• 호남수학학술지
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• 제29권3호
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• pp.481-493
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• 2007

We will construct several types of semi-regular tilings of a hyperbolic unit disk model by defining geometric features of the definition of distance in a hyperbolic plane, area of triangle, and isometry of inversions. We researched the method of regular tilings and semi-regular tilings of hyperbolic unit disk model and wrote an semi-regular tiling construction algorithm using Cabri2 program and Cinderella program. Lastly, We want to make a product related to traditional heritage cultural patterns using Photoshop, so we'll model the advertising photos of cites; Seoul, Gwangju.

• Journal of applied mathematics & informatics
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• 제37권5_6호
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• pp.469-480
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• 2019

A generalized tiling is defined as a generalization of the properties of tiling a region of ${\mathbb{Z}}^2$ with dominoes, and comprises tiling with rhombus and any other tilings that admits height functions which can be ordered into a distributive lattice. By using properties of the distributive lattice, we prove that the Markov chain consisting of moving from one height function to the next by a flip is fast mixing and the mixing time ${\tau}({\epsilon})$ is given by ${\tau}({\epsilon}){\leq}(kmn)^3(mn\;{\ln}\;k+{\ln}\;{\epsilon}^{-1})$, where mn is the area of the grid ${\Gamma}$ that is a k-regular polycell. This result generalizes the result of the authors (T-tetromino tiling Markov chain is fast mixing, Theor. Comp. Sci. (2018)) and improves on the mixing time obtained by using coupling arguments by N. Destainville and by M. Luby, D. Randall, A. Sinclair.

• 대한원격탐사학회:학술대회논문집
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• 대한원격탐사학회 2006년도 Proceedings of ISRS 2006 PORSEC Volume I
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• pp.417-420
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• 2006

In these days, mobile application dealing with information contents on mobile or handheld devices such as mobile communicator, PDA or WAP device face the most important industrial needs. The motivation of this study is the design and implementation of mobile application using high resolution satellite imagery, large-sized image data set. Although major advantages of mobile devices are portability and mobility to users, limited system resources such as small-sized memory, slow CPU, low power and small screen size are the main obstacles to developers who should handle a large volume of geo-based 3D model. Related to this, the previous works have been concentrated on GIS-based location awareness services on mobile; however, the mobile 3D terrain model, which aims at this study, with the source data of DEM (Digital Elevation Model) and high resolution satellite imagery is not considered yet, in the other mobile systems. The main functions of 3D graphic processing or pixel pipeline in this prototype are implemented with OpenGL|ES (Embedded System) standard API (Application Programming Interface) released by Khronos group. In the developing stage, experiments to investigate optimal operation environment and good performance are carried out: TIN-based vertex generation with regular elevation data, image tiling, and image-vertex texturing, text processing of Unicode type and ASCII type.

• 대한원격탐사학회지
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• 제22권5호
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• pp.351-356
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• 2006

Based on current practical needs for geo-spatial information on mobile platform, the main theme of this study is a design and implementation of dynamic 3D terrain rendering system using spaceborne imagery, as a kind of texture image for photo-realistic 3D scene generation on mobile environment. Image processing and 3D graphic techniques and algorithms, such as TIN-based vertex generation with regular spacing elevation data for generating 3D terrain surface, image tiling and image-vertex texturing in order to resolve limited resource of mobile devices, were applied and implemented by using graphic pipeline of OpenGL|ES (Embedded System) API. Through this implementation and its tested results with actual data sets of DEM and satellite imagery, we demonstrated the realizable possibility and adaptation of complex typed and large sized 3D geo-spatial information in mobile devices. This prototype system can be used to mobile 3D applications with DEM and satellite imagery in near future.