• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.25 no.3
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• pp.66-81
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• 2021

In this paper, we review the lowest order staggered discontinuous Galerkin methods on polygonal meshes in 2D. The proposed method offers many desirable features including easy implementation, geometrical flexibility, robustness with respect to mesh distortion and low degrees of freedom. Discrete function spaces for locally H¹ and H(div) spaces are considered. We introduce special properties of a sub-mesh from a given star-shaped polygonal mesh which can be utilized in the construction of discrete spaces and implementation of the staggered discontinuous Galerkin method. For demonstration purposes, we consider the lowest case for the Poisson equation. We emphasize its efficient computational implementation using only geometrical properties of the underlying mesh.

• Structural Engineering and Mechanics
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• v.30 no.1
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• pp.119-129
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• 2008

A small strain and elastoplastic formulation of Polygonal Element Method (PEM) is developed for efficient analysis of elastoplastic solids. In this work, the polygonal elements are constructed based on traditional triangular finite meshes. The construction method of polygonal mesh can directly utilize the sophisticated triangularization algorithm and reduce the difficulty in generating polygonal elements. The Wachspress rational finite element basis function is used to construct the approximations of polygonal elements. The incremental variational form and a von Mises type model are used for non-linear elastoplastic analysis. Several small strain elastoplastic numerical examples are presented to verify the advantages and the accuracy of the numerical formulation.

• Korean Journal of Computational Design and Engineering
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• v.9 no.4
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• pp.294-305
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• 2004

Highly detailed geometric models are rapidly becoming commonplace in computer graphics and other applications. These complex models, which is often represented as complex1 triangle meshes, mainly suffer from the vast memory requirement for real-time manipulation of arbitrary geometric shapes without loss of data. Various techniques have been devised to challenge these problems in views of geometric processing, not a representation scheme. This paper proposes the new mesh structure for the compact representation and the efficient handling of the highly complex models. To verify the compactness and the efficiency, the memory requirement of our representation is first investigated and compared with other existing representations. And then we analyze the time complexity of our data structure by the most critical operation, that is, the enumeration of the so-called one-ring neighborhood of a vertex. Finally, we evaluate some elementary modeling functions such as mesh smoothing, simplification, and subdivision, which is to demonstrate the effectiveness and robustness of our mesh structure in the context of the geometric modeling and processing.

• 한국전산유체공학회:학술대회논문집
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• 2000.05a
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• pp.178-183
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• 2000

An efficient Newton-GMRES algorithm is presented for computing two-dimensional steady compressible viscous flows on unstructured hybrid meshes. The scheme is designed on cell-centered finite volume method which accepts general polygonal meshes. Steady-state solution is obtained with pseudo-transient continuation strategy. The preconditioned, restarted general minimum residual(GMRES) method is employed in matrix-free form to solve the linear system arising at each Newton iteration. The incomplete LU fartorization is employed for the preconditioning of linear system. The Spalart-Allmars one equation turbulence model is fully coupled with the flow equations to simulate turbulence effect. The accuracy, efficiency and robustness of the presently developed method are demonstrated on various test problems including laminar and turbulent flows over flat plate and airfoils.

• The Research Journal of the Costume Culture
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• v.10 no.6
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• pp.709-717
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• 2002

In the apparel industry, the technology has been advanced rapidly. The use of 3D scanning systems fur the capture and measurement of human body is becoming common place. Three dimensional digital image can be used for design, inspection, reproduction of physical objects. The purpose of this study is to develop a method that drafts men's basic bodice pattern from scanned 3D body surface shape data. In order to pursue this purpose the researchers developed pattern drafting algorithm. The 3D scanner used in this study was Cyberware Whole Body Scanner WB-4. The bodice pattern drafting algorithm from 3D body surface shape data developed in this study is as follows. First, convert geometric 3D body surface data to 3D polygonal mesh data. Second, develop algorithm to lay out 3D polygonal patches onto a plane using Auto Lisp program. The polygon meshes are coplanar, and the individual mesh is continuously in contact with next one The bodice front surface shape data in polygonal patches form was lined up in bust and waist levels. The back bodice was drafted by lining up the polygonal mesh in scapula, chest, and waist levels. in the drafts, gaps between polygons were formed into the darts.

