• Proceedings of the Korean Society for the Gifted Conference
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• 2001.05a
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• pp.33-35
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• 2001

• Journal for History of Mathematics
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• v.21 no.2
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• pp.71-80
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• 2008

From the ancient Korea, our ancestor had designed the unique pattern which is Dan-chung, in architectures such as palace and Buddhist temple. In Dan-chung pattern, there are many various kinds, that is geometric pattern, arabesque pattern, plant pattern, flower pattern, animal pattern, Buddhist pattern and living pattern. So, we can see the tessellations in the Dan-chung pattern, moreover we can find the beauty of tessellation in the Korean traditional architectures and crafts. In this paper, I'll show you Korean traditional tessellations via GSP 4.0. which means geomeric program Geometer's SkechPad.

• 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.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.13 no.4
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• pp.293-305
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• 2009

In this article, we study a reduced-order modelling for distributed feedback control problem of the Burgers equations. Brief review of the centroidal Voronoi tessellation (CVT) are provided. A weighted (nonuniform density) CVT is introduced and low-order approximate solution and compensator-based control design of Burgers equation is discussed. Through weighted CVT (or CVT-nonuniform) method, obtained low-order basis is applied to low-order functional gains to design a low-order controller, and by using the low-order basis order of control modelling was reduced. Numerical experiments show that a solution of reduced-order controlled Burgers equation performs well in comparison with a solution of full order controlled Burgers equation.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2011.06a
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• pp.155-156
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• 2011

• Korean Institute of Interior Design Journal
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• v.17 no.5
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• pp.40-50
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• 2008

This article examined the applicability of spatial configuration to Escher's works through configurative logics and rules and studied the contrasting relations among the unit elements in Escher's works and their characteristics and the creative process of the characteristics. As the results of the study on the bases to maintain and create the partial elements revealed as the characteristics, it was shown that Escher's sequential transformative works demonstrated diverse expressive characteristics as a creative process of Inter-complementary contrasting relations based on the independence of the unit elements. It was also shown that the creative process of the unit elements was actualized through the maintenance base of the fixed and absolute characteristic as the logic for the creation and the creation base of the dynamic and relative characteristic. Therefore, it was interpreted that by applying the logics for creation to Escher's unit elements through the spatial interpretation of the maintenance base and the creation base as well as by configuring the units created in such a way according to the characteristics of Escher's works, spatial possibility canbe derived out from Escher's contrasting tessellation works. The process of spatial configuration is the process to make a balance between various conditions, artists own understanding of the space and his/her intention of the space. From this viewpoint, the logics for maintenance base and for creation base seem to have the potentiality as a spatial configuration to consistently meet the given conditions as well as to derive out novelty through the transformation to maintain the fixed and absolute condition(base) and the characteristics of the independent(additional) transformation arising together with the implicit relations among the transformative units.

• The Transactions of the Korea Information Processing Society
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• v.3 no.7
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• pp.1894-1905
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• 1996

Delauuany triangulation which is the dual of Dirichlet tessellation is not affine invariant. In other words, the triangulation is dependent upon the choice of the coordinate axes used to represent the vertices. In the same reason, Delahanty tetrahedrization does not have an affine iveariant transformation property. In this paper, we present a new type of tetrahedrization of spacial points sets which is unaffected by translations, scalings, shearings and rotations. An affine invariant tetrahedrization is discussed as a means of affine invariant 2 -D triangulation extended to three-dimensional tetrahedrization. A new associate norm between two points in 3-D space is defined. The visualization of the structure of tetrahedrization can discriminate between Delaunay tetrahedrization and affine invariant tetrahedrization.

• Journal of KIISE:Computer Systems and Theory
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• v.33 no.10
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• pp.768-776
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• 2006

Given an unstructured point set, we use an MLS (melting least-squares) approximation to estimate the local curvatures and their derivatives at a point by means of an approximation surface Then, we compute neighbor information using a Delaunay tessellation. feature points can then be detected as zero-crossings, and connected using curvature directions. Also this approach has a fast computation time than previous methods, which based on triangle meshes. We demonstrate our method on several large point-sampled models, rendered by point-splatting, on which the feature lines are rendered with line width determined from curvatures.

• Journal of the Korea Computer Graphics Society
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• v.4 no.2
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• pp.29-32
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• 1998

When rendering polyhedral models, normal vectors at polygon vertices are necessary for smooth shading. The most commonly used technique of approximating a vertex normal vector by averaging normal vectors of faces around the vertex yields, however, different results on different tessellations Further, continuous deformation of models may cause abrupt discontinuous changes in normal vector directions. In this paper, a variation of the above technique is proposed to avoid these problems. Specifically, it uses a weighted average of normal vectors of faces around the vertex, where the weight of a face being the angular span of the two edges incident on the vertex.

• Journal of the Korean Institute of Intelligent Systems
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• v.14 no.6
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• pp.674-677
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• 2004

This paper deals with a systematic approach for the construction of the fixed-delay tree search (FDTS) detector in the intersymbol interference channel. The approach is based on the efficient multi-dimensional space partitioning. The Voronoi diagram (VoD) and the Delaunay tessellation (DT) of the multi-dimensional space are applied to implement the algorithm. In the proposed approach, utilizing the geometric information contained in the VOD/DT, the relative location of the observation sequence is determined which has been shown to reduce the implementation complexity. Detailed construction procedures are discussed followed by an example from the intersymbol interference communication channel.