• The Journal of Korean Association of Computer Education
• /
• v.9 no.1
• /
• pp.89-95
• /
• 2006

The local geometric properties such as curvatures and normal vectors play important roles for analyzing the local shape of objects in the fields of computer graphics and computer vision. The result of the geometric operations such as mesh simplification and mesh smoothing is dependent on how to compute the curvatures of meshes because there is no exact mathematical definition of curvature at vertices on 3D meshes. Therefore, In this paper, we indicate the fatal error in computing the sectional curvatures of the most previous discrete curvature estimations. Moreover, we present a discrete curvature estimation to overcome the error, which is based on the parabola interpolation and the geometric properties of Bezier curves. Therefore, We can well distinguish between the sharp vertices and the flat ones, so our method may be applied to a variety of geometric operations.

• Structural Engineering and Mechanics
• /
• v.74 no.4
• /
• pp.547-557
• /
• 2020

In this paper, an automatic adaptive mesh refinement procedure is presented for two-dimensional problems on the basis of a new probabilistic error estimator. First-order perturbation theory is employed to determine the lower and upper bounds of the structural displacements and stresses considering uncertainties in geometric sizes, material properties and loading conditions. A new probabilistic error estimator is proposed to reduce the mesh dependency of the responses dispersion. The suggested error estimator neglects the refinement at the critical points with stress concentration. Therefore, the proposed strategy is combined with the classic adaptive mesh refinement to achieve an optimal mesh refined properly in regions with either high gradients or high dispersion of the responses. Several numerical examples are illustrated to demonstrate the efficiency, accuracy and robustness of the proposed computational algorithm and the results are compared with the classic adaptive mesh refinement strategy described in the literature.

• Korean Journal of Computational Design and Engineering
• /
• v.2 no.3
• /
• pp.175-185
• /
• 1997

Given the widespread use of the Finite Element Method in strength analysis, automatic mesh generation is an important component in the computer-aided design of parts and assemblies. For a given resolution of geometric accuracy, the purpose of mesh generators is to discretize the continuous model of a part within this error limit. Sticking to this condition often produces many small elements around small features in spite that these regions are usually of little interest and computer resources are thus wasted. Therefore, it is desirable to selectively suppress small features from the model before discretization. This can be achieved by low-pass filtering a CAD model. A spatial function of one dimension higher than the model of interest is represented using the Fourier basis functions and the region where the function yields a value greater than a prescribed value is considered as the extent of a shape. Subsequently, the spatial function is low-pass filtered, yielding a shape without the small features. As an undesirable effect to this operation, all sharp corners are rounded. Preservation of sharp corners is important since stress concentrations might occur there. This is why the LPF (low-pass filtered) model can not be directly used. Instead, the distances of the boundary elements of the original shape from the LPF model are calculated and those that are far from the LPF model are identified and removed. It is shown that the number of mesh elements generated on the simplified model is much less than that of the original model.

• Journal of the Korea Institute of Information and Communication Engineering
• /
• v.12 no.8
• /
• pp.1377-1383
• /
• 2008

Parameterization of a 3D triangular mesh is a fundamental problem in various applications of geometric modeling and computer graphics. There are two major paradigms in mesh parameterization: energy functional minimization and the convex combination approach. In general, the convex combination approach is wifely used because of simple concept and one-to-one mapping. However, the approach has some problems such as high distortion near the boundary and time complexity. Moreover, the stability of the linear system may not be preserved according to the geometric information of the mesh. In this paper, we present an extension of the convex combination approach based on the mean value coordinates, which resolves the drawbacks of the convex combination approach. This may be a more practical solution because it is able to generate a stable linear system in a short time.

• Korean Journal of Computational Design and Engineering
• /
• v.1 no.3
• /
• pp.189-202
• /
• 1996

Complex geometric shapes can be defined simply and efficiently by combining and operating various surface primitives. These primitives and their intersection curves are used in finite element mesh generation to form an easy and intuitive procedure for finite element modelling of curved surfaces. This paper proposes techniques of automatic mesh generation on surface primitives with arbitrarily shaped boundaries and control curves, which may be created by surface to surface intersection. A method of automatic mesh generation on plane, which was previously developed by the author, has been modified for application to the surface mesh generation. Owing to the mesh generation-wise differences between planes and surfaces, the surfaces should be transformed into conceptual plane so that the modified plane mesh generation method can be applied. Surface development, mapping and mesh reconstruction are the key techniques suggested in this paper. The selection of the technique to apply can be determined automatically on the basis of the developability, existence of singularity and other characteristics of the surfaces on which the mesh is to be generated. The suggested techniques were implemented into parts of mesh generation functions of the finite element software, MacTran. Their validity and practicality were manifested by the actual use of this software.

