• 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.

• Journal of Mechanical Science and Technology
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• v.17 no.11
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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.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.36 no.4B
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• pp.378-385
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• 2011

The three-dimensional triangulation algorithm that the beacon nodes can be allocated to dynamically in not the experimental region but the practical region is suggested, and the performance of the localization system adapting the suggested algorithm is analyzed. The suggested algorithm adapts the computation method of the three dimensional point that the surfaces of three spheres overlapped, while the traditional triangulation algorithm adapts the computation method of the two dimensional point that three circles are overlapped in order to compute the distance between beacon nodes and mobile node that means a radius. In addition to this, to analyze the performance of the localization system adapting the suggested algorithm, first of all, the allocation layout of beacon nodes is made, and the allocation layout is modeled by selection of ten random distance values between mobile node and beacon nodes for computer simulation of the practical model. Next, the two dimensional coordinator of mobile node that is calculated by the suggested algorithm and the traditional triangulation algorithm is compared with each other. The localization measuring performance about three dimensional coordinator(z axis) of the suggested algorithm is also obtained by comparing with that of the practical model.

• Journal of Engineering Education Research
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• v.15 no.5
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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.

• Journal of Korean Institute of Industrial Engineers
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• v.23 no.1
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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.

• Korean Journal of Computational Design and Engineering
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• v.1 no.3
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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.

• Journal of Institute of Control, Robotics and Systems
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• v.9 no.5
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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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• v.5 no.3
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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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• v.13 no.5
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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.

• The Transactions of the Korea Information Processing Society
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• v.3 no.7
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• pp.1894-1905
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• 1996

Delauuany triangulation which is the dual of Dirichlet tessellation is not affine invariant. In other words, the triangulation is dependent upon the choice of the coordinate axes used to represent the vertices. In the same reason, Delahanty tetrahedrization does not have an affine iveariant transformation property. In this paper, we present a new type of tetrahedrization of spacial points sets which is unaffected by translations, scalings, shearings and rotations. An affine invariant tetrahedrization is discussed as a means of affine invariant 2 -D triangulation extended to three-dimensional tetrahedrization. A new associate norm between two points in 3-D space is defined. The visualization of the structure of tetrahedrization can discriminate between Delaunay tetrahedrization and affine invariant tetrahedrization.