• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.29 no.4
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• pp.329-341
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• 2011

The object of this paper is to compare the accuracy and the characteristic of various methods of solving the geodetic inverse problem for the geodesic lines which be in the standard case and special cases(antipodal, near antipodal, equatorial, and near equatorial situation) on the WGS84 reference ellipsoid. For this, the various algorithms (classical and recent solutions) to deal with the geodetic inverse problem are examined, and are programmed in order to evaluate the calculation ability of each method for the precise geodesic determination. The main factors of geodetic inverse problem, the distance and the forward azimuths between two points on the sphere(or ellipsoid) are determined by the 18 kinds of methods for the geodetic inverse solutions. After then, the results from the 17 kinds of methods in the both standard and special cases are compared with those from the Karney method as a reference. When judging these comparison, in case of the standard geodesics whose length do not exceed 100km, all of the methods show the almost same ability to Karney method. Whereas to the geodesics is longer than 4,000km, only two methods (Vincenty and Pittman) show the similar ability to the Karney method. In the cases of special geodesics, all methods except the Modified Vincenty method was not proper to solve the geodetic inverse problem through the comparison with Karney method. Therefore, it is needed to modify and compensate the algorithm of each methods by examining the various behaviors of geodesics on the special regions.

• Journal of Korean Society of Steel Construction
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• v.22 no.1
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• pp.33-42
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• 2010

Patterning with a geodesic line is essential for economical or efficient usage of membrane materialsin fabric tension membrane structural engineering and analysis. The numerical algorithm to determine the geodesic line for membrane structures is generally classified into two. The first algorithm finds a non-linear shape using a fictitious geodesic element with an initial pre-stress, and the other algorithm is the geodesic line cutting or searching algorithm for arbitrarily curved 3D surface shapes. These two algorithms are still being used only for the three-node plane stress membrane element, and not for the four-node element. The lack of a numerical algorithm for geodesic lines with four-node membrane elements is the main reason for the infrequent use of the four-node membrane element in membrane structural engineering and design. In this paper, a modified numerical algorithm is proposed for the generation of a geodesic line that can be applied to three- or four-node elements at the same time. The explicit non-linear static Dynamic Relaxation Method (DRM) was applied to the non-linear geodesic shape-finding analysis by introducing the fictitiously tensioned 'strings' along the desired seams with the three- or four-node membrane element. The proposed algorithm was used for the numerical example for the non-linear geodesic shape-finding and patterning analysis to demonstrate the accuracy and efficiency, and thus, the potential, of the algorithm. The proposed geodesic shape-finding algorithm may improve the applicability of the four-node membrane element for membrane structural engineering and design analysis simultaneously in terms of the shape-finding analysis, the stress analysis, and the patterning analysis.

• The Journal of the Convergence on Culture Technology
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• v.5 no.1
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• pp.385-388
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• 2019

Considering spherically symmetric spacetimes embedded in a 5-dimensional static Lorentzian manifold, within the large distance limit of DGP model, we study null geodesic equations. We discuss possible relations of particles following the geodesics with the gravitational waves detected recently, in comparison with the electromagnetic waves propagaing in these brane spacetimes.

• Journal of the Korea Computer Graphics Society
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• v.28 no.1
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• pp.11-19
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• 2022

In this paper we present a new method for interactive segmentation of a triangle mesh by using the concavity-sensitive harmonic field and anisotropic geodesic. The proposed method only requires a single vertex in a desired feature region, while most of existing methods need explicit information on segmentation boundary. From the user-clicked vertex, a candidate region which contains the desired feature region is defined and concavity-senstive harmonic field is constructed on the region by using appropriate boundary constraints. An initial isoline is chosen from the uniformly sampled isolines on the harmonic field and optimal points on the initial isoline are determined as interpolation points. Final segmentation boundary is then constructed by computing anisotropic geodesics passing through the interpolation points. In experimental results, we demonstrate the effectiveness of the proposed method by selecting several features in various 3D models.

• Journal of Korean Association for Spatial Structures
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• v.12 no.4
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• pp.15-22
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• 2012

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.5 no.1
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• pp.23-31
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• 1987

Maps need the suitable map projection according to the scale of its seeing that the distortion is increasing between the projected geodesic line on the map and the ellipsoidal line owing to the scale up. In this paper, the optimum map projection for the large scale mapping as well as analysis of current mapping in Korea is proposed.

• Journal of KIISE:Computer Systems and Theory
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• v.31 no.7
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• pp.414-420
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• 2004

Among the desirable properties of a piecewise linear parameterization, guaranteeing a one-to-one mapping (i.e., no triangle flips in the parameter plane) is often sought. A one-to-one mapping is accomplished by non-negative coefficients in the affine transformation. In the Floater's method, the coefficients were computed after the 3D mesh was flattened by geodesic polar-mapping. But using this geodesic polar map introduces unnecessary local distortion. In this paper, a simple variant of the original shape-preserving mapping technique by Floater is introduced. A new simple method for calculating barycentric coordinates by using straightest geodesics is proposed. With this method, the non-negative coefficients are computed directly on the mesh, reducing the shape distortion introduced by the previously-used polar mapping. The parameterization is then found by solving a sparse linear system, and it provides a simple and visually-smooth piecewise linear mapping, without foldovers.

• Journal of Korean Association for Spatial Structures
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• v.12 no.1
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• pp.109-119
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• 2012

For membrane structure, there are three main steps in design and construction, which are form finding, statistical load analysis, and cutting patterning. Unlike the first two stages, the step of cutting pattern involves the translation of a double-curved surface in 3D space into a 2D plane with minimal error. For economic reasons, the seam lines of generated cutting patterns rely greatly on the geodesic line. Generally, as searching regions of the seam line are plane elements in the step of shape analysis, the seam line is not a smooth curve, but an irregularly divided straight line. So, it is how we make an irregularly divided straight line a smooth curve that defines the quality of the pattern. Accordingly, in this paper, we analyzed interpolation schemes using spline, and apply these methods to cutting pattern generation on the curved surface. To generate the pattern, three types of spline functions were used, i.e., cubic spline function, B-spline, and least-square spline approximation, and simple model and the catenary-shaped membrane was adopted to examine the result of generation. The result of comparing the approximation curves by the number of elements and the number of extracted nodes of simple model revealed that the seam line for less number of extracted nodes with large number of elements were more efficient, and the least-square spline approximation provided smoother seam line than other methods.

• Journal of Korean Association for Spatial Structures
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• v.6 no.1 s.19
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• pp.117-127
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• 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 cooing 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 cooing pattern generation using geodesic line, and investigate the result of example's cooing pattern in detail.

• Journal of Korean Society for Geospatial Information Science
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• v.15 no.1 s.39
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• pp.47-53
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• 2007

Astronomic surveying has been regarded as an important method for absolute positioning of geodetic datum in each countries under the local geodetic reference system. The purposes of this study are to determine astrogeodetic geoidal heights referred to Bessel ellipsoid and to determine deflection of the vertical and geoidal heights referred to GRS80 of World Geodetic System by astronomic surveying data which have been surveyed after 1970 in Korea. The results show that $\xi$ component of the deflection of the vertical distribute from -5.725" to 8.005" and $\eta$ component distribute from -14.917" to 6.2" and astrogeodrtic geoidal heights distribute from 23 m to 27 m in the study area. Also, we could see that GRS80 was more optimal ellipsoid than Bessel 1841 ellipsoid to Korea through comparing both astrogeotic geoidal heights referred to GRS80 and Bessel 1841 ellipsoid.