• Title/Summary/Keyword: Delaunay triangulation method

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Modified Delaunay Triangulation Based on Data Structure of Geometric Modeller (형상 모델러의 자료구조에 의한 수정 Delaunay 삼각화)

  • Chae E.-M.;Sah J.-Y.
    • Journal of computational fluids engineering
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    • v.2 no.2
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    • pp.97-103
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    • 1997
  • A modified Delaunay triangulation technique is tested for complicated computational domain. While a simple geometry. both in topology and geometry, has been well discretized into triangular elements, a complex geometry having difficulty in triangulation had to be divided into small sub-domains of simpler shape. The present study presents a modified Delaunay triangulation method based on the data structure of geometric modeller. This approach greatly enhances the reliability of triangulation, especially in complicated computational domain. We have shown that efficiency of Delaunay triangulation can be much improved by using both the GUI (Graphic User Interface) and OOP (Object-Oriented Programming).

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Acceleration of Delaunay Refinement Algorithm by Geometric Hashing (기하학적 해싱을 이용한 딜러니 개선 알고리듬의 가속화)

  • Kim, Donguk
    • Korean Journal of Computational Design and Engineering
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    • v.22 no.2
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    • pp.110-117
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    • 2017
  • Delaunay refinement algorithm is a classical method to generate quality triangular meshes when point cloud and/or constrained edges are given in two- or three-dimensional space. It computes the Delaunay triangulation for given points and edges to obtain an initial solution, and update the triangulation by inserting steiner points one by one to get an improved quality triangulation. This process repeats until it satisfies given quality criteria. The efficiency of the algorithm depends on the criteria and point insertion method. In this paper, we propose a method to accelerate the Delaunay refinement algorithm by applying geometric hashing technique called bucketing when inserting a new steiner point so that it can localize necessary computation. We have tested the proposed method with a few types of data sets, and the experimental result shows strong linear time behavior.

Application of Delaunay Triangulation on RP (Delaunay삼각형 분할법의 RP에의 응용)

  • 명태식;채희창;김옥현
    • Journal of the Korean Society of Manufacturing Technology Engineers
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    • v.8 no.3
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    • pp.35-41
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    • 1999
  • 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.

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Automatic Mesh Generation by Delaunay Triangulation and Its Application to Remeshing (Delaunay 삼각화기법을 이용한 유한요소망의 자동생성과 격자재구성에의 응용)

  • Jeong, Hyeon-Seok;Kim, Yong-Hwan
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.20 no.2
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    • pp.553-563
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    • 1996
  • An algorithm for automatic mesh generation of two-dimensional arbitrary planar domain is proposed by using Delaunay triangulation algorithm. An efficient algorithm is proposed for the construction of Delaunay triangulation algorithm over convex planar domain. From the definition of boundary, boundary nodes are first defined and then interior nodes are generated ensuring the Delaunay property. These interior nodes and the boundary nodes are then linked up together to produce a valid triangular mesh for any finite element analysis. Through the various example, it is found that high-quality triangular element meshes are obtained by Delaunay algorithm, showing the robustness of the current method. The proposed mesh generation scheme has been extended to automatic remeshing, which is applicable to FE analysis including large deformation and large distortion of elements.

3D Mesh Creation using 2D Delaunay Triangulation of 3D Point Clouds (2차원 딜로니 삼각화를 이용한 3차원 메시 생성)

  • Choi, Ji-Hoon;Yoon, Jong-Hyun;Park, Jong-Seung
    • Journal of the Korea Computer Graphics Society
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    • v.13 no.4
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    • pp.21-27
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    • 2007
  • The 3D Delaunay triangulation is the most widely used method for the mesh creation via the triangulation of a 3D point cloud. However, the method involves a heavy computational cost and, hence, in many interactive applications, it is not appropriate for surface triangulation. In this paper, we propose an efficient triangulation method to create a surface mesh from a 3D point cloud. We divide a set of object points into multiple subsets and apply the 2D Delaunay triangulation to each subset. A given 3D point cloud is cut into slices with respect to the OBB(Oriented Bounding Box) of the point set. The 2D Delaunay triangulation is applied to each subset producing a partial triangulation. The sum of the partial triangulations constitutes the global mesh. As a postprocessing process, we eliminate false edges introduced in the split steps of the triangulation and improve the results. The proposed method can be effectively applied to various image-based modeling applications.

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Adaptive finite elements by Delaunay triangulation for fracture analysis of cracks

  • Dechaumphai, Pramote;Phongthanapanich, Sutthisak;Bhandhubanyong, Paritud
    • 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.

Development of Delaunay Triangulation Algorithm Using Oct-subdivision in Three Dimensions (3차원 8분할 Delaunay 삼각화 알고리즘 개발)

  • Park S.H.;Lee S.S.
    • Korean Journal of Computational Design and Engineering
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    • v.10 no.3
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    • pp.168-178
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    • 2005
  • The Delaunay triangular net is primarily characterized by a balance of the whole by improving divided triangular patches into a regular triangle, which closely resembles an equiangular triangle. A triangular net occurring in certain, point-clustered, data is unique and can always create the same triangular net. Due to such unique characteristics, Delaunay triangulation is used in various fields., such as shape reconstruction, solid modeling and volume rendering. There are many algorithms available for Delaunay triangulation but, efficient sequential algorithms are rare. When these grids involve a set of points whose distribution are not well proportioned, the execution speed becomes slower than in a well-proportioned grid. In order to make up for this weakness, the ids are divided into sub-grids when the sets are integrated inside the grid. A method for finding a mate in an incremental construction algorithm is to first search the area with a higher possibility of forming a regular triangular net, while the existing method is to find a set of points inside the grid that includes the circumscribed sphere, increasing the radius of the circumscribed sphere to a certain extent. Therefore, due to its more efficient searching performance, it takes a shorer time to form a triangular net than general incremental algorithms.

Triangulation of Voronoi Faces of Sphere Voronoi Diagram using Delaunay Refinement Algorithm (딜러니 개선 알고리듬을 이용한 삼차원 구의 보로노이 곡면 삼각화)

  • Kim, Donguk
    • 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.

Automatic Multi-Block Grid Generation Technique Based on Delaunay Triangulation (Delaunay 삼각화 기법을 활용한 다중-블록 정렬 격자의 자동 생성 기법)

  • Kim Byoungsoo
    • 한국전산유체공학회:학술대회논문집
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    • 1999.11a
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    • pp.108-114
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    • 1999
  • In this paper. a new automatic multi=block grid generation technique for general 2D regions is introduced. According to this simple and robust method, the domain of interest is first triangulated by using Delaunay triangulation of boundary points, and then geometric information of those triangles is used to obtain block topology. Once block boundaries are obtained. structured grid for each block is generated such that grid lines have $C^0-continuity$ across inter-block boundaries. In the final step of the present method, an elliptic grid generation method is applied to smoothen grid distribution for each block and also to re-locale the inter-block boundaries, and eventually to achieve a globally smooth multi-block structured grid system with $C^1-continuity$.

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Higher Order Elements by Delaunay Triangulation (드로네이기법에 의한 고차 유한요소 생성)

  • 송영준
    • 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.

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