• Structural Engineering and Mechanics
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• v.75 no.6
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• pp.685-699
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• 2020

Polygonal finite element provides a great flexibility in mesh generation of crack propagation problems where the topology of the domain changes significantly. However, the control of the discretization error in such problems is a main concern. In this paper, a polygonal-FEM is presented in modeling of crack propagation problems via an automatic adaptive mesh refinement procedure. The adaptive mesh refinement is accomplished based on the Zienkiewicz-Zhu error estimator in conjunction with a weighted SPR technique. Adaptive mesh refinement is employed in some steps for reduction of the discretization error and not for tracking the crack. In the steps that no adaptive mesh refinement is required, local modifications are applied on the mesh to prevent poor polygonal element shapes. Finally, several numerical examples are analyzed to demonstrate the efficiency, accuracy and robustness of the proposed computational algorithm in crack propagation problems.

• 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.

• Journal of Institute of Convergence Technology
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• v.10 no.1
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• pp.7-12
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• 2020

We describe a efficient surface reconstruction method that reconstructs a 3D manifold polygonal mesh approximately passing through a set of 3D oriented points. Our algorithm includes 3D convex hull, octree data structure, signed distance function (SDF), and marching cubes. The 3D convex hull provides us with a fast computation of SDF, octree structure allows us to compute a minimal distance for SDF, and marching cubes lead to iso-surface generation with SDF. Our approach gives us flexibility in the choice of the resolution of the reconstructed surface, and it also enables to use on low-level PCs with minimal peak memory usage. Experimenting with publicly available scan data shows that we can reconstruct a polygonal mesh from point cloud of sizes varying from 10,000 ~ 1,000,000 in about 1~60 seconds.

• 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 Korea Multimedia Society
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• v.12 no.1
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• pp.50-57
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• 2009

This paper proposes a extraction of feature lines on a polygonal model using local implicit surface fitting technique. To extract feature lines on a polygonal model, the previous technique addressed to compute the curvature and their derivatives at mesh vertices via global implicit surface fitting. It needs a user-specified precision parameter for finding an accurate projection of the mesh vertices onto an approximating implicit surface and requires high-time consumption. But we use a local implicit surface fitting technique to estimate the local differential information near a vertex by means of an approximating surface. Feature vertices are easily detected as zero-crossings, and can then be connected along the direction of principal curvature. Our method, demonstrated on several large polygonal models, produces a good fit which leads to improved visualization.

• 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.

• 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.

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 2003.11a
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• pp.23-26
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• 2003

3차원 Polygonal Mesh는 그래픽스, 에니메이션, 게임에서 3차원 객체에 대한 표현에 사용되고, 이러한 3차원 모델에 대한 IndexedFaceSet 노드에 3차원 정전정보와 연결정보를 압축하는데 MPEG-4 3DMC를 사용한다. 이러한 연결정보는 다각형의 Mesh 형태로 3차원 모델을 구성하는 정보를 갖는데, 이는 Tepological Surgery 라고 하는 방법을 통해서 2차원의 스트립 단위의 데이터로 분해된다. 이러한 3D 데이터는 방송환경과 같은 재전송이 불가능한 네트워크의 환경에서 유무선 네트워크 상에서 채널문제로 인해서 데이터의 손실이 있게 되면, 복호화 된 데이터는 데이터의 손상이 발생하게 된다. 이러한 현상은 3D 모델의 좌표의 연결정보에 손상을 주게 되고, 여기서 복호화 된 데이터는 스트립 단위로 손상이 발생하게 된다. 이러한 현상은 3차원 모델의 좌표의 연결정보에 손상을 주게 된다. 본 논문은 이러한 3차원 정보의 손상을 효과적으로 복원하기 위한 연구에 관한 것이며, Mesh의 면을 이루는 각 꼭지점의 좌표들의 연결 정보가 손실되지 않는 스트립에서는 약간의 차이는 있을 수 있으나, 완벽한 복원을 하였고, 두 개 이상의 스트립이 붙어서 손상된 경우나, 좌표의 연결 정보가 없는 경우에는 조건에 따라 현저히 좋은 격과를 얻을 수 있었다.

• Structural Engineering and Mechanics
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• v.86 no.3
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• pp.311-324
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• 2023

Herein, we present effective polygonal finite elements to which the strain-smoothed element (SSE) method is applied. Recently, the SSE method has been developed for conventional triangular and quadrilateral finite elements; furthermore, it has been shown to improve the performance of finite elements. Polygonal elements enable various applications through flexible mesh handling; however, further development is still required to use them more effectively in engineering practice. In this study, piecewise linear shape functions are adopted, the SSE method is applied through the triangulation of polygonal elements, and a smoothed strain field is constructed within the element. The strain-smoothed polygonal elements pass basic tests and show improved convergence behaviors in various numerical problems.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.40 no.6
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• pp.132-140
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• 2003

In this paper, we propose a new scheme for view-dependent transmission of three-dimensional (3-D) polygonal mesh models with hierarchial partitioning. In order to make a view-dependent representation of 3-D mesh models, we combine sequential and progressive mesh transmission techniques. By setting higher priorities to visible parts than invisible parts, we can obtain good qualify of 3-D models in a limited transmission bandwidth. In this paper, we use a multi -layer representation of 3-D mesh models based on hierarchical partitioning. After representing the 3-D mesh model in a hierarchical tree, we determine resolutions of partitioned submeshes in the last level. Then, we send 3-D model data by view-dependent selection using mesh merging and mesh splitting operations. By the partitioned mesh merging operation, we can reduce the joint boundary information coded redundantly in the partitioned submeshes. We may transmit additional mesh information adaptively through the mesh spritting operation.