• Proceedings of the Korean Information Science Society Conference
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• 2005.11a
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• pp.964-966
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• 2005

This paper proposes a distributed algorithm to maintain the Delaunay triangulation of moving points. We assume that every point is a processor which can only communicate with the adjacent points connected by edges in the Delaunay triangulation. The topology changes of the Delaunay triangulation due to the movement of the points are updated automatically by local operations of the points without any centralized processor or global information.

• Computational Structural Engineering
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• v.9 no.4
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• pp.141-154
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• 1996

Delaunay triangulation is a very powerful method of mesh generation for its versatility such as handling complex geometries, element density control, and local/global remeshing capability, The limit of generating simplex elements(3-node elements in 2-D) only is resolved by adding generation module of 6-node quadratic elements. Since proposed adjacency does not change from 3-node element mesh to 6-node mesh, generation module can utilize the original simplex element generator. Therefore, versatility of the Delaunay triangulation is preserved. A simple upsetting problem is employed to show the possibility of the algorithm.

• Structural Engineering and Mechanics
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• v.15 no.5
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• pp.563-578
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• 2003

Delaunay triangulation is combined with an adaptive finite element method for analysis of two-dimensional crack propagation problems. The content includes detailed descriptions of the proposed procedure which consists of the Delaunay triangulation algorithm and an adaptive remeshing technique. The adaptive remeshing technique generates small elements around the crack tips and large elements in the other regions. Three examples for predicting the stress intensity factors of a center cracked plate, a compact tension specimen, a single edge cracked plate under mixed-mode loading, and an example for simulating crack growth behavior in a single edge cracked plate with holes, are used to evaluate the effectiveness of the procedure. These examples demonstrate that the proposed procedure can improve solution accuracy as well as reduce total number of unknowns and computational time.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.41 no.4
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• pp.123-130
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• 2018

Triangulation is one of the fundamental problems in computational geometry and computer graphics community, and it has huge application areas such as 3D printing, computer-aided engineering, surface reconstruction, surface visualization, and so on. The Delaunay refinement algorithm is a well-known method to generate quality triangular meshes when point cloud and/or constrained edges are given in two- or three-dimensional space. In this paper, we propose a simple but efficient algorithm to triangulate Voronoi surfaces of Voronoi diagram of spheres in 3-dimensional Euclidean space. The proposed algorithm is based on the Ruppert's Delaunay refinement algorithm, and we modified the algorithm to be applied to the triangulation of Voronoi surfaces in two ways. First, a new method to deciding the location of a newly added vertex on the surface in 3-dimensional space is proposed. Second, a new efficient but effective way of estimating approximation error between Voronoi surface and triangulation. Because the proposed algorithm generates a triangular mesh for Voronoi surfaces with guaranteed quality, users can control the level of quality of the resulting triangulation that their application problems require. We have implemented and tested the proposed algorithm for random non-intersecting spheres, and the experimental result shows the proposed algorithm produces quality triangulations on Voronoi surfaces satisfying the quality criterion.

• Journal of the Korea Computer Graphics Society
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• v.6 no.4
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• pp.23-28
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• 2000

We introduce a new method for constructing a dynamic Delaunay triangulation for a set S of n sites in the plane under the $L_{\infty}(L_1)$ metric. We find that the quadrant neighbor graph is contained in the Delaunay triangluation and that at least one edge of each triangle in the Delaunay triangulation is contained in the quadrant neighbor graph. By using these observations and employing a range tree scheme, we present a method that dynamically maintains the $L_{\infty}(L_1)$ Delaunay triangulation under insertions and deletions in $O(log^2n)$ amortized time and O(log n) expected time.

• 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 the Computational Structural Engineering Institute of Korea
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• v.14 no.4
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• pp.525-535
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• 2001

In this paper, a new adaptive analysis scheme for element-free Galerkin method(EFGM) is proposed. The novel point of this scheme is that the triangular cell structure based on the Delaunay triangulation is used in the numerical integration and the node adding/removing process. In adaptive analysis with this scheme, there is no need to divide the integration cell and the memory cell structure. For the adaptive analysis of crack propagation, the reconstruction of cell structure by adding and removing the nodes on integration cells based the estimated error should be carried out at every iteration step by the Delaunay triangulation technique. This feature provides more convenient user interface that is closer to the real mesh-free nature of EFGM. The analysis error is obtained basically by calculating the difference between the values of the projected stresses and the original EFG stresses. To evaluate the performance of proposed adaptive procedure, the crack propagation behavior is investigated for several examples.

• The Journal of Korea Robotics Society
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• v.5 no.1
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• pp.41-47
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• 2010

This paper proposes a path planning method of a mobile robot in two-dimensional work space. The path planning method is based on a cell decomposition approach. To create a path which consists of a number of line segments, the Delaunay Triangulation algorithm is used. Using the cells produced by the Delaunay Triangulation algorithm, a mesh generation algorithm connects the starting position to the goal position. Dijkstra algorithm is used to find the shortest distance path. Greedy algorithm optimizes the path by deleting the path segments which detours without collision with obstacles.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2001.04a
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• pp.53-56
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• 2001

Reverse engineering has been widely used for the shape reconstruction of an object without CAD data and it includes some steps such as scanning of a clay or wood model, and generating some manufacturing data in an STL file. A new approach to remove point data with Delaunay triangulation is introduced to deal with the size problems of STL file and the difficulties in the operation of RP process. This approach can be used to reduce a number of measuring data from laser scanner within a specified tolerance, thus it can avoid the time for handing point data during modeling process and the time for verifying and slicing STL model during RP process. Developed software enables the user to specify the criteria for the selection of group of triangles either by the angle between triangles or the percentage of triangles reduced, and thus RP models with accuracy will be helpful to automated process.

• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• 1998.03a
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• pp.129-134
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• 1998

STL which is used in Rapid Prototyping is composed of a lot of triangular facets. The number of triangles and the shapes of these triangles determine the quality of STL. Therefore, proper algorithm is necessary to enhance the quality of triangular patch. In this paper we used the Delaunay triangulation method to apply to following processes. 1) On processing for reducing sharp triangles which cause errors on intersection. 2) On processing for connecting two or more collinear edges. 3) On processing for deleting unnecessarily inserted points in coplanar polygon.