• Title/Summary/Keyword: NURBS Interpolation

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Applicability Analysis of Measurement Data Classification and Spatial Interpolation to Improve IUGIM Accuracy (지하공간통합지도의 정확도 향상을 위한 계측 데이터 분류 및 공간 보간 기법 적용성 분석)

  • Lee, Sang-Yun;Song, Ki-Il;Kang, Kyung-Nam;Kim, Wooram;An, Joon-Sang
    • Journal of the Korean Geotechnical Society
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    • v.38 no.10
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    • pp.17-29
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    • 2022
  • Recently, the interest in integrated underground geospatial information mapping (IUGIM) to ensure the safety of underground spaces and facilities has been increasing. Because IUGIM is used in the fields of underground space development and underground safety management, the up-to-dateness and accuracy of information are critical. In this study, IUGIM and field data were classified, and the accuracy of IUGIM was improved by spatial interpolation. A spatial interpolation technique was used to process borehole data in IUGIM, and a quantitative evaluation was performed with mean absolute error and root mean square error through the cross-validation of seven interpolation results according to the technique and model. From the cross-validation results, accuracy decreased in the order of nonuniform rational B-spline, Kriging, and inverse distance weighting. In the case of Kriging, the accuracy difference according to the variogram model was insignificant, and Kriging using the spherical variogram exhibited the best accuracy.

THE RECOVERY TECHNIQUE OF ERRONEOUS BLOCKS BASED ON THE SPATIAL INTERPOLATION (영상의 공간적 보간을 응용한 손상된 영상 구획의 복원 기법)

  • 박종욱;이상욱
    • Proceedings of the Korean Society of Broadcast Engineers Conference
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    • 1996.06a
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    • pp.229-232
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    • 1996
  • 본 논문에서는 공간적 보간을 응용하여 손상된 영상 구획의 데이터를 복원하는 기법을 제시한다. 이러한 기법은 손상된 영상을 부가 정보 없이 복원하는 오류 은폐의 핵심으로 Park[3], Wang[4], Sun[9], Lee[7], Hemami[8] 등에 의해서 여러 가지 기법들이 제안되었다. 그러나 이러한 기법들은 단순히 주변 구획과의 경계면에서의 연속성만을 고려하여 복원하므로 구획 내부의 데이터를 복원하는데 한계가 있으며 계산량도 많은 단점이 있다. 따라서 본 논문에서는 이러한 기존의 기법들의 단점을 극복하기 위하여 Non-Unform Rational B-Spline(NURBS)을 응용한 복원 기법을 제안한다. 제시된 주변 구획의 오류 유무와 윤곽선의 방향에 따라 주변 구획의 화소 정보에 할당되는 가중치를 적절히 변경하여 NURBS를 적용한다. 따라서 윤곽선의 방향을 더욱 견실하게 복원함으로써 주관적, 객관적 관점에서 기존의 기법보다 우수한 영상 구획 복원 성능을 얻을 수 있다. 정지 영상에 대한 컴퓨터 모의 실험 결과 제안하는 알고리듬을 기존의 기법보다 30% 구획 손실율에서 0.5 dB이상 성능 향상을 얻을 수 있음을 관찰하였다.

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Stabilization of a High-Speed and Intelligent CNC System (고속 지능형 CNC 시스템의 안정화)

  • 김경돈;이강주;최인휴;김형내;김찬봉
    • Proceedings of the Korean Society of Machine Tool Engineers Conference
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    • 2004.04a
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    • pp.359-364
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    • 2004
  • A high-speed and intelligent CNC system has been developed by Turbotek Co., Ltd. This paper presents the study for commercialization of the developed CNC system. In order to acquire stability and reliability of the developed CNC system, its hardwares and softwares ate improved. The CNC main unit is revised to a compact box-type CNC controller. Moreover, the integrated CNC main unit that has built-in and expandable I/O modules is also developed. Remote monitoring, fault diagnosis End NURBS interpolation functions are realized on the CNC system as software modules. Through these efforts, the developed CNC system can be loaded on machine tools successfully.

