• 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.

• 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.

• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• 2000.10a
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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.

• Journal of the Korean Society for Precision Engineering
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• v.16 no.3 s.96
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• pp.53-61
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• 1999

STL has several errors such as orientation error, hole error, and acute triangle error on being translated from CAD software. These errors should be corrected before using in Rapid Prototyping. So the software is necessary to correct errors. In this study, STL Editor which is a system for STL error correction and shape modification is developed and contains following characteristics. 1.Apply the triangle based data st겨cture. 2.Use the graphic user interface for easy work. 3.Use the Diet method to reduce data size. 4.Use the Delaunay triangulation method to enhance the quality of STL. 5.Modify the STL errors manually.

• 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.

• Journal of Digital Contents Society
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• v.19 no.1
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• pp.213-220
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• 2018

Face morphing, one of the most powerful image processing techniques that are often used in image processing and computer graphic fields, as it is a technique to change the image progressively and naturally from the original image to the target image. In this paper, we propose a method to generate Delaunay triangles using the facial landmark vertices generated by the Dlib face landmark detector and to implement morphing through warping and cross dissolving of Delaunay triangles between the original image and the target image. In this paper, we generate vertex points for face not manually but automatically, which is the major feature of the face such as eye, eyebrow, nose, and mouth, and is used to generate Delaunay triangles automatically which is the main characteristic of our face morphing method. Simulations show that we can add vertices manually and get more natural morphing results.

• Proceedings of the IEEK Conference
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• 2000.09a
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• pp.721-724
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• 2000

This paper presents fingerprint authentication method based on minutiae quadrangle definded by neighboring two Delaunay triangles. In this method, we first make minutiae triangle through Delaunay triangulation which adaptively connect neighboring minutiae according to the local minutiae density distribution, and then use feature vectors in authentication which is extracted from the minutiae quadrangle formed by neighboring two minutiae triangles. This prevents the degradation of matching ratio caused by the errors in image processing or local deformation of the fingerprint, and we can authenticate more discriminately as this method reflects wider local area's topological features than the features extracted from the individual minutiae triangles. To evaluate the proposed algorithm's performance, experiment are conducted on 120 fingerprints, of which size is 256 ${\times}$ 364 with 500dpi resolution. Robust authentications are possible with low FRR.

• 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.

• 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.

• Journal of Mechanical Science and Technology
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• v.20 no.11
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• pp.1881-1890
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• 2006

In this paper, a Petrov-Galerkin natural element method (PG-NEM) based upon the natural neighbor concept is presented for the free vibration and dynamic response analyses of two-dimensional linear elastic structures. A problem domain is discretized with a finite number of nodes and the trial basis functions are defined with the help of the Voronoi diagram. Meanwhile, the test basis functions are supported by Delaunay triangles for the accurate and easy numerical integration with the conventional Gauss quadrature rule. The numerical accuracy and stability of the proposed method are verified through illustrative numerical tests.