• 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.

• 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.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2007.06a
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• pp.69-70
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• 2007

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.32 no.2
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• pp.87-93
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• 2014

Cadastral parcel objects as polygons are fundamental dataset which represent land administration and management of the real world. Thus it is necessary to assure topological seamlessness of cadastral datasets which means no overlaps or gaps between adjacent parcels. However, the problem of overlaps or gaps are frequently found due to non-coinciding edges between adjacent parcels. These erroneous edges are called uncertain edges, and polygons containing at least one uncertain edge are called uncertain polygons. In this paper, we proposed a new algorithm to efficiently search parcels of uncertain polygons between two adjacent cadastral datasets. The algorithm first selects points and polylines around adjacent datasets. Then the Constrained Delaunay Triangulation (CDT) is applied to extract triangles. These triangles are tagged by the number of the original cadastral datasets which intersected with the triangles. If the tagging value is zero, the area of triangles mean gaps, meanwhile, the value is two, the area means overlaps. Merging these triangles with the same tagging values according to adjacency analysis, uncertain edges and uncertain polygons could be found. We have performed experimental application of this automated derivation of partitioned boundary from a real land-cadastral dataset.

• Korean Journal of Computational Design and Engineering
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• v.8 no.1
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• pp.10-18
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• 2003

FEM (Finite Element Method) is a fundamental numerical analysis technique in wide spread use in engineering application. As the solving time occupies small portion of entire FEM analysis time because of development of hardware, the relative lime to the whole analysis time to make mesh mod-els is growing. In particular, in the case of stiffeners such as features attached to plate in ship structure, the line constraints are imposed on mesh model together with other constraints such as holes. To auto-matically generate two dimensional quadrilateral mesh with the line constraints, an algorithm is pro-posed based on the constrained Delaunay triangulation and Q-Morph algorithm in which the line constraints are not considered. The performance of the proposed algorithm is evaluated. And some numerical results of our proposed algorithm ate presented.

• Journal of the Korean Association of Geographic Information Studies
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• v.10 no.3
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• pp.113-122
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• 2007

The rapid growth of aerial survey and remote sensing technology has enabled the rapid acquisition of very large amounts of geographic data, which should be analyzed using real-time visualization technology. The level of detail(LOD) algorithm is one of the most important elements for realizing real-time visualization. We chose the triangulated irregular network (TIN) method to generate normalized digital elevation model(DEM) data. First, we generated TIN data using contour lines obtained from a two-dimensional(2D) digital map and created a 2D grid array fitting the size of the area. Then, we generated normalized DEM data by calculating the intersection points between the TIN data and the points on the 2D grid array. We used constrained Delaunay triangulation(CDT) and ray-triangle intersection algorithms to calculate the intersection points between the TIN data and the points on the 2D grid array in each step. In addition, we simulated a three-dimensional(3D) terrain model based on normalized DEM data with real-time visualization using a Microsoft Visual C++ 6.0 program in the DirectX API library and a quad-tree LOD algorithm.

• Proceedings of the Korean Information Science Society Conference
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• 2001.04b
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• pp.625-627
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• 2001

기존의 종이지도를 수치지도 처리과정으로 얻어진 등고선(contour line) 데이터는 원격탐사(Remote Sensing)와 지리정보시스템(GIS)의 응용분야에서 주로 사용되어지는 데이터이다. 이러한 등고선은 해당 지역의 DTM(Digital Terrain Model) 데이터 생성을 위해 보간(interpolation)하여 생성하는 데 연구가 집중되어 왔다. 본 논문에서는 DEM(Digital levation Model)으로부터 얻어진 등고선 데이터를 이용하여 사용자에게 3차원으로 가시화 해 줄 수 있는 기법을 소개한다. 등고선 추출을 위한 방법으로는 기존의 소개되어진 Marching Square 알고리즘을 적용하였고, 지역적인 최고점(local minimum)과 최소점(maximum)을 구하기 위해 등고선을 열린 등고선(open contour)과 닫힌 등고선(closed contour)으로 분류하게 된다. 지역적 최고, 최소점을 찾기 위한 탐색공간을 줄이기 위해 닫힌 등고선만을 닫힌 등고만을 대상으로 등고선 트리를 생성하였으며, 생성된 트리의 리프노드에 대해서 최고, 최소점에 대한 근사(approximation)를 수행하게 된다. 이렇게 구해진 근사된 장점들과 등고선 데이털 입력으로 하여 제한된 딜로니 삼각분할(Constrained Delaunay Triangulation)을 수행함으로써, 3차원 지형을 재구성할 수 있다. 실험에서 간단한 그리드 샘플데이터와 USGS로 획득한 데이터를 이용하여 속도 측정을 하였다. 결과적으로 저장공간 측면에서 적은 량의 데이터를 가지면서 등고선을 표현할 수 있는 3차원 지형을 랜더링할 수가 있음을 알 수 있다.

