• Communications of Mathematical Education
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• v.31 no.3
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• pp.257-277
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• 2017

The purpose of this research is divide into two kinds. First, develop the mathematical modeling program for mathematically gifted students focused on Voronoi diagram and Delaunay triangulation, and then gifted teachers can use it in the class. Voronoi diagram and Delaunay triangulation are Spatial partition theory use in engineering and geography field and improve gifted student's mathematical connections, problem solving competency and reasoning ability. Second, after applying the developed program to the class, I analyze gifted student's core competency. Applying the mathematical modeling program, the following findings were given. First, Voronoi diagram and Delaunay triangulation are received attention recently and suitable subject for mathematics gifted education. Second,, in third enrichment course(Student's Centered Mathematical Modeling Activity), gifted students conduct the problem presentation, division of roles, select and collect the information, draw conclusions by discussion. In process of achievement, high level mathematical competency and intellectual capacity are needed so synthetic thinking ability, problem solving, creativity and self-directed learning ability are appeared to gifted students. Third, in third enrichment course(Student's Centered Mathematical Modeling Activity), problem solving, mathematical connections, information processing competency are appeared.

• Korean Journal of Remote Sensing
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• v.28 no.1
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• pp.55-67
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• 2012

Real-time image georeferencing is required to generate spatial information rapidly from the image sequences acquired by multi-sensor systems. To complement the performance of position/attitude sensors and process in real-time, we should employ on-line aerial triangulation based on a sequential estimation algorithm. In this study, we thus attempt to derive an efficient on-line aerial triangulation algorithm for real-time georeferencing of image sequences. We implemented on-line aerial triangulation using the existing Given transformation update algorithm, and a new inverse normal matrix update algorithm based on observation classification, respectively. To compare the performance of two algorithms in terms of the accuracy and processing time, we applied these algorithms to simulated airborne multi-sensory data. The experimental results indicate that the inverse normal matrix update algorithm shows 40 % higher accuracy in the estimated ground point coordinates and eight times faster processing speed comparing to the Given transformation update algorithm. Therefore, the inverse normal matrix update algorithm is more appropriate for the real-time image georeferencing.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.27 no.2
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• pp.249-260
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• 2009

The georeferencing accuracy of the sensory data acquired by an aerial monitoring system heavily depends on the performance of the GPS/IMU mounted on the system. The employment of a high performance but expensive GPS/IMU unit causes to increase the developmental cost of the overall system. In this study, we simulate the images and GPS/IMU data acquired by an UAV-based aerial monitoring system using an inexpensive integrated GPS/IMU of a MEMS type, and perform the image georeferencing by applying the aerial triangulation to the simulated sensory data without any GCP. The image georeferencing results are then analyzed to assess the accuracy of the estimated exterior orientation parameters of the images and ground points coordinates. The analysis indicates that the RMSEs of the exterior orientation parameters and ground point coordinates is significantly decreased by about 90% in comparison with those resulted from the direct georeferencing without the aerial triangulation. From this study, we confirmed the high possibility to develop a low-cost real-time aerial monitoring system.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.36 no.4B
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• pp.378-385
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• 2011

The three-dimensional triangulation algorithm that the beacon nodes can be allocated to dynamically in not the experimental region but the practical region is suggested, and the performance of the localization system adapting the suggested algorithm is analyzed. The suggested algorithm adapts the computation method of the three dimensional point that the surfaces of three spheres overlapped, while the traditional triangulation algorithm adapts the computation method of the two dimensional point that three circles are overlapped in order to compute the distance between beacon nodes and mobile node that means a radius. In addition to this, to analyze the performance of the localization system adapting the suggested algorithm, first of all, the allocation layout of beacon nodes is made, and the allocation layout is modeled by selection of ten random distance values between mobile node and beacon nodes for computer simulation of the practical model. Next, the two dimensional coordinator of mobile node that is calculated by the suggested algorithm and the traditional triangulation algorithm is compared with each other. The localization measuring performance about three dimensional coordinator(z axis) of the suggested algorithm is also obtained by comparing with that of the practical model.

