• Korean Journal of Computational Design and Engineering
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• v.2 no.4
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• pp.237-243
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• 1997

A new method is introduced for the interpolation in NURBS Surface. This method uses the basis functions to assign the parameter values to the arbitrary set of geometric data and uses the iteration method to compute the control net. The advantages of this method are the feasible transformation of the data set to the matrix form and the effective surface generation as a result, especially to the design engineer.

• Korean Journal of Computational Design and Engineering
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• v.3 no.4
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• pp.243-250
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• 1998

In parametric surface interpolation, the choice of the parameter values to the set of scattered points makes a great deal of difference in the resulting surface. A new method is developed and tested for the parametrization in NURBS surface global interpolation. This method uses the parameter value at the maximal value of relevant rational basis function, to assign the parameter values to the arbitrary set of design data. This method gives us several important advantages in geometric modeling, the freedom of the selection of knot values, the feasible transformation of the data set to the matrix, the possibility of affinite transformation between the design data and generated surface, etc.

• 한국HCI학회:학술대회논문집
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• 2006.02a
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• pp.480-485
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• 2006

본 논문에서는 사용자가 NURBS 곡면을 다양한 형태로 변형을 손쉽게 할 수 있는 수정된 유한요소법을 이용한 곡면 변형의 방법을 제시한다. 수정된 유한요소법은 NURBS 기저함수를 전통적 유한요소법의 형상함수를 대신하여 유한요소해석을 한다. 모델링된 객체는 NURBS 곡면으로 이루어져 있고, 각각의 세그먼트별로 나누어진 기저함수와 제어점으로 구성되어있기 때문에 번거롭게 요소와 형상함수를 따로 구하지 않아도 되며, 자체 보간 방식이므로 기존의 유한요소법에 비해 적은 요소와 절점으로 곡면을 해석 할 수 있다. NURBS 곡면 변형은 각각의 제어점에 의해 구역이 나눠지고 각 구역은 변형될 지점과 가장 가까운 제어점으로 구성된 구역의 제어점들을 변형시킬 지점과 각 제어점의 거리 비례에 따라서 제어점 들의 속도가 지정되어 변형을 완성한다. 제시된 변형 방법은 다른 변형들과 같이 초기 입력에 의해 변형이 한 순간에 진행되는 것이 아니라 점진적 변형이 일어나며, NURBS 의 특징인 전체 제어점 변형으로 인해 의도하지 않은 변형이 일어나는 것을 변형 중간에 각각의 제어점의 속도를 제어함으로써 사용자의 의도한 변형으로 빠른 시간에 완성할 수 있게 된다.

• Journal of the Korean Society for Precision Engineering
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• v.23 no.9 s.186
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• pp.156-163
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• 2006

The purpose of this study is to improve the machining of free-formed NURBS surfaces using newly defined G-codes which can directly deal with shapes defined from CAD/CAM programs on a surface basis and specialize in rough and finish cut. To this purpose, a NURBS surface interpolation system is proposed in this paper. The proposed interpolation system includes online tool-path planning, real-time interpolation and feedrate regulation considering an effective machining method and minimum machining time all suitable for unit NURBS surface machining. The corresponding algorithms are simultaneously executed in an online manner. The proposed NURBS surface interpolation system is integrated and implemented with a PC-based 3-axis CNC milling system. A graphic user interface (GUI) and a 3D tool-path viewer which interprets the G-codes for NURBS surfaces and displays whole tool-paths are also developed and included in our real-time control system. The proposed system is evaluated through actual machining in terms of size of NC data, machining time, regulation of feedrate and cutting force focused on finish cut in comparison with the existing method.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2004.10a
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• pp.471-474
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• 2004

In this paper, a NURBS surface interpolator is proposed which can deal with shapes defined from CAD/CAM programs on a surface basis and can improve contour accuracy. The proposed interpolator is based on newly defined G-codes and includes online tool-path planning suitable for NURBS surface machining. The real-time interpolation algorithm, considering an effective machining method for each machining process and minimum machining time, is executed in an online manner. The proposed interpolator is implemented on a PC-based 3-axis CNC milling system and evaluated through actual machining in terms of machining time and regulation of feedrate and cutting force in comparison with the existing method.

• Korean Journal of Computational Design and Engineering
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• v.10 no.5
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• pp.303-313
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• 2005

This paper proposes a generalized NURBS model, called Volumetric NURBS or VNURBS for representing volumetric objects with multiple attributes embedded in multidimensional space. This model provides a mathematical framework for modeling complex structure of heterogeneous objects and analyzing inside of objects to discover features that are directly inaccessible, for deeper understanding of complex field configurations. The defining procedure of VNURBS, which explains two directional extensions of NURBS, shows VNURBS is a generalized volume function not depending on the domain and its range dimensionality. And the recursive a1gorithm for VNURBS derivatives is described as a computational basis for efficient and robust volume modeling. In addition, the specialized versions of VNURBS demonstrate that VNURBS is applicable to various applications such as geometric modeling, volume rendering, and physical field modeling.

• 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 of Korean Association for Spatial Structures
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• v.14 no.2
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• pp.59-68
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• 2014

A study on the vibration and buckling analyses of laminated composite plates is described in this paper. In order to carry out the analyses of laminated composite plates, a NURBS-based isogeometric general plate element based on Reissner-Mindlin (RM) theory is developed. The non-uniform rational B-spline (NURBS) is used to represent the geometry of plate and the unknown displacement field and therefore, all terms required in this element formulation are consistently derived by using NURBS basis function. Numerical examples are conducted to investigate the accuracy and reliability of the present plate element. From numerical results, the present plate element can produce the isogeometric solutions with sufficient accuracy. Finally, the present isogeometric solutions are provided as future reference solutions.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.24 no.1
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• pp.55-60
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• 2011

In the present work, isogeometric analysis in linear elasticity problem is conducted using the basis functions from NURBS. The objectives of isogeometric analysis introduced is to integrate both geometric modeling(CAD) and computational analysis(CAE), and this can be accomplished from direct usage of geometric modeling by NURBS as the computational mesh. The merit of the isogeometry analysis is that NURBS surface are able to represent exact geometry from the control points and knot vectors, and also subsequent refinement is relatively simple relatively. In order to verify the computer codes developed in this study, it has been applied to two structural models of which geometry are simple ; 1) circular cylinder subjected to the constant internal pressure loading, 2) square plate with circular hole at center subjected to uniform tension. The exact solutions of these two models are available. Convergence of the approximate solutions by the present code for the isogeometry analysis are investigated by mesh refinement with inserting knots (h-refinement) and by mesh refinement with order elevation of the basis functions (p-refinement).

• Journal of the Korean Society for Precision Engineering
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• v.23 no.9 s.186
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• pp.200-207
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• 2006

In this paper a new approach which combines implicit surface scheme and NURBS surface interpolation method is proposed in order to generate a complete surface model from unorganized point cloud data. In the method a base surface was generated by creating smooth implicit surface from the input point cloud data through which the actual surface would pass. The implicit surface was defined by a combination of shape functions including quadratic polynomial function, cubic polynomial functions and radial basis function using adaptive domain decomposition method. In this paper voxel data which can be extracted easily from the base implicit surface were used in order to generate rectangular net with good quality using the normal projection and smoothing scheme. After generating the interior points and tangential vectors in each rectangular region considering the required accuracy, the NURBS surface were constructed by interpolating the rectangular array of points using boundary tangential vectors which assure C$^1$ continuity between rectangular patches. The validity and effectiveness of this new approach was demonstrated by performing numerical experiments for the various types of point cloud data.