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Modeling of a Functional Surface using a Modified B-spline

  • Hwang, Jong-Dae;Jung, Jong-Yun;Jung, Yoon-Gyo
    • International Journal of Precision Engineering and Manufacturing
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    • v.6 no.1
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    • pp.15-22
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    • 2005
  • This research presents modeling of a functional surface that is constructed with a free-formed surface. The modeling of functional surfaces, being introduced in this paper, adopts a modified B-spline that utilizes an approximating technique. The modified B-Spline is constructed with altered control vertices. It is applied to measure the surface of an impeller blade. This research builds an algorithm accepting inputs of measured points. Generating the cutter-paths for NC machining employs the model of the constructed surfaces. The machined surfaces that are generated in several cases are compared with each other in the aspect of machining accuracy.

Shape Design Sensitivity Analysis using Isogeometric Approach (CAD 형상을 활용한 설계 민감도 해석)

  • Ha, Seung-Hyun;Cho, Seon-Ho
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • 2007.04a
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    • pp.577-582
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    • 2007
  • A variational formulation for plane elasticity problems is derived based on an isogeometric approach. The isogeometric analysis is an emerging methodology such that the basis functions in analysis domain arc generated directly from NURBS (Non-Uniform Rational B-Splines) geometry. Thus. the solution space can be represented in terms of the same functions to represent the geometry. The coefficients of basis functions or the control variables play the role of degrees-of-freedom. Furthermore, due to h-. p-, and k-refinement schemes, the high order geometric features can be described exactly and easily without tedious re-meshing process. The isogeometric sensitivity analysis method enables us to analyze arbitrarily shaped structures without re-meshing. Also, it provides a precise construction method of finite element model to exactly represent geometry using B-spline base functions in CAD geometric modeling. To obtain precise shape sensitivity, the normal and curvature of boundary should be taken into account in the shape sensitivity expressions. However, in conventional finite element methods, the normal information is inaccurate and the curvature is generally missing due to the use of linear interpolation functions. A continuum-based adjoint sensitivity analysis method using the isogeometric approach is derived for the plane elasticity problems. The conventional shape optimization using the finite element method has some difficulties in the parameterization of boundary. In isogeometric analysis, however, the geometric properties arc already embedded in the B-spline shape functions and control points. The perturbation of control points in isogeometric analysis automatically results in shape changes. Using the conventional finite clement method, the inter-element continuity of the design space is not guaranteed so that the normal vector and curvature arc not accurate enough. On tile other hand, in isogeometric analysis, these values arc continuous over the whole design space so that accurate shape sensitivity can be obtained. Through numerical examples, the developed isogeometric sensitivity analysis method is verified to show excellent agreement with finite difference sensitivity.

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Shape Design Optimization using Isogeometric Analysis Method (등기하 해석법을 이용한 형상 최적 설계)

  • Ha, Seung-Hyun;Cho, Seon-Ho
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • 2008.04a
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    • pp.216-221
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    • 2008
  • Shape design optimization for linear elasticity problem is performed using isogeometric analysis method. In many design optimization problems for real engineering models, initial raw data usually comes from CAD modeler. Then designer should convert this CAD data into finite element mesh data because conventional design optimization tools are generally based on finite element analysis. During this conversion there is some numerical error due to a geometry approximation, which causes accuracy problems in not only response analysis but also design sensitivity analysis. As a remedy of this phenomenon, the isogeometric analysis method is one of the promising approaches of shape design optimization. The main idea of isogeometric analysis is that the basis functions used in analysis is exactly same as ones which represent the geometry, and this geometrically exact model can be used shape sensitivity analysis and design optimization as well. In shape design sensitivity point of view, precise shape sensitivity is very essential for gradient-based optimization. In conventional finite element based optimization, higher order information such as normal vector and curvature term is inaccurate or even missing due to the use of linear interpolation functions. On the other hands, B-spline basis functions have sufficient continuity and their derivatives are smooth enough. Therefore normal vector and curvature terms can be exactly evaluated, which eventually yields precise optimal shapes. In this article, isogeometric analysis method is utilized for the shape design optimization. By virtue of B-spline basis function, an exact geometry can be handled without finite element meshes. Moreover, initial CAD data are used throughout the optimization process, including response analysis, shape sensitivity analysis, design parameterization and shape optimization, without subsequent communication with CAD description.

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