• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제9권2호
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• pp.29-43
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• 2005

We consider a surface reconstruction problem from geometrical points (i.e., points given without any order) distributed on a series of smooth parallel cross sections in ${\mathbb{R}}^3$. To solve the problem, we utilize the natural points ordering method in ${\mathbb{R}}^2$, described in [18], which is a method of reconstructing a curve from a set of sample points and is based on the concept of diffusion motions of a small object from one point to the other point. With only the information of the positions of these geometrical points, we construct an acceptable surface consisting of triangular facets using a heuristic algorithm to link a pair of parallel cross-sections constructed via the natural points ordering method. We show numerical simulations for the proposed algorithm with some sets of sample points.

• 한국생산제조학회지
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• 제6권4호
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• pp.19-26
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• 1997

The manufacture of an impeller typically requires the 5-axis CNC machining, since the impeller is usually under working conditions such as high speed, high temperature, and high pressure. Thus, this study contributes to development of an exclusive CAM system for effective 5-axis CNC machining of a ruled surface type impeller. In this study, the sampled impeller is made of blades and a body and the blade consists of ruled surfaces between hub curve and shroud curve. In the post processing for 5-axis NC part program, the cutter axis direction vector is the straighten vector on ruled surface. The position of ball center in ball end mill cutter is decided on the interference check between the cutter and body surface of impeller using with the modified z-map method that z-axis is the same of cutter axis direction vector. The exclusive CAM system for an impeller developed in this study was very effective for designs and 50-axis machining of a ruled surface type impeller.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2008년도 추계학술대회A
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• pp.612-617
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• 2008

In this present work, trimmed surface analysis for the 2D elasticity problem is presented. The main benefit of the proposed method is that no additional modeling for analysis of a trimmed surface is necessary. As the first attempt to deal with a trimmed surface in spline FEM, the information of the trimming curve and trimmed surface exported from CAD system is directly utilized for analysis. For this, trimmed elements are searched through employing projection scheme. For the integration of the trimmed elements, NURBSenhanced integration scheme which is used in NEFEM is adopted. The quadtree refinement of integration cell is performed for the complicated trimmed cases. The information of trimming curve is used for obtaining integration points as well as constructing stiffness matrix. The robustness and effectiveness of the proposed method are investigated by presenting various numerical examples.

• 대한수학회보
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• 제61권3호
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• pp.585-595
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• 2024

We show that a pseudo-Anosov map constructed as a product of the large power of Dehn twists of two filling curves always has a geodesic axis on the curve graph of the surface. We also obtain estimates of the stable translation length of a pseudo-Anosov map, when two filling curves are replaced by multicurves. Three main applications of our theorem are the following: (a) determining which word realizes the minimal translation length on the curve graph within a specific class of words, (b) giving a new class of pseudo-Anosov maps optimizing the ratio of stable translation lengths on the curve graph to that on Teichmüller space, (c) giving a partial answer of how much power is needed for Dehn twists to generate right-angled Artin subgroup of the mapping class group.

• 한국지반공학회:학술대회논문집
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• 한국지반공학회 2005년도 춘계 학술발표회 논문집
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• pp.384-391
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• 2005

Three dimensional finite difference elastic wave model was developed to estimate the feasibility of surface wave applications in geotechnical problems. The wave motions calculated by the developed program in this study shows good agreement with well known analytic solutions. The surface wave motions calculated from layered dam type structure can be interpreted as a infinite layer structure using dispersion curve but it is need a special source of which high energy in frequency band lower than 10 Hz to get information of physical properties in few tens meter deep. The source which has high energy in the low frequency band, however, can give defect on dam and this will make some limitation in real field applications. The dispersion curves calculated from the surface wave motion of homogeneous and center core type dam models will give rise to fatal errors if the conventional infinite layer structure used in their interpretation because the surrounding materials and boundaries of dam make some distortion in dispersion curve of surface wave. So it is strongly recommended to use three dimensional inversion model for correct interpretation and estimation of physical properties of dam materials.

• 한국공작기계학회:학술대회논문집
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• 한국공작기계학회 2001년도 춘계학술대회 논문집(한국공작기계학회)
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• pp.405-410
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• 2001

In this paper, a new parametric curve interpolator is proposed based on a 3D(3-dimensional) NURBS curve. A free curve is generally divided into small linear segments or circular arcs in CNC machining. The method has caused to a command error, the limitation of machining speed, and the irregular machining surface. The proposed real-time 3D NURBS interpolator continuously generates a linear segment within the range of allowable acceleration/deceleration in the motion controller. Therefore, the algorithm calculates the curvature and the remained distance of a command curve for the smoothing machining. It is expected to attaining high speed and high precision machining in CNC Machine Tool.

• 한국정밀공학회지
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• 제16권4호통권97호
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• pp.129-137
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• 1999

A parametric curve interpolator has been proposed for machining curves instead of a linear interpolator in which curves are approximated by a set of line segment. The parametric curve interpolator is superior to linear interpolator in machining time and contour error and generate exact position commands directly from curve equations. In this paper, a new toolpath generation method is proposed based on the parametric curve interpolator. This method retains all the benefits of parametric curve interpolator and can bound the scallop height within a specified value. By interpolating curves and surfaces directly from the mathematical equations, the amount of data from CAD/CAM system to CNC controller can be significantly reduced. The proposed method was implemented on a CNC controller and was confirmed to give a better result than the other existing method.

• 제어로봇시스템학회논문지
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• 제19권12호
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• pp.1152-1159
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• 2013

This paper proposes an effective walking system for a hexapod robot on uneven terrain. To overcome the deficiencies of two-pair walking systems, which are effective on even terrain, the use of only three legs changes the steps required for movement. The proposed system receives feedback data from switches attached to the bottom of the legs and gyro sensor to carry out stable walking using the Bezier curve algorithm. From the coordinates of the Bezier curve, which guarantees the circular motion of legs, the motor's angle value can be obtained using inverse kinematics. The angle values are sent to each motor though RS-485 communication. If a switch is pushed by the surface during navigation in the Bezier curve pattern, the robot is designed to change its circular course. Through the changed course, each leg can be located on an optimal surface and the wobble phenomenon is reduced by using a normal vector algorithm. The simulation and experiment results show the efficiency of the proposed algorithm.

• 전자공학회논문지S
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• 제34S권12호
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• pp.90-97
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• 1997

This paper presents a new algorithm for surface segmentation and feature description. The algorithm extracts the signature of an edge image based on the signature technqique[12] in the first stage. If there exists a range in the angle axis where more than two signatures form a closed curve, we can conclude there is a surface inside the range. Using this feature of the signature, surfaces can be segmented. The surface features such as number of vertices, number of edges, and type of surfaces can also be extracted by finding the signatures of individual surfaces. This algorithm has distinguished advantages: it can easily recover the lost part occuring in the edge iage using the curve fitting method and it can extract surface features even when surfaces are rotated in 3-D space.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2005년도 ICCAS
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• pp.1990-1993
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• 2005

Stereovision is known to be one of the most important tools for robot vision systems. Previously, 2D active contour model has been applied to stereovision by defining the contour on the 3D space instead of image plane. However, the proposed model is still that of curve so that some complex shapes such as surfaces with high curvature can not be properly estimated because of occlusion phenomena. In this paper, the authors extend the curve model to the surface model. The surface is approximated by polygons and new energy function and its optimization method for surface estimation is proposed. Its effectiveness is examined by experiments with real stereo images.