• Journal of KIISE:Computer Systems and Theory
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• v.27 no.3
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• pp.245-254
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• 2000

This paper proposes a new discrete curvature error metric to generate LOD meshes. For mesh simplification, discrete curvatures are defined with geometric attributes, such as angles and areas of triangular polygonal model, and dihedral angles without any smooth approximation. They can represent characteristics of polygonal surface well. The new error metric based on them, discrete curvature error metric, increases the accuracy of simplified model by preserving the geometric information of original model and can be used as a global error metric. Also we suggest that LOD should be generated not by a simplification ratio but by an error metric. Because LOD means the degree of closeness between original and each level's simplified model. Therefore discrete curvature error metric needs relatively more computations than known other error metrics, but it can efficiently generate and control LOD meshes which preserve overall appearance of original shape and are recognizable explicitly with each level.

• International Journal of CAD/CAM
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• v.5 no.1
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• pp.91-98
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• 2005

This paper presents a scheme for interpolating intersecting uniform cubic B-spline curves by Catmull-Clark subdivision surfaces. The curves are represented by polygonal complexes and the neighborhoods of intersection points are modeled by X-Configurations. When these structures are embedded within a control polyhedron, the corresponding curves will automatically be interpolated by the surface limit of subdivision of the polyhedron. The paper supplies a construction which clearly shows that interpolation can still be guaranteed even in the absence of symmetry at the X-configurations. In this sense, this scheme generalizes an already existing technique by the same authors, thereby allowing more freedom to designers.

• Journal of the Korean Institute of Landscape Architecture
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• v.27 no.4
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• pp.137-142
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• 1999

The purpose of this study is to develope a CAD-based tool for rasterization of polygonal vector map in AutoCAD. To identity the layer property of polygonal entity with user-defined coordinates as topology, algorithm in processing entity data of selection set that intersected with scan line was used, and the layers were extracted sequentially by sorted intersecting points in data-list. In addition to the functions for querying and modifying topology, two options for mapping were set up to construct plan projection type and to change meshes' properties in existing DTM data. In case of plan projection type, user-defined cell size of 3DFACE mesh is available for more detailed edge, and topological draping on landform can be executed in case of referring DTM data as an AutoCAD's drawing. The concept of algorithm was simple and clear, but some unexpectable errors were found in detecting intersected coordinates that were AutoCAD's error, not the utility's. Also, the routines to check these errors were included in algorithmic processing. Developed utility named MESHMAP was written in entity data control functions of AutoLISP language and dialog control language(DCL) for the purpose of user-oriented interactive usage. MESHMAP was proved to be more effective in data handling and time comparing with GRIDMAP module in LANDCADD which has similar function.

• Steel and Composite Structures
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• v.51 no.4
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• pp.363-375
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• 2024

Within the optimization field, addressing the intricate posed by fluidic pressure loads on functionally graded structures with frequency-related designs is a kind of complex design challenges. This paper thus introduces an innovative density-based topology optimization strategy for frequency-constraint functionally graded structures incorporating Darcy's law and a drainage term. It ensures consistent treatment of design-dependent fluidic pressure loads to frequency-related structures that dynamically adjust their direction and location throughout the design evolution. The porosity of each finite element, coupled with its drainage term, is intricately linked to its density variable through a Heaviside function, ensuring a seamless transition between solid and void phases. A design-specific pressure field is established by employing Darcy's law, and the associated partial differential equation is solved using finite element analysis. Subsequently, this pressure field is utilized to ascertain consistent nodal loads, enabling an efficient evaluation of load sensitivities through the adjoint-variable method. Moreover, this novel approach incorporates load-dependent structures, frequency constraints, functionally graded material models, and polygonal meshes, expanding its applicability and flexibility to a broader range of engineering scenarios. The proposed methodology's effectiveness and robustness are demonstrated through numerical examples, including fluidic pressure-loaded frequency-constraint structures undergoing small deformations, where compliance is minimized for structures optimized within specified resource constraints.

• The Bulletin of The Korean Astronomical Society
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• v.40 no.1
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• pp.50.1-50.1
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• 2015

We present a new hydrodynamic simulation based on the unstructured moving mesh scheme. The simulation utilizes the Voronoi tessellation technique that produces polygonal cells composed of, on average, 13 surfaces each in 3D. We devise the incremental expanding method (IEM) and hybrid-neighbor searching algorithm and achieve the CPU time just proportional to the number of particles, i.e., O(N). We show the results of requisite tests for hydrodynamic simulations and demonstrate superiority of our code over the conventional codes using the stationary meshes. The applications in the context of cosmological and galactic simulations are also discussed.