• 산업경영시스템학회지
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• 제41권4호
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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 Mechanical Science and Technology
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• 제17권11호
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• pp.1665-1673
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• 2003

We propose an image-based three-dimensional shape determination system. The shape, and thus the three-dimensional coordinate information of the 3-D object, is determined solely from captured images of the 3-D object from a prescribed set of viewpoints. The approach is based on the shape-from-silhouette (SFS) technique, and the efficacy of the SFS method is tested using a sample data set. The extracted three-dimensional shape is modeled with polygons generated by a new iterative triangulation algorithm, and the polygon model can be exported to commercial software. The proposed system may be used to visualize the 3-D object efficiently, or to quickly generate initial CAD data for reverse engineering purposes, including three dimensional design applications such as 3-D animation and 3-D games.

• 한국통신학회논문지
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• 제36권4B호
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• pp.378-385
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• 2011

본 논문에서는 제한된 실험 영역이 아닌 실제 영역에서 동적으로 비컨노드를 배치할 수 있는 3차원 삼각측량 알고리즘을 제안하고 이를 위치인식 시스템에 적용한 후 그 성능을 분석하였다. 비컨노드와 이동노드간의 거리를 계산함에 있어서 기존의 삼각측량법에서는 이들 노드간의 거리를 반지름으로 하는 3개의 원이 중첩되는 2차원 지점을 계산하지만, 제안하는 알고리즘에서는 3개의 구 표면이 중첩되는 3차원 지점을 계산하는 방법을 적용한다. 또한 제안하는 알고리즘에 의한 위치인식 시스템의 성능을 분석하기 위해 먼저 비컨노드의 배치형태를 실제의 모형으로 제작하고, 사면체인 실제 모형을 컴퓨터에서 시뮬레이션 할 수 있도록 이동노드의 거리 값 및 비컨노드 간의 임의의 거리 값 10개를 추출하여 모델링하였다. 그 다음 제안된 알고리즘과 2 차원 삼각측량법에 의해 계산된 각 이동노드의 2차원 좌표를 서로 비교하고, 제안하는 알고리즘의 3차원 좌표(z축)에 대한 위치정확도를 실제 모형의 3차원 좌표와 비교하여 확인하였다.

• 공학교육연구
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• 제15권5호
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• pp.93-97
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• 2012

Most of ubiquitous computing devices such as stereo camera, ultrasonic sensor based MIT cricket system and other wireless sensor network devices are widely applied to the 2 Dimensional(2D) localization system in today. Because stereo camera cannot estimate the optimal location between moving node and beacon node in Wireless Personal Area Network(WPAN) under Non Line Of Sight(NLOS) environment, it is a great weakness point to the design of the 2D localization system in indoor environment. But the conventional 2D triangulation scheme that is adapted to the MIT cricket system cannot estimate the 3 Dimensional(3D) coordinate values for estimation of the optimal location of the moving node generally. Therefore, the 3D triangulation scheme based on the space segmentation in WPAN is suggested in this paper. The measuring data in the suggested scheme by computer simulation is compared with that of the geographic measuring data in the AutoCAD software system. The average error of coordinates values(x,y,z) of the moving node is calculated to 0.008m by the suggested scheme. From the results, it can be seen that the location correctness of the suggested scheme is very excellent for using the localization system in WPAN.

• 대한산업공학회지
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• 제23권1호
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• pp.215-222
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• 1997

This paper deals with the problem of generating a uniform tetrahedral mesh which fills a 3-D space with the tetrahedra which are close to the equilateral tetrahedra as possible. This problem is particularly interesting in finite element modeling where a fat triangulation minimizes the error of an analysis. Fat triangulation is defined as a scheme for generating an equilateral triangulation as possible in a given dimension. In finite element modeling, there are many algorithms for generating a mesh in 2-D and 3-D. One of the difficulties in generating a mesh in 3-D is that a 3-D object can not be filled with uniform equilateral tetrahedra only regardless of the shape of the boundary. Fat triangulation in 3-D has been proved to be the one which fills a 3-D space with the tetrahedra which are close to the equilateral as possible. Topological and geometrical properties of the fat triangulation and its application to meshing algorithm are investigated.

