• Proceedings of the Korean Society of Marine Engineers Conference
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• 2001.05a
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• pp.163-167
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• 2001

The paper introduce the basic concept for the variable graph description of blending functions in NURBS using some control method; the control points, knot vectors and weight points in 3D space.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.24 no.3
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• pp.329-335
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• 2011

The finite element method (FEM) has been used for various fields like mathematics and engineering. However, the FEM has a difficulty in describing the geometric shape exactly due to its property of piecewise linear discretization. Recently, however, a so-called isogeometric analysis method that uses the non-uniform rational B-spline(NURBS) basis function has been developed. The NURBS can be used to describe the geometry exactly and play a role of basis functions for the response analysis. Nevertheless, constructing the NURBS basis functions in analysis is as costly as a meshing process in the FEM. Since the isogeometric method shares geometric data with CAD, it is possible to intactly import the model data from commercial CAD tools. In this paper, we use the Rhinoceros 3D software to create CAD models and export in the form of STEP file. The information of knot vectors and control points in the NURBS is utilized in the isogeometric analysis. Through some numerical examples, the accuracy of isogeometric method is compared with that of FEM. Also, the efficiency of the isogeometric method that includes the CAD and CAE in a unified framework is verified.

• Journal for History of Mathematics
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• v.27 no.5
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• pp.329-345
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• 2014

CAGD(Computer Aided Geometric Design) is a branch of applied mathematics concerned with algorithms for the design of smooth curves and surfaces and for their efficient mathematical representation. The representation is used for the computation of the curves and surfaces, as well as geometrical quantities of importance such as curvatures, intersection curves between two surfaces and offset surfaces. The $B\acute{e}zier$ curves, B-spline, rational $B\acute{e}zier$ curves and NURBS(Non-Uniform Rational B-Spline) are basically and widely used in CAGD. The definitions and properties of these curves are presented in this paper. And a brief history of study on the bound for derivative of rational curves in CAGD is also presented.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.46 no.2
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• pp.106-113
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• 2018

The Intense acoustic wave generated by the jet flame at the lift-off causes the vehicle to vibrate in the form of acoustic loads. The DSM-II(Distributing Source Method-II), which is a representative empirical acoustic loads prediction method, is a method of distributing a noise source along a jet flame axis and has advantages in calculation cost and accuracy. However, due to the limitation of the distributing method, there is a limit to accurately reflect the various launch pad configurations. In this study, acoustic loads prediction method which can freely distribute noise sources is studied. by introducing NURBS(Non-Uniform Rational B-Spline) modeling into empirical prediction method. For the verification of the newly introduced analytical technique of the NURBS, the acoustic loads prediction for the Epsilon rocket's low-noise launch pad shape was performed and the results of the analysis were compared with the existing prediction methods and experimental results.

• Proceedings of the KSME Conference
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• 2003.04a
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• pp.1111-1117
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• 2003

NURBS (Non Uniform Rational B-Spline) is widely used in CAD system and NC data for high speed machining. Conventional CAM system changes NURBS surface to tessellated meshes or Z-map model, and produces linear tool path. The linear tool path is not good for precise machining and high speed machining. In this paper, an algorithm to change linear tool path to NURBS one was studied, and the machining result of NURBS tool path was compared with that of linear tool path. The N-post, post-processing and virtual machining software was developed. The N-Post post-processes linear tool path to NURBS tool path and quickly shades machined product on OpenGL view and compares a machined product with original CAD surface. A virtual machined model of original tool path and post-processed tool path was compared to original CAD model. The machining error of post-processed NURBS tool path was reduced to 43%. The original tool path and NURBS tool path was used to machine general model using same machine tool and machining condition. The machining time of post-processed NURBS tool path was reduced up to 38%.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2001.04a
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• pp.979-982
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• 2001

In CNC machining, demands on precision machining of free formed surface model are increasing. Most of the CAD/CAM systems provide the NURBS(Non-Uniform Rational B-Spline) interpolator. NURBS is defined with NURBS parameter by control point, weight value and knot value. This paper shows the realtime NURBS interpolation algorithms and compared with each other. One is based on the equal length of curve segments rather than equal increment of the parameter Δu. The other is to limit the interpolation error to any desired level by adjusting the feedrate considering the curvature of the shape and sampling time.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.31 no.1 s.256
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• pp.105-112
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• 2007

The linkage framework of geometric modeling based on NURBS(Non-Uniform Rational B-Spline) surface and shell finite analysis is developed in the present study. For this purpose, geometrically exact shell finite element is implemented. NURBS technology is employed to obtain the exact geometric quantities for the analysis. Especially, because NURBS is the most powerful and wide-spread method to represent general surfaces in the field of computer graphics and CAD(Computer Aided Design) industry, the direct computation of surface geometric quantities from the NURBS surface equation without approximation shows great potential for the integration between geometrically exact shell finite element and geometric modeling in the CAD systems. Some numerical examples are given to verify the performance and accuracy of the developed linkage framework. In additions, trimmed surfaces with some cutouts are considered for more practical applications.

• Journal of the Korean Society for Precision Engineering
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• v.17 no.1
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• pp.192-197
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• 2000

In CNC machining, a free curve is cut into small linear segments using the linear interpolation(G01) method. Therefore, the interpolation error along the curve is not constant due to the changing curvature. This paper presents a NURBS (Non-Uniform Rational B-Spline) interpolation algorithm for machining free curves with high precision and high speed. The proposed NURBS interpolation defines the tool path with NURBS parameters and limits the interpolation error to any desired level by adjusting the feed rate considering the curvature of the shape and sampling time. Both linear and NURBS interpolations are compared to show the validity of the proposed algorithm.

• Journal of the Korean Society for Precision Engineering
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• v.21 no.12
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• pp.60-66
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• 2004

Increasing demands on precision machining of 3D free-form surface have necessitated the tool to move smoothly with varying feedrate. To this regard, parametric interpolators such as NURBS (Non-Uniform Rational B-Spline) interpolator have been introduced in CNC machining system. Such interpolators reduce the data burden in NC code, increase data transfer rate into NC controller, and finally give smooth motion while machining. In this research, a new concept to control cutting load in NURBS Interpolator was tried based on the curvature of curve. This is to protect cutting tool, and to have good machinability. For proof of the system, cutting force and surface topography were evaluated. From the experimental results. the interpolator is good enough for machining a free-form surface.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.7
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• pp.1227-1233
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• 2003

NURBS (Non Uniform Rational B-Spline) is widely used in CAD system and NC data for high speed machining. Conventional CAM system changes NURBS surface to tessellated meshes or Z-map model, and produces linear tool path. The linear tool path is not good fur precise machining and high speed machining. In this paper, an algorithm to change linear tool path to NURBS one was studied and the machining result of NURBS tool path was compared with that of linear tool path. The N-post including both a post-processing and a virtual machining software was developed. The N-Post transforms linear tool path to NURBS tool path and quickly shades a machined product on OpenGL view, while comparing a machined surface with a original CAD one. A virtulal machined model of original tool path and post-processed tool path was compared to original CAD model. The machining error and machining time of post-processed NURBS tool path were investigated.