• Proceedings of the Korea Information Processing Society Conference
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• 2001.10a
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• pp.641-644
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• 2001

기존의 종이지도를 수치지도 처리과정으로 얻어진 등고선(contour line) 데이터는 원격탐사(Remote Sensing)와 지리정보시스템(GIS)의 응용분야에서 주로 사용되어지는 데이터이다. 이러한 등고선은 해당 지역의 DTM(Digital Terrain Model) 데이터 생성을 위해 보간(interpolation)하여 생성하는 데 연구가 집중되어 왔다. 본 논문에서는 DEM(Digital Elevation Model)으로부터 얻어진 등고선 데이터를 이용하여 사용자에게 3 차원으로 가시화 해 줄 수 있는 기법을 소개한다. 등고선 추출을 위한 방법으로는 기존의 소개되어진 Marching Square 알고리즘을 적용하였고, 지역적인 최고점(local minimum)과 최소점(maximum)을 구하기 위해 등고선을 열린 등고선(open contour)과 닫힌 등고선(closed contour)으로 분류하게 된다. 지역적 최고, 최소점을 찾기 위한 탐색공간을 줄이기 위해 닫힌 등고선만을 대상으로 등고선 트리를 생성하였으며, 생성된 트리의 리프노드에 대해서 최고, 최소점에 대한 근사(approximation)를 수행하게 된다. 이렇게 구해진 근사된 정점들과 등고선 데이터를 입력으로 하여 제한된 딜로니 삼각분할(Constrained Delaunay Triangulation)을 수행함으로써, 3 차원 지형을 재구성할 수 있다. 실험에서 USGS 로부터 획득한 지형 데이터를 이용하여 속도 측정을 하였다. 결과적으로 저장공간 측면에서 적은 량의 데이터를 가지면서 등고선을 표현할 수 있는 3 차원 지형을 렌더링 할 수 있음을 알 수 있다.

• Journal of Astronomy and Space Sciences
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• v.38 no.2
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• pp.119-134
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• 2021

The data set collected during the night of the discovery of a minor body constitutes a too-short arc (TSA), resulting in failure of the differential correction procedure. This makes it necessary to recover the object during subsequent nights to gather more observations that will allow a preliminary orbit to be calculated. In this work, we present a recovery technique based on sampling the admissible region (AdRe) by the constrained Delaunay triangulation. We construct the AdRe in its topocentric and geocentric variants, using logarithmic and exponential metrics, for the following near-Earth-asteroids: (3122) Florence, (3200) Phaethon, 2003 GW, (1864) Daedalus, 2003 BH84 and 1977 QQ5; and the main-belt asteroids: (1738) Oosterhoff, (4690) Strasbourg, (555) Norma, 2006 SO375, 2003 GE55 and (32811) Apisaon. Using our sampling technique, we established the ephemeris region for these objects, using intervals of observation from 25 minutes up to 2 hours, with propagation times from 1 up to 47 days. All these objects were recoverable in a field of vision of 95' × 72', except for (3122) Florence and (3200) Phaethon, since they were observed during their closest approach to the Earth. In the case of 2006 SO375, we performed an additional test with only two observations separated by 2 minutes, achieving a recovery of up to 28 days after its discovery, which demonstrates the potential of our technique.