• Proceedings of the Korean Society of Precision Engineering Conference
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• 2011.06a
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• pp.1189-1190
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• 2011

• Journal of IKEEE
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• v.11 no.4
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• pp.348-357
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• 2007

Due to the improved performance and cost of personal mobile devices and rapid progress of wireless communication technology, the number of users who utilize these devices is increasing. This trend requires various types of services be available to users. So far, there have been many solutions provided for the shortest path problem. But, technologies which can offer various recommendation services to user depending on user’s current location are focused on Euclidean spaces rather than road network. Thus, in this paper, we extend the previous work to satisfy this requirement on road network database. Our proposed scheme requires pre-computation for the efficient query processing. In the preprocessing step, we first partition the input road network into a fixed number of Voronoi polygons and then pre-compute routing information for each polygon. In the meantime, we select the number of Voronoi polygons in proposition to the scale of road network. Through this selection, the required size of pre-computation is linearly increasing to the size of road network. Using this pre-computated information, we can process queries more quickly. Through experiments, we have shown that our proposed scheme can achieve excellent performance in terms of scheduling time and the number of visited nodes.

• Korean Institute of Interior Design Journal
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• v.20 no.1
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• pp.89-97
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• 2011

Furniture design is no exception to human desire for pursuit of the nature. In various design fields, it has turned out nature-decorative method in the past, and also recently it has turned out bio-adaptive method which is more root design process using principal of generation in nature world. The purpose of this study is to analyze application methods and characteristics of fractal geometry and voronoi diagram which are most representative principals of generative design in nature by research on the example of furniture design using these principals. The results of having analyzed fumitures by generative design can be summarized as follows; design principals of fractal; superposition, scaling, repetition & gradation, deformation, distortion and voronoi diagram; individual speciation, variational patten, repetition gradation, ambiguous boundary create new design concept and emergent form in furniture design. Application methods are 'form emergence by algorithm', 'conventional process based on principals of generative design', and 'reproduction of pattern from generative design'. Biological reinterpretations and new explorations of principals of nature generation offer unbounded possibilities for furniture design.

• Journal of Korean Institute of Industrial Engineers
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• v.33 no.4
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• pp.469-479
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• 2007

This paper focuses on the capacitated vehicle routing problem that determines the routes of vehicles in such a way that each customer must be visited exactly once by one vehicle starting and terminating at the depot while the vehicle capacity and the travel time constraints must be satisfied. The objective is to minimize the total traveling cost. Due to the complexity of the problem, we suggest a tabu search algorithm that combines the features of the existing search heuristics. In particular, our algorithm incorporates the neighborhood reduction method using the proximity information of the Voronoi diagram corresponding to each problem instance. To show the performance of the Voronoi tabu search algorithm suggested in this paper, computational experiments are done on the benchmark problems and the test results are reported.

• Proceedings of the KSME Conference
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• 2003.04a
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• pp.822-827
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• 2003

Topological maps have drawn more attention recently because they are compact, provide natural interfaces, and are applicable to path planning easily. To build a topological map incrementally, Voronoi diagram was used by many researchers. The Voronoi diagram, however, has difficulty in applying to arbitrarily shaped objects and needs long computation time. In this paper, we present a new method for global topological map from the local topological maps incrementally. The local topological maps are created through a thinning algorithm from a local grid map, which is built based on the sensor information at the current robot position. A thinning method requires simpler computation than the Voronoi diagram. Localization based on the topological map is usually difficult, but additional nodes created by the thinning method can improve localization performance. A series of experiments have been conducted using a two-wheeled mobile robot equipped with a laser scanner. It is shown that the proposed scheme can create satisfactory topological maps.

• International Journal of CAD/CAM
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• v.7 no.1
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• pp.91-101
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• 2007

To understand the structure of molecules, various computational methodologies have been extensively investigated such as the Voronoi diagram of the centers of atoms in molecule and the power diagram for the weighted points where the weights are related to the radii of the atoms. For a more improved efficiency, constructs like an $\alpha$-shape or a weighted $\alpha$-shape have been developed and used frequently in a systematic analysis of the morphology of molecules. However, it has been recently shown that $\alpha$-shapes and weighted $\alpha$-shapes lack the fidelity to Euclidean distance for molecules with polysized spherical atoms. We present the theory as well as algorithms of $\beta$-shape and $\beta$-complex in $\mathbb{R}^3$ which reflects the size difference among atoms in their full Euclidean metric. We show that these new concepts are more natural for most applications and therefore will have a significant impact on applications based on particles, in particular in molecular biology. The theory will be equivalently useful for other application areas such as computer graphics, geometric modeling, chemistry, physics, and material science.

• The KIPS Transactions:PartA
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• v.19A no.4
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• pp.169-174
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• 2012

We present an algorithm that computes a 3 dimensional Voronoi diagram for a protein molecule in this paper. The molecule is represented as a set of spheres with van der Waals radii. The Voronoi diagram is constructed in the 3D space by finding the voxels containing it. For the feasibility of the computation, we represent the molecule as a BVH (bounding volume hierarchy), and our system is accelerated by modern graphics hardware with CUDA programming support. Compared to single-core CPU implementations, experimental results show 323 times faster performance in the computation time, when the space is partitioned into $2^{24}$ voxels.

• Journal of the Korean Society for Precision Engineering
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• v.29 no.7
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• pp.785-792
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• 2012

Foam structure is usually hard to model due to the complexity of the geometry of cells. So, many simplified models to represent complicated foam structures have been proposed, but most of them are not actually describe the random feature of the cell structure well. So, in this study, two dimensional isotropic and anisotropic closed cell structures of the foam were modeled using the concept of Voronoi cells. The elasto-plastic deformation behavior under compressive loads was investigated by finitie element analysis, and the results were compared with ideal honeycomb structure. In addition, the effect of anisotropy of Voronoi cell structures of the foam on Young's modulus and yield stress under compressive loads was studied.

• 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.

• 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.