• Journal of architectural history
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• v.11 no.4 s.32
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• pp.45-69
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• 2002

This study aims to find out the genetic characteristics of gridded subdivision area which has its origin from ancient local administrative city-Sangju, Jeonju, Namwon, Kwangju, Chungju. The spatial structure, based on the inter-relationship among gridded subdivision area, city wall, and topographic condition, and the morphological characteristics of gridded subdivision area are analyzed. The points of analysis on morphological characteristics of gridded subdivision area consist of the size of unit block, the organization system of unit block, the orientation of subdivision line. As a result of the analysis, three main characteristics are found. Firstly there can be found no same land subdivision rule among study areas. Secondly, the morphological features of study area were the products of cumulative process of different subdivision areas which were developed in different periods. Thirdly, the original regular gridded land subdivision seems to have been carried out in the object of a farm-land cultivation around 7th century. And there was a change of land-use from farm land to urban land-use during the later 7th century and 8th century.

• Communications of the Korean Mathematical Society
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• v.31 no.2
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• pp.395-414
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• 2016

In this work, we study on subdivision schemes reproducing polynomials and build a symmetric subdivision scheme reproducing polynomials of a certain predetermined degree, which is a slight variant of the family of Deslauries-Dubic interpolatory ones. Related to polynomial reproduction, a necessary and sufficient condition for a subdivision scheme to reproduce polynomials of degree L was recently established under the assumption of non-singularity of subdivision schemes. In case of stepwise polynomial reproduction, we give a characterization for a subdivision scheme to reproduce stepwise all polynomials of degree ${\leq}L$ without the assumption of non-singularity. This characterization shows that we can investigate the polynomial reproduction property only by checking the odd and even masks of the subdivision scheme. The minimal-support condition being relaxed, we present explicitly a general formula for the mask of (2n + 4)-point symmetric subdivision scheme with two parameters that reproduces all polynomials of degree ${\leq}2n+1$. The uniqueness of such a symmetric subdivision scheme is proved, provided the two parameters are given arbitrarily. By varying the values of the parameters, this scheme is shown to become various other well known subdivision schemes, ranging from interpolatory to approximating.

• Honam Mathematical Journal
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• v.27 no.4
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• pp.665-672
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• 2005

By its simplicity and efficiency, subdivision is a widely used technique in computer graphics, computer aided design and data compression. In this paper we prove a regularity theorem for ternary interpolatory subdivision scheme that can be applied to non-stationary subdivision. This theorem converts the convergence of the limit curve of a ternary interpolatory subdivision to the analysis of the rate of the contraction of differences of the polygons.

• International Journal of CAD/CAM
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• v.5 no.1
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• pp.29-38
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• 2005

A non-uniform 3-point ternary interpolatory subdivision scheme with variable subdivision weights is introduced. Its support is computed. The $C^0$ and $C^1$ convergence analysis are presented. To elevate its controllability, a modified edition is proposed. For every initial control point on the initial control polygon a shape weight is introduced. These weights can be used to control the shape of the corresponding subdivision curve easily and purposefully. The role of the initial shape weight is analyzed theoretically. The application of the presented schemes in designing smooth interpolatory curves and surfaces is discussed. In contrast to most conventional interpolatory subdivision scheme, the presented subdivision schemes have better locality. They can be used to generate $C^0$ or $C^1$ interpolatory subdivision curves or surfaces and control their shapes wholly or locally.

• Communications of the Korean Mathematical Society
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• v.39 no.3
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• pp.803-819
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• 2024

In our study, the integration of fuzzy graphs into classical graph theory gives rise to a novel concept known as "Fuzzy Super Subdivision." Let SS_f (G) be the fuzzy super subdivision graphs, by substituting a complete bipartite graph k_(2,m) (m = 1, 2, . . .) for each edge of a fuzzy graph. The attributes and properties of this newly proposed concept are briefly outlined, in addition to illustrative examples. Furthermore, significant findings are discussed on connectivity, size, degree and order of fuzzy super subdivision structures. To illustrate the practical implications of our approach, we present an application focused on analyzing the growth of infections in blood or urine samples using the Fuzzy Super Subdivision model.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2003.04a
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• pp.253-260
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• 2003

In computer-aided geometric modeling(CAGD), subdivision surfaces are frequently employed to construct free-form surfaces. In the present study, Loop scheme and Catmull-Clark scheme are applied to generate smooth surfaces. To be consistent with the limit points of target surface, the initial sampling points are properly rearranged. The pointwise errors of curvature and position in the sequence of subdivision process are evaluated in both Loop scheme & Catmull-Clark subdivision scheme. In partcural, a general subdivision method in order to generate considering extraordinary points are implemented free from surface with arbitrary sampling point information.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.95-104
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• 2007

We study stationary subdivision schemes based on radial basis function interpolation. Each scheme has a tension parameter, say ${\lambda}$, which actually belongs to the radial basis function. In particular, adapted subdivision rules on bounded intervals are developed.

• International Journal of CAD/CAM
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• v.6 no.1
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• pp.139-148
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• 2006

Catmull-Clark subdivision scheme provides a powerful method for building smooth and complex surfaces. But the number of faces in the uniformly refined meshes increases exponentially with respect to subdivision depth. Adaptive tessellation reduces the number of faces needed to yield a smooth approximation to the limit surface and, consequently, makes the rendering process more efficient. In this paper, we present a new adaptive tessellation method for general Catmull-Clark subdivision surfaces. Different from previous control mesh refinement based approaches, which generate approximate meshes that usually do not interpolate the limit surface, the new method is based on direct evaluation of the limit surface to generate an inscribed polyhedron of the limit surface. With explicit evaluation of general Catmull-Clark subdivision surfaces becoming available, the new adaptive tessellation method can precisely measure error for every point of the limit surface. Hence, it has complete control of the accuracy of the tessellation result. Cracks are avoided by using a recursive color marking process to ensure that adjacent patches or subpatches use the same limit surface points in the construction of the shared boundary. The new method performs limit surface evaluation only at points that are needed for the final rendering process. Therefore it is very fast and memory efficient. The new method is presented for the general Catmull-Clark subdivision scheme. But it can be used for any subdivision scheme that has an explicit evaluation method for its limit surface.

• Korean Journal of Computational Design and Engineering
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• v.8 no.1
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• pp.1-9
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• 2003

Recently, designing 3D objects using various modeling techniques become getting more important issues in related industrial fields. The subdivision scheme is a technique that generates a smooth sur-face through many times of refinement processes that split polygons of control mesh into several smaller polygons. In this paper, we propose a new subdivision algorithm that preserves sharp-edges of control mesh after several refinement processes in the Doo-Sabin subdivision scheme. Using the pro-posed algorithm, the Doo-Sabin subdivision scheme can be well applied to modeling 3D objects with sharp-edges.

• Proceedings of the Korea Society of Design Studies Conference
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• 2002.05b
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• pp.262-263
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• 2002