• Journal of Korean Society of Industrial and Systems Engineering
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• v.41 no.4
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• pp.123-130
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• 2018

Triangulation is one of the fundamental problems in computational geometry and computer graphics community, and it has huge application areas such as 3D printing, computer-aided engineering, surface reconstruction, surface visualization, and so on. The Delaunay refinement algorithm is a well-known method to generate quality triangular meshes when point cloud and/or constrained edges are given in two- or three-dimensional space. In this paper, we propose a simple but efficient algorithm to triangulate Voronoi surfaces of Voronoi diagram of spheres in 3-dimensional Euclidean space. The proposed algorithm is based on the Ruppert's Delaunay refinement algorithm, and we modified the algorithm to be applied to the triangulation of Voronoi surfaces in two ways. First, a new method to deciding the location of a newly added vertex on the surface in 3-dimensional space is proposed. Second, a new efficient but effective way of estimating approximation error between Voronoi surface and triangulation. Because the proposed algorithm generates a triangular mesh for Voronoi surfaces with guaranteed quality, users can control the level of quality of the resulting triangulation that their application problems require. We have implemented and tested the proposed algorithm for random non-intersecting spheres, and the experimental result shows the proposed algorithm produces quality triangulations on Voronoi surfaces satisfying the quality criterion.

• 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 Computational Design and Engineering
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• v.12 no.6
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• pp.422-428
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• 2007

Presented in the paper is a procedure to reconstruct a triangular mesh from a point cloud. Although, the proposed procedure is based on the well-known Voronoi diagram approach, it introduces a selection method of 'Pole' to improve the quality of resulting mesh. To select the appropriate Poles for high quality of Triangular mesh, the patterns that the Poles affect to the mesh quality are carefully analyzed. It is possible to improve the mesh quality by controlling the selection method of 'Pole' in terms of distance limit. The initial mesh obtained by the proposed procedure may include invalid triangles. To relieve this problem, a slicing method is proposed to remove invalid triangles from the initial mesh. At last, correcting technique of normal vectors of generated mesh is introduced.

• Proceedings of the IEEK Conference
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• 2003.11a
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• pp.297-300
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• 2003

In this paper, fingerprint minutiae mosaicking algorithm using minutiae of fingerprint is proposed. First, minutiae map is generated from minutiae of fingerprint and minutiae constellation is generated from fingerprint minutiae map. Minutiae constellation is constellation-shaped structure generated from Voronoi Diagram and Delaunay Triangulation using information of minutiae. Secondly, common region is detected by similarity of minutiae constellation of fingerprint minutiae map and minutiae map of individual fingerprint image is composed. Consequently composite minutiae map by mosaicking of fingerprint minutiae improve the performance of the fingerprint matching system.

• 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.

• Proceedings of the KSME Conference
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• 2003.11a
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• pp.1274-1279
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• 2003

In this paper, a new meshfree technique which improves the numerical integration accuracy is introduced. This new method called the Petrov-Galerkin natural element(PG-NE) 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(BG-NE). But, unlike BG-NE method, the test shape function is differently chosen from the trial shape function. The proposed technique ensures that the numerical integration error is remarkably reduced.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.18 no.2
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• pp.103-111
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• 2005

In this paper, a new meshfree technique which improves the numerical integration accuracy is introduced. This new method called thc Petrov-Galerkin natural clement method(PG-NEM) by authors is based on the Voronoi diagram and the Delaunay triangulation which is based on the same concept used lot conventional natural clement method called the Bubnov-Galerkin natural element method(BG-NEM). But, unlike the BG-NEM, the test basis function is differently chosen, based on the concept of Petrov-Galerkin, such that its support coincides exactly with a regular integration region in background mesh. Therefore, it is expected that the proposed technique ensures the remarkably improved numerical integration accuracy in comparison with the BG-NEM.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.37 no.12
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• pp.847-853
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• 1988

A method of three-demensional finite element mesh generation is presented in this paper. This method is based on the Delaunay's triangulation whose dual is Voronoi's diagram. A set of points is given on the boundary surface of the concerning domain and the initial tetrahedra are generated by the given set of points. Then, the quality of every tetrahedron is investigated and the interior points are generated near the tetrahedra which are inferior in quality and the tetrahedra of good quality can be controlled by the density of the initial boundary points. Regions with different material constant can be refined in tetrahedra respectively. To confirm the effectiveness of this algorithm,the total volume of tetrahedra was compared to the true volume and this mesh generator was applied to a three-dimensional electostatic problem.

• 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.

• 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.