• Title/Summary/Keyword: Delaunay triangulation

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Development of Delaunay Triangulation Algorithm Using Subdivision (분할 Delaunay 삼각화 알고리즘 개발)

  • 박시형;이성수
    • Korean Journal of Computational Design and Engineering
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    • v.7 no.4
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    • pp.248-253
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    • 2002
  • Delaunay triangulation is well balanced in the sense that the triangles tend toward equiangularity. And so, Delaunay triangulation hasn't some slivers triangle. It's commonly used in various field of CAD applications, such as reverse engineering, shape reconstruction, solid modeling and volume rendering. For Example, In this paper, an improved Delaunay triangulation is proposed in 2-dimensions. The suggested algorithm subdivides a uniform grids into sub-quad grids, and so efficient where points are nonuniform distribution. To get the mate from quad-subdivision algorithm, the area where triangulation-patch will be most likely created should be searched first.

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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Development of Delaunay triangulation algorithm using quad subdivision (Quad-Subdivision을 이용한 Delaunay 삼각화 알고리즘 개발)

  • 박시형;이성수
    • Proceedings of the Korean Society of Machine Tool Engineers Conference
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    • pp.151-156
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    • 2000
  • Delaunay triangulation is well balanced in the sense that the triangles tend toward equiangularity. And so, Delaunay triangulation hasn't some slivers triangle. It's commonly used in various field of CAD applications, such as shape reconstruction, solid modeling and volume rendering. In this paper, an improved Delaunay triangulation is proposed in 2-dimensions. The suggested algorithm subdivides a uniform grids into sub-quad grids, and so efficient where points are non-uniform distribution. To get the mate from quad-subdivision algorithm, the area where triangulation-patch will be most likely created should be searched first.

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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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Distributed Kinetic Delaunay Triangulation

  • Yoo Taewon;Choi Sunghee;Lee Hyonik;Lee Jinwon
    • Proceedings of the Korean Information Science Society Conference
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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.

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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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Fingerprint Identification Based on Hierarchical Triangulation

  • Elmouhtadi, Meryam;El Fkihi, Sanaa;Aboutajdine, Driss
    • Journal of Information Processing Systems
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    • v.14 no.2
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    • pp.435-447
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    • 2018
  • Fingerprint-based biometric identification is one of the most interesting automatic systems for identifying individuals. Owing to the poor sensing environment and poor quality of skin, biometrics remains a challenging problem. The main contribution of this paper is to propose a new approach to recognizing a person's fingerprint using the fingerprint's local characteristics. The proposed approach introduces the barycenter notion applied to triangles formed by the Delaunay triangulation once the extraction of minutiae is achieved. This ensures the exact location of similar triangles generated by the Delaunay triangulation in the recognition process. The results of an experiment conducted on a challenging public database (i.e., FVC2004) show significant improvement with regard to fingerprint identification compared to simple Delaunay triangulation, and the obtained results are very encouraging.

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.

Integration of T-Search and Dynamic-Window Concept for Accelerated Searching Speed in Delaunay Triangulation (Delaunay Triangulation의 폴리건 검색속도 개선을 위한 T-Search와 Dynamic-Window 개념의 결합)

  • Kang, Hyun-Joo;Yoon, Sug-Joon;Kong, Ji-Young;Kim, Kang-Soo
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.27 no.5
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    • pp.681-687
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    • 2003
  • Terrain surfaces have to be modeled in very detail and wheel-surface contacting geometry must be well defined in order to obtain proper ground-reaction and friction forces fur realistic simulation of off-road vehicles. Delaunay triangulation is one of the most widely used methods in modeling 3-dimensional terrain surfaces, and the T-search is a relevant algorithm for searching resulting triangular polygons. The T-search method searches polygons in a successive order and may not allow real-time computation of off-road vehicle dynamics if the terrain is modeled with many polygons, depending on the computer performance used in the simulation. The dynamic T-search, which is proposed in this paper, combines conventional T-search and the concept of the dynmaic-window search which uses reduced searching windows or sets of triangular surface polygons at each frame by taking advantage of the information regarding dynamic charactereistics of a simulated vehicle. Numerical tests show improvement of searching speeds by about 5% for randomly distributed triangles. For continuous search following a vehicle path, which occurs in actual vehicle simulation, the searching speed becomes 4 times faster.

A Dynamic Delaunay Triangulation in the L(L1) Metric (L(L1) 동적 디루니 삼각분할 방법)

  • Wee, Youngcheul;Kimn, Hajine;Seo, Sangku
    • 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.

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