• Journal of the Institute of Electronics Engineers of Korea SP
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• v.37 no.3
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• pp.17-30
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• 2000

In this paper, we propose an efficient algorithm to produce 3-D surface model from a set of range data, based on NURBS (Non-Uniform Rational B-Splines) surface fitting technique. It is assumed that the range data is initially unorganized and scattered 3-D points, while their connectivity is also unknown. The proposed algorithm consists of three steps: initial model approximation, hierarchical representation, and construction of the NURBS patch network. The mitral model is approximated by polyhedral and triangular model using K-means clustering technique Then, the initial model is represented by hierarchically decomposed tree structure. Based on this, $G^1$ continuous NURBS patch network is constructed efficiently. The computational complexity as well as the modeling error is much reduced by means of hierarchical decomposition and precise approximation of the NURBS control mesh Experimental results show that the initial model as well as the NURBS patch network are constructed automatically, while the modeling error is observed to be negligible.

• Proceedings of the KSME Conference
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• 2007.05a
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• pp.1564-1569
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• 2007

This study concerns an advanced NURBS surface reconstruction method, which is based on the NURBS surface model fitting to the unstructured point cloud measured from an arbitrary complex shape. The concept of generating a simple triangular mesh model was introduced to generate a quadrilateral mesh model well-representing the topological characteristics of point cloud. The NURBS surface reconstruction processes required the use of the various methodologies such as QEM algorithm, merging scheme of pair-wise triangular mesh, creation algorithm of $G^1$ continuous tensor product NURBS surface patch, and so on. The effectiveness and reliability of the proposed NURBS surface reconstruction method were validated through the simulation results for the geometrically and topologically complex shapes.

• 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.

• 한국전산유체공학회:학술대회논문집
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• 2001.10a
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• pp.144-151
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• 2001

NURBS 곡면식으로 정의된 물체 표면상에서 표면 정렬 격자를 생성할 수 있는 방법을 소개하였다. 공학 응용분야에서의 물체 표면 정의는 여러 개의 패치들로 표현되는 것이 일반적이고, 여기서 소개하는 표면격자 생성기법은 이러한 여러 패치들에 걸쳐서 분포되는 정렬격자를 쉽게 생성할 수 있도록 한다 이 기법은 매개변수 형태의 타원형 격자생성 방정식의 해를 구하되, 여러 NURBS 패치에 걸쳐서 투영/분포된 초기 격자계를 타원형 방정식 반복계산 과정의 매개변수형 표면 정의식으로 임시 활용한다. 매개변수형 타원형 방정식의 해가 얻어지고 나면, 그 결과 격자계를 다시 NURBS 패치에 투영을 시키고 타원형 방정식의 해를 구하는 과정이 반복된다. 이러한 반복과정이 전체적으로 수렴이 이루어질 때까지 반복된다. 이 방법에 의해서 얻어지는 표면 정렬 격자계들은 타원형 격자생성기법의 특징인 완만성을 가지면서 정의된 물체표면에서 벗어나지 않는 격자점들이 된다. 소개된 방법은 간단하면서도 하나의 NURBS 곡면만이 아니라 여러 개의 NURBS 곡면에 걸쳐있는 정렬격자계를 효율적으로 생성할 수 있도록 해주며, 그 기본적인 접근법은 NURBS 곡면식 만이 아니라 다른 형태의 매개변수형 형상 정의식에도 적용이 가능하다.

• 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 Korea Game Society
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• v.2 no.1
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• pp.62-68
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• 2002

This paper presents a method for tessellating trimmed NURBS surface with preserving sharp shape Although several existing approaches need a large number of triangular meshes to represent sharp shape of surface, resulting triangular meshes may not reflect sharp edges properly. In this study, we flit detect the sharp shape of NURBS surface automatically using C1 continuous condition and then use constraint Delaunay triangulation method to present exact sharp shape with the minimum triangular meshes. And we also use approximated developed surface domain as triangulation domain of rimmed NURBS surface. In this way, the shape of triangular elements on the triangular domains is approximately preserved and can avoid distortion when mapped into three-dimensional space. finally, we show examples that demonstrate the effectiveness of the proposed scheme in terms of reducing the number of triangular meshes and preserving sharp shape of surface more exactly.

• Journal of the Korean Society for Precision Engineering
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• v.20 no.10
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• pp.208-217
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• 2003

In order to construct the extrusion die surface of T -shaped sections, an automatic surface construction method based on NURBS surface and area mapping method is proposed in the present work. In the present study, a center point for area mapping is determined by introducing the mapping concept based on constant area proportionality between original billet and final product. The characteristic points of inlet profile are determined using the traditional area mapping method and the root finding numerical method. The inlet and outlet profiles are precisely described with NURBS curves using the characteristic points of entry and exit sections. For the construction of NURBS surface, an interpolation method for the pre-determined two section curves has been developed to be used in the generation of interior control points and weights. To show the validity of the proposed method, automatic die surface generation is carried out for the T-shaped section and T-shaped section with rounded corners.

• Transactions of Materials Processing
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• v.12 no.2
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• pp.151-160
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• 2003

In the present study, an advanced surface construction method based on NURBS surface scheme is proposed to construct the extrusion die surface. The inlet and outlet profiles we precisely described with NURBS curves using the cubic appropriate control points and weights. The interior control Points of surface are generated using the cubic interpolation of the weights at the inlet and outlet sections. In order to verify of the proposed method, automatic surface generation is carried out for the various types of extrusion die surface.

• Journal of KIISE:Computer Systems and Theory
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• v.34 no.1
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• pp.38-48
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• 2007

In this paper, we propose an image-based method for modeling 3D objects with curved surfaces based on the NURBS (Non-Uniform Rational B-Splines) representation. Starting from a few calibrated images, the user specifies the corresponding curves by means of an interactive user interface. Then, the 3D curves are reconstructed using stereo reconstruction. In order to fit the curves easily using the interactive user interface, NURBS curves and surfaces are employed. The proposed surface modeling techniques include surface building methods such as bilinear surfaces, ruled surfaces, generalized cylinders, and surfaces of revolution. In addition to these methods, we also propose various advanced surface modeling techniques, including skinned surfaces, swept surfaces, and boundary patches. Based on these surface modeling techniques, it is possible to build various types of 3D shape models with textured curved surfaces without much effort. Also, it is possible to reconstruct more realistic surfaces by using proposed view-dependent texture acquisition algorithm. Constructed 3D shape model with curves and curved surfaces can be exported in VRML format, making it possible to be used in different 3D graphics softwares.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.20 no.2
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• pp.181-190
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• 2007

The linkage framework of surface geometric modeling based on the NURBS and shell finite element analysis is developed in this study. In the geometrically exact shell finite element analysis, the accuracy of the analysis strongly depends upon the accurate computation of the surface geometric quantities. Therefore if we obtain the necessary geometric quantities from the NVRBS surface equation, it's possible to construct the effective linkage framework of surface modeling in the CAD systems and shell finite element analysis using geometrically exact shell finite element. Besides, the linkage framework can be applied to the analysis of general and complex surfaces as well as simple surfaces. In this study, the shell surfaces are generated by interpolating given set of data points based on the NURBS surfaces. These data points usually can be obtained from surface scanning. But the representations of the generated NURBS surface are not same to one another. The accuracy depends on the chosen parameterization methods used in NURBS. Therefore, it is needed to select the suitable parameterization method according to the geometry of the surfaces. To verify the performance and accuracy of our developed linkage framework, we solve several well-known benchmark problems and assess the performance of the developed method.