• Journal of Mechanical Science and Technology
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• v.20 no.11
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• pp.1881-1890
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• 2006

In this paper, a Petrov-Galerkin natural element method (PG-NEM) based upon the natural neighbor concept is presented for the free vibration and dynamic response analyses of two-dimensional linear elastic structures. A problem domain is discretized with a finite number of nodes and the trial basis functions are defined with the help of the Voronoi diagram. Meanwhile, the test basis functions are supported by Delaunay triangles for the accurate and easy numerical integration with the conventional Gauss quadrature rule. The numerical accuracy and stability of the proposed method are verified through illustrative numerical tests.

• Tunnel and Underground Space
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• v.31 no.6
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• pp.593-609
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• 2021

We proposed a numerical method for the thermo-mechanical behavior of rock fracture using a grain-based distinct element model (GBDEM) and simulated thermally induced fracture slip. The present study is the benchmark simulation performed as part of DECOVALEX-2023 Task G, which aims to develop a numerical method to estimate the coupled thermo-hydro-mechanical processes within the crystalline rock fracture network. We represented the rock sample as an assembly of Voronoi grains and calculated the interaction of the grains (blocks) and their interfaces (contacts) using a distinct element code, 3DEC. Based on an equivalent continuum approach, the micro-parameters of grains and contacts were determined to reproduce rock as an elastic material. Then, the behavior of the fracture embedded in the rock was characterized by the contacts with Coulomb shear strength and tensile strength. In the benchmark simulation, we quantitatively examined the effects of the boundary stress and thermal stress due to heat conduction on fracture behavior, focusing on the mechanism of thermally induced fracture slip. The simulation results showed that the developed numerical model reasonably reproduced the thermal expansion and thermal stress increment, the fracture stress and displacement and the effect of boundary condition. We expect the numerical model to be enhanced by continuing collaboration and interaction with other research teams of DECOVALEX-2023 Task G and validated in further study experiments.

• Proceedings of the Korean Society of Computational and Applied Mathematics Conference
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• 2003.09a
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• pp.1-1
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• 2003

In this talk, a reduced-order modeling methodology based on centroidal Voronoi tessellations (CVT's)is introduced. CVT's are special Voronoi tessellations for which the generators of the Voronoi diagram are also the centers of mass (means) of the corresponding Voronoi cells. The discrete data sets, CVT's are closely related to the h-means clustering techniques. Even with the use of good mesh generators, discretization schemes, and solution algorithms, the computational simulation of complex, turbulent, or chaotic systems still remains a formidable endeavor. For example, typical finite element codes may require many thousands of degrees of freedom for the accurate simulation of fluid flows. The situation is even worse for optimization problems for which multiple solutions of the complex state system are usually required or in feedback control problems for which real-time solutions of the complex state system are needed. There hava been many studies devoted to the development, testing, and use of reduced-order models for complex systems such as unsteady fluid flows. The types of reduced-ordered models that we study are those attempt to determine accurate approximate solutions of a complex system using very few degrees of freedom. To do so, such models have to use basis functions that are in some way intimately connected to the problem being approximated. Once a very low-dimensional reduced basis has been determined, one can employ it to solve the complex system by applying, e.g., a Galerkin method. In general, reduced bases are globally supported so that the discrete systems are dense; however, if the reduced basis is of very low dimension, one does not care about the lack of sparsity in the discrete system. A discussion of reduced-ordering modeling for complex systems such as fluid flows is given to provide a context for the application of reduced-order bases. Then, detailed descriptions of CVT-based reduced-order bases and how they can be constructed of complex systems are given. Subsequently, some concrete incompressible flow examples are used to illustrate the construction and use of CVT-based reduced-order bases. The CVT-based reduced-order modeling methodology is shown to be effective for these examples and is also shown to be inexpensive to apply compared to other reduced-order methods.

• Journal of Korea Multimedia Society
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• v.9 no.10
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• pp.1282-1295
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• 2006

This paper proposes a method of image tile mosaics to preserve detailed depiction of the source image. This method enhance the shortcoming of the previous mosaic methods that cannot express the detailed depiction because of the gap between tiles. Our method is implemented by the usage of image tiles to preserve detailed depiction of the source image, as well as the usage of 2-layered tiles to.eliminate the gap between tiles. The method suggested in this paper are composed of following process. First of all, the position of the upper layer tile is located through a centroidal voronoi diagram to which an edge avoidance technique is applied, and the position of the lower layer tile is calculated using Delaunay triangulation. Secondly, discover the size and direction field of the tile considering the relation between tiles. Thirdly, adopt a photomosaic technique to use the image tiles. At this time, the technique of multi-level indexing is used to accelerate the speed of image searching. Through above process, the gap between tiles is minimized against other methods and a mosaic image with a maximized detailed description is achieved.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.34 no.1
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• pp.74-80
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• 2006

This paper addresses the trajectory optimization of Unmanned Aerial Vehicles(UAVs) under multiple ground threats like enemy's anti-air radar sites. The power of radar signal reflected by the vehicle and the flight time are considered in the performance cost to be minimized. The bank angle is regarded as control input for a 1st-order lag vehicle, and input parameter optimization method based on Sequential Quadratic Programming (SQP) is used for trajectory optimization. The proposed path planning method provides more practical trajectories with enhanced survivability than those of Voronoi diagram method.