• Proceedings of the Korean Society of Surveying, Geodesy, Photogrammetry, and Cartography Conference
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• 2003.10a
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• pp.225-230
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• 2003

Efficient representation is crucial in the analysis of complex geospatial information. In case of aerial triangulation, most of currently available software are designed as black boxes where only an experienced user would be able to prepares the preformatted input file and interprete the result of the adjustment. This paper introduces a solution to this problem through the UML design of a Graphical User Interface (GUI) for the aerial triangulation task. The design was then implemented with ArcGIS. The error of the exterior orientation of each aerial Imagery was represented with a 3-D error ellipse, enabling the visualization of the adjustment result. The attributes of images and points (control points, tie points and image points) were maintained as a database which enables the searching and querying of adjustment information.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2004.10a
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• pp.690-695
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• 2004

A new dimension measuring method for the measurement of diameter of an object has been developed using laser triangulation. The 3-D data of an object was calculated from the 2dimensional image information obtained by the laser stripe using the laser triangulation. The system can measure the diameter of hole not only in a normal plane but also in an incline plane. We can experiment with magnification that is optimized according to size of object using zoom lens. In this paper, the theoretical formula and calibration of the system were described. The measuring precision of the system was investigated by experiment.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.2
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• pp.553-563
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• 1996

An algorithm for automatic mesh generation of two-dimensional arbitrary planar domain is proposed by using Delaunay triangulation algorithm. An efficient algorithm is proposed for the construction of Delaunay triangulation algorithm over convex planar domain. From the definition of boundary, boundary nodes are first defined and then interior nodes are generated ensuring the Delaunay property. These interior nodes and the boundary nodes are then linked up together to produce a valid triangular mesh for any finite element analysis. Through the various example, it is found that high-quality triangular element meshes are obtained by Delaunay algorithm, showing the robustness of the current method. The proposed mesh generation scheme has been extended to automatic remeshing, which is applicable to FE analysis including large deformation and large distortion of elements.

• Journal of Mechanical Science and Technology
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• v.17 no.11
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• pp.1665-1673
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• 2003

We propose an image-based three-dimensional shape determination system. The shape, and thus the three-dimensional coordinate information of the 3-D object, is determined solely from captured images of the 3-D object from a prescribed set of viewpoints. The approach is based on the shape-from-silhouette (SFS) technique, and the efficacy of the SFS method is tested using a sample data set. The extracted three-dimensional shape is modeled with polygons generated by a new iterative triangulation algorithm, and the polygon model can be exported to commercial software. The proposed system may be used to visualize the 3-D object efficiently, or to quickly generate initial CAD data for reverse engineering purposes, including three dimensional design applications such as 3-D animation and 3-D games.

• The Journal of Korea Robotics Society
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• v.5 no.1
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• pp.41-47
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• 2010

This paper proposes a path planning method of a mobile robot in two-dimensional work space. The path planning method is based on a cell decomposition approach. To create a path which consists of a number of line segments, the Delaunay Triangulation algorithm is used. Using the cells produced by the Delaunay Triangulation algorithm, a mesh generation algorithm connects the starting position to the goal position. Dijkstra algorithm is used to find the shortest distance path. Greedy algorithm optimizes the path by deleting the path segments which detours without collision with obstacles.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2001.04a
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• pp.53-56
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• 2001

Reverse engineering has been widely used for the shape reconstruction of an object without CAD data and it includes some steps such as scanning of a clay or wood model, and generating some manufacturing data in an STL file. A new approach to remove point data with Delaunay triangulation is introduced to deal with the size problems of STL file and the difficulties in the operation of RP process. This approach can be used to reduce a number of measuring data from laser scanner within a specified tolerance, thus it can avoid the time for handing point data during modeling process and the time for verifying and slicing STL model during RP process. Developed software enables the user to specify the criteria for the selection of group of triangles either by the angle between triangles or the percentage of triangles reduced, and thus RP models with accuracy will be helpful to automated process.