• 한국전산유체공학회:학술대회논문집
• /
• 2011.05a
• /
• pp.294-301
• /
• 2011

A two-dimensional hybrid flaw solver has been developed for the accurate and efficient simulation of steady and unsteady flaw fields. The flow solver was cast to accommodate two different topologies of computational meshes. Triangular meshes are adopted in the near-body region such that complex geometric configurations can be easily modeled, while adaptive Cartesian meshes are, utilized in the off-body region to resolve the flaw more accurately with less numerical dissipation by adopting a spatially high-order accurate scheme and solution-adaptive mesh refinement technique. A chimera mesh technique has been employed to link the two flow regimes adopting each mesh topology. Validations were made for the unsteady inviscid vol1ex convection am the unsteady turbulent flaws over an NACA0012 airfoil, and the results were compared with experimental and other computational results.

• International Journal of Contents
• /
• v.5 no.4
• /
• pp.55-61
• /
• 2009

In this paper, we propose a hierarchical method for segmenting a given 3D mesh, which hierarchically clusters sharp vertices of the mesh using the metric of geodesic distance among them. Sharp vertices are extracted from the mesh by analyzing convexity that reflects global geometry. As well as speeding up the computing time, the sharp vertices of this kind avoid the problem of local optima that may occur when feature points are extracted by analyzing the convexity that reflects local geometry. For obtaining more effective results, the sharp vertices are categorized according to the priority from the viewpoint of cognitive science, and the reasonable number of clusters is automatically determined by analyzing the geometric features of the mesh.

• Journal of Computational Design and Engineering
• /
• v.1 no.2
• /
• pp.96-102
• /
• 2014

In the field of design and manufacturing, there are many problems with managing dynamic states of three-dimensional (3D) objects. In order to solve these problems, the four-dimensional (4D) mesh model and its modeling system have been proposed. The 4D mesh model is defined as a 4D object model that is bounded by tetrahedral cells, and can represent spatio-temporal changes of a 3D object continuously. The 4D mesh model helps to solve dynamic problems of 3D models as geometric problems. However, the construction of the 4D mesh model is limited on the time-series 3D voxel data based method. This method is memory-hogging and requires much computing time. In this research, we propose a new method of constructing the 4D mesh model that derives from the 3D mesh model with continuous rigid body movement. This method is realized by making a swept shape of a 3D mesh model in the fourth dimension and its tetrahedralization. Here, the rigid body movement is a screwed movement, which is a combination of translational and rotational movement.

• Korean Journal of Computational Design and Engineering
• /
• v.1 no.1
• /
• pp.65-75
• /
• 1996

This paper describes an automatic finite element(FE) mesh generation for three-dimensional structures consisting of free-form surfaces. This mesh generation process consists of three subprocesses: (a) definition of geometric model, i.e. analysis model, (b) generation of nodes, and (c) generation of elements. One of commercial solid modelers is employed for three-dimensional solid and shell structures. Node is generated if its distance from existing node points is similar to the node spacing function at the point. The node spacing function is well controlled by the fuzzy knowledge processing. The Delaunay method is introduced as a basic tool for element generation. Automatic generation of FE meshes for three-dimensional solid and shell structures holds great benefits for analyses. Practical performances of the present system are demonstrated through several mesh generations for three-dimensional complex geometry.

• 한국전산유체공학회:학술대회논문집
• /
• 2001.10a
• /
• pp.152-156
• /
• 2001

Three dimensional orthogonal grid generation is able to control effectively the grid spacing near the boundaries, but there are some difficulty to meshing complex geometry. The mesh complex geometry by orthogonal grid generation method must divide block of geometry It is required a careful skill, and long time. Its also difficulty to make unstructured mesh on complex geometry. Particularly, three dimensional geometry must have more time and effort. Recently, there have been growing interests in mesh generation of complex grometry, aslike an automobile headlamp, the heart. The method of easily meshing complex geometry is resarched to solve them. We suggest octree grid into one among these methods. As octrce grid is automaticaly adapted at the boundaries by determine the level operations to control the grid spacing near the boundaries are unnecessary. In this paper we showed throe dimensional mesh generation, and heat-flow analysis on the octree mesh.