似展開法)을 사용(使用)한다. 특(特)히 선박(船舶) cost를 절감(節減)하기 위하여 공수절약(工數節約), 공기단축(工期短縮) 및 오작(誤作)을 적게한다는 점(點)에서 생각해 볼 때, 아무리 완전(完全)에 가까운 전개법(展開法)이라도 복잡(複雜)하면 실용가치(實用價値)가 없다. 공원(工員)이 작업(作業)을 간단(簡單)히, 신속(迅速)히 할 수 있다면 완전(完全)한 가전면(可展面)의 경우라도 근사법(近似法)을 따르는 것이 좋다. 물론(勿論) 이때 실용상(實用上) 지장(支障)이 없을 정도(程度)의 오차(誤差)로 끝여야한다. 대한조선공사(大韓造船公社)의 현도장(現圖場)에서 사용(使用)하는 외판(外板)의 각늑골(各肋骨) 사이에서 하나씩 전개(展開)해가는 직각송법(直角送法), 송반법(送返法), 대각선법(對角線法), 방사선법(放射線法) 및 삼각법(三角法)과 외판일매(外板一枚)를 한번에 전개(展開)하는 기선법(基線法)이 있으며, 전자(前者)의 정도(精度)와 같고, 후자(後者)와 같이 현도전개(現圖展開)를 안하고 직접(直接) marking 할 수 있는 점(點)을 동시(同時)에 구비(具備)한 측지선법(測地線法)이 있다. 이 측지선법(測地線法)보다 작업(作業)이 간단(簡單)하고 용이(容易)하며 거의 동일(同一)한 정도(情度)를 가지는 등분선법(等分線法)과 기준선(基準線)이 Roller축(軸)이 되는 축선법(軸線法)이 있는데 이들 방법(方法)에 관(關)하여 간단(簡單)히 생각한다.