• 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.

• The Bulletin of The Korean Astronomical Society
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• v.38 no.2
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• pp.101.2-101.2
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• 2013

We present a new computational fluid dynamic (CFD) simulation code. The code employs the moving and polyhedral unstructured mesh scheme, which is known as a superior approach to the conventional SPH (smoothed particle hydrodynamics) and AMR (adaptive mesh refinement) schemes. The code first generates unstructured meshes by the Voronoi tessellation at every time step, and then solves the Riemann problem for surfaces of every Voronoi cell to update the hydrodynamic states as well as to move former generated meshes. For the second-order accuracy, the MUSCL-Hancock scheme is implemented. To increase efficiency for generating Voronoi tessellation we also develop the incremental expanding method, by which the CPU time is turned out to be just proportional to the number of particles, i.e., O(N). We will discuss the applications of our code in the context of cosmological simulations as well as numerical experiments for galaxy formation.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2005.05a
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• pp.179-187
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• 2005

In this paper, we consider the problem of regrouping a number of service sites into a smaller number of service sites called centers. Each service site is represented as a point in the plane and has an associated value of service demand. We aim to group the sites so that each group has the balanced service demand and the sum of distances from the sites in the group to their corresponding center is minimized. To solve this problem, we propose a hybrid genetic algorithm that is combined with Voronoi diagrams. We provide a variety of experimental results by changing the weights of the two factors: service demands and distances. Our hybrid algorithm finds better solutions in a shorter computation time in comparison with a pure genetic algorithm.

• Proceedings of the KIEE Conference
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• 2004.07d
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• pp.2450-2452
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• 2004

Map building is essential to a mobile robot navigation system. Localization and path planning methods depend on map building strategies. A topological map is commonly constructed using the GVG(Generalized Voronoi Graph). The advantage of the GVG based topological map is compactness. But the GVG method have many difficulties because it consists of collision-free path. In this paper, we proposed an extended map building method, the AVG (Areal Voronoi Graph) based topological map. The AVG based topological map consists of collision-free area. This feature can improve map building, localization and path planning performance.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.24 no.1
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• pp.98-102
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• 2015

This paper proposes an autonomous navigation method for a nonholonomic mobile robot, based on the generalized Voronoi diagram (GVD). We define the look-ahead point for a given motion constraint to determine the direction of motion, which solves the problem of a minimum turning radius for the real nonholonomic mobile robot. This method can be used to direct the robot to explore an unknown environment and construct smooth feedback curves for the nonholonomic robot. As the trajectories can be smoothed, the position of the robot can be stabilized in the plane. The simulation results are presented to verify the performance of the proposed methods for the nonholonomic mobile robot. Furthermore, this approach is worth drawing on the experience of any other mobile robots.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.8 no.11
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• pp.3896-3915
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• 2014

The Reverse k Nearest Neighbor (RkNN) query is valuable for finding objects influenced by a specific object and is widely used in both scientific and commercial systems. However, the influence level of each object is unknown, information that is critical for some applications (e.g. target marketing). In this paper, we propose a new query type, Ordered Reverse k Nearest Neighbor (ORkNN), and make efforts to adapt it in an on-demand scenario. An Order-k Voronoi diagram based approach is used to answer ORkNN queries. In particular, for different values of k, we pre-construct only one Voronoi diagram. Algorithms on both the server and the clients are presented. We also present experimental results that suggest our proposed algorithms may have practical applications.

• Korean Journal of Computational Design and Engineering
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• v.15 no.1
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• pp.33-42
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• 2010

In this study, new medial surface calculation methods using Voronoi diagrams are investigated for the point samples extracted on closed surface models. The medial surface is defined by the closure of all points having more than one closest point on the shape boundary. It is a one of essential geometric information in 3D and can be used in many areas such as 3D shape analysis, dimension reduction, freeform shape deformation, image processing, computer vision, FEM analysis, etc. In industrial parts, the idealized solid parts and shell shapes including sharp edges and vertices are frequently used. Other medial surface extraction methods using Voronoi diagram have inherent separation and branch problems, so that they are not appropriate to the sharp edged objects and have difficulties to be applied to industrial parts. In addition, the branched surfaces on sharp edges in shell shapes should be eliminated to obtain representative medial shapes. In order to avoid separation and branch problems, the new approach by analyzing the shapes and specially sampling on surfaces has been developed.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.54 no.6
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• pp.417-422
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• 2005

This paper presents an EMG pattern classification method to identify motion commands for the control of the artificial arm by SOM-TVC(self organizing map - tracking Voronoi cell) based on neural network with a feature parameter. The eigenvalue is extracted as a feature parameter from the EMG signals and Voronoi cells is used to define each pattern boundary in the pattern recognition space. And a TVC algorithm is designed to track the movement of the Voronoi cell varying as the condition of additive noise. Results are presented to support the efficiency of the proposed SOM-TVC algorithm for EMG pattern recognition and compared with the conventional EDM and BPNN methods.

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 1999.06a
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• pp.69-76
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• 1999

This paper proposes a new region-oriented coding scheme of still images. The scheme first segments an image into homogeneous regions by making use of Voronoi diagrams. Then luminance components in each Voronoi region are encoded using a transform coding technique which employs the Schmidt's orthogonalization method to produce orthonormal basis-functions for arbitrarily shaped regions. In this technique, coding efficiency depends on the properties of initial vectors to be orthogonalized. Therefore we adaptively select a set of initial vectors as well as the order in which these vectors are orthogonalized. Simulation results indicate that the proposed coding scheme achieves higher coding performance with much less computation than the KLT-based scheme which we reported formerly.

• Proceedings of the Korean Information Science Society Conference
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• 1999.10a
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• pp.3-5
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• 1999

최근접 검색(nearest neighbor search)을 위해서 대부분의 기존 기법들은 데이터를 특정한 공간 인덱스 구조를 이용하여 인덱싱하고 이 인덱스를 이용하여 질의를 수행하는 방법을 사용하였다. 본 연구에서는 이러한 데이터 자체를 인덱싱하는 방법과는 달리 미리 최근접 질의의 결과가 되는 Vorononi 다이어그램을 생성해두고, 이를 통하여 최근접 검색을 수행하는 VGrid(Voronoi diagram-Grid) 기법을 제안한다. 이 방법은 미리 모든 데이터에 대한 Voronoi 다이어그램을 계산하고 그 결과를 격자(grid)를 이용하여 인덱싱한 다음 최근접 검색 질의가 주어지면 이 격자 인덱스를 이용하여 빠르게 결과를 찾아낸다. 이 방법을 이용하면 처음 인덱스를 생성할 때는 많은 계산 시간이 소모되지만, 일단 인덱스가 구성되고 나면 최근접 검색 질의 처리 시 디스크 접근 회수가 줄기 때문에 기존의 기법에 비해 빠르게 최근접 검색 질의를 수행할 수 있다.