• 한국CDE학회논문집
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• 제1권3호
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• pp.224-233
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• 1996

An automatic mesh generation scheme with triangular finite elements on three-dimensional surfaces has been developed. The surface triangulation process is performed as follows. To begin, surfaces with key nodes are transformed to two-dimensional planes and the meshes with triangular elements are constructed in these planes. Finally, the constructed meshes are transformed back to the original 3D surfaces. For the mesh generation, an irregular mesh generation scheme is employed in which local mesh densities are assigned by the user along the boundaries of the analysis domain. For this purpose a looping algorithm combined with an advancing front technique using basic operators has been developed, in which the loops are recursively subdivided into subloops with the use of the best split lines and then the basic operators generate elements. Using the split lines, the original boundaries are split recursively until each loop contains a certain number of key nodes, and then using the basic operators such as type-1 and type-2, one or two triangular elements are generated at each operation. After the triangulation process has been completed for each meshing domain, the resulting meshes are finally improved by smoothing process. Sample meshes are presented to demonstrate the versatility of the algorithm.

• 제어로봇시스템학회논문지
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• 제9권5호
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• pp.368-373
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• 2003

This paper presents a cost-effective 3D foot scanner system that provides the 3-dimensional point cloud foot data to design the custom footwear. To measure the 3-dimensional point cloud data of the foot, a CCD camera, a Non-Gaussian laser line projector and optical triangulation method are employed. Furthermore, the integrated system employs a measurement base, a frame grabber, a CCD moving cart, a stepping motor and a computer. The measurement result is saved as 3D dxf format and it could be converted to 2D essential data fer a shoe design. The experimental results demonstrate that the proposed system have the decent resolution of 1mm which is enough for last and shoe design.

• Current Optics and Photonics
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• 제5권3호
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• pp.298-305
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• 2021

Modern distance sensing methods employ various measurement principles, including triangulation, time-of-flight, confocal, interferometric and frequency comb. Among them, the triangulation method, with a laser light source and an image sensor, is widely used in low-cost applications. We developed an omnidirectional two-dimensional (2D) distance sensor based on the triangulation principle for indoor floor mapping applications. The sensor has a range of 150-1500 mm with a relative resolution better than 4% over the range and 1% at 1 meter distance. It rotationally scans a compact one-dimensional (1D) distance sensor, composed of a near infrared (NIR) laser diode, a folding mirror, an imaging lens, and an image detector. We designed the sensor layout and configuration to satisfy the required measurement range and resolution, selecting easily available components in a special effort to reduce cost. We built a prototype and tested it with seven representative indoor wall specimens (white wallpaper, gray wallpaper, black wallpaper, furniture wood, black leather, brown leather, and white plastic) in a typical indoor illuminated condition, 200 lux, on a floor under ceiling mounted fluorescent lamps. We confirmed the proposed sensor provided reliable distance reading of all the specimens over the required measurement range (150-1500 mm) with a measurement resolution of 4% overall and 1% at 1 meter, regardless of illumination conditions.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제13권5호
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• pp.2414-2433
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• 2019

The aim of this paper is to design a 3D laser radar prototype based on laser triangulation. The mathematical model of distance sensitivity is deduced; a pixel-distance conversion formula is discussed and used to complete 3D scanning. The center position extraction algorithm of the spot is proposed, and the error of the linear laser, camera distortion and installation are corrected by using the proposed weighted average algorithm. Finally, the three-dimensional analytic computational algorithm is given to transform the measured distance into point cloud data. The experimental results show that this 3D laser radar can accomplish the 3D object scanning and the environment 3D reconstruction task. In addition, the experiment result proves that the product of the camera focal length and the baseline length is the key factor to influence measurement accuracy.

• 한국정보처리학회논문지
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• 제3권7호
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• pp.1894-1905
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• 1996

Dirichlet tessellation 과 쌍대관계에 있는 Delaunay triangulation은 어파인 불변성을 가지지 못한다. 즉, 삼각형 분할을 이루는데 있어서 각 꼭지점들을 나타내는 좌표축의 선택에 영향을 받는다. 같은 이유로 Delaunay triangulation (사면체 분할법) 도 어파인 불변성을 가지지 못한다. 본 논문에서는 공간상 점들로 사면체 분할하는데 있어서 변환, 확대 축소, 일그러뜨림, 회전에도 여향을 받지 않는 새로운 유형의 사면체 분할 방법을 제시하였다. 어파인 사면체 분할을 논의 할 때 기존의 어파인 불변성 평면적 삼각형 분할을 삼차원 분할을 삼차원적 사면체 분할로 연장시키는 방법을 사용 하였다. 삼차원 공간상의 두 점간의 거리를 새롭게 정의 하였다. 사면체 구조의 가시 화를 통하여 Delaunay 사면체 분할과 어파인 불변성 사면체 분하라 결과를 구별시 킬 수 있었다.