• Journal of Biomedical Engineering Research
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• v.27 no.3
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• pp.125-130
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• 2006

The number of the living endothelial cells and the shape of those are very import clinical parameters for the evaluation of the quality of cornea. In this paper, we developed the automated endothelial cell counting and shape analysis algorithm for a confocal microscope. Since, the endothelial images from the confocal microscope has a non-uniform illumination and low contrast between cell boundaries and cell bodies, it is very difficult to segment the cells from the endothelial images. To cope with these difficulties, we proposed the new two stage image processing algorithm. At first stage algorithm, we used a high-pass filter and histogram equalization to compensate the non-uniform brightness pattern and a morphological filter and a watershed method are applied to detect the boundary of cells. From this stage, we could count the number of cells in an endothelial image. At second stage algorithm, we used a Voronoi diagram method to classify the shape of cells. This cell shape analysis and the percent of hexagonal cells are very sensitive in detecting the early endothelium damage. To evaluate the performance of the proposed system, we p개cessed seven endothelial images obtained using a confocal microscope. The proposed system correctly counted 95.5% cells and classified 92.0% of hexagonal cell shapes. This result is better than any others in this research area.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2004.04a
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• pp.333-340
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• 2004

This paper deals with geometric nonlinear analyses using a new meshfree technique which improves the numerical integration accuracy. The new method called the Petrov-Galerkin natural element method (PGNEM) is based on the Voronoi diagram and the Delaunay triangulation which is based on the same concept used for conventional natural element method called the Bubnov-Galerkin natural element method (BGNEM). But, unlike BGNEM, the test shape function is differently chosen from the trial shape function. In the linear static analysis, it is ensured that the numerical integration error of the PGNEM is remarkably reduced. In this paper, the PGNEM is applied to large deformation problems, and the accuracy of the proposed numerical technique is verified through the several examples.

• Korean Journal of Computational Design and Engineering
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• v.22 no.2
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• pp.110-117
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• 2017

Delaunay refinement algorithm is a classical method to generate quality triangular meshes when point cloud and/or constrained edges are given in two- or three-dimensional space. It computes the Delaunay triangulation for given points and edges to obtain an initial solution, and update the triangulation by inserting steiner points one by one to get an improved quality triangulation. This process repeats until it satisfies given quality criteria. The efficiency of the algorithm depends on the criteria and point insertion method. In this paper, we propose a method to accelerate the Delaunay refinement algorithm by applying geometric hashing technique called bucketing when inserting a new steiner point so that it can localize necessary computation. We have tested the proposed method with a few types of data sets, and the experimental result shows strong linear time behavior.

• Journal of Institute of Control, Robotics and Systems
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• v.16 no.1
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• pp.53-60
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• 2010

We propose a motion planning method for autonomous mobile robots. In order to minimize traveling time, a smooth path and a time optimal velocity profile should be generated under kinematic and dynamic constraints. In this paper, we develop an effective and practical method to generate a good solution with lower computation time. The initial path is obtained from voronoi diagram by Dijkstra's algorithm. Then the path is improved by changing the graph and path simultaneously. We apply the dynamic programming algorithm into the stage of improvement. Simulation results are presented to verify the performance of the proposed method.

• Journal of the Korea Computer Graphics Society
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• v.7 no.2
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• pp.11-19
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• 2001

This paper proposes a colored paper mosaic rendering technique based on image segmentation that can automatically generate torn and tagged colored paper mosaic effect. and 3D effect that come about in human-made mosaic work can be represented by generating shadow using difference of paper thickness. Previous method did not produce satisfactory results due to the ineffectiveness of having to use pieces of the same size. The proposed two methods for determination of paper shape and location that are based on segmentation can subdivide image area by considering characteristics of image. The first method is to generate Voronoi polygon after subdividing the segmented image again using quad tree. And the second method is to apply the Voronoi diagram on each segmentation layer. Through these methods, the characteristic of the image is expressed in more detail than previous colored paper mosaic rendering method and these methods enable to produce image that is closer to human-made mosaic work.