• Structural Engineering and Mechanics
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• 제30권2호
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• pp.225-245
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• 2008

T-splines are recently proposed mathematical tools for geometric modeling, which are generalizations of B-splines. Local refinement can be performed effectively using T-splines while it is not the case when B-splines or NURBS are used. Using T-splines, patches with unmatched boundaries can be combined easily without special techniques. In the present study, an analysis framework using T-splines is proposed. In this framework, T-splines are used both for description of geometries and for approximation of solution spaces. This analysis framework can be a basis of a CAD/CAE integrated approach. In this approach, CAD models are directly imported as the analysis models without additional finite element modeling. Some numerical examples are presented to illustrate the effectiveness of the current analysis framework.

• International Journal of CAD/CAM
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• 제9권1호
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• pp.47-53
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• 2010

In this paper we propose a new type of splines-biquadratic submesh splines over hierarchical T-meshes. The biquadratic submesh splines are in rational form consisting of some biquadratic B-splines defined over tensor-product submeshes of a hierarchical T-mesh, where every submesh is around a cell in the crossing-vertex relationship graph of the T-mesh. We provide an effective algorithm to locate the valid tensor-product submeshes. A local refinement algorithm is presented and the application of submesh splines in surface fitting is provided.

• Journal of Information Processing Systems
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• 제10권1호
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• pp.23-35
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• 2014

Recently, novel application areas in digital geometry processing, such as simulation, dynamics, and medical surgery simulations, have necessitated the representation of not only the surface data but also the interior volume data of a given 3D object. In this paper, we present an efficient framework for the shape approximations of spherical solid objects based on trivariate B-splines. To do this, we first constructed a smooth correspondence between a given object and a unit solid cube by computing their harmonic mapping. We set the unit solid cube as a rectilinear parametric domain for trivariate B-splines and utilized the mapping to approximate the given object with B-splines in a coarse-to-fine manner. Specifically, our framework provides user-controllability of shape approximations, based on the control of the boundary condition of the harmonic parameterization and the level of B-spline fitting. Experimental results showed that our method is efficient enough to compute trivariate B-splines for several models, each of whose topology is identical to a solid sphere.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2005년도 학술대회 논문집 정보 및 제어부문
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• pp.17-19
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• 2005

In this paper, using B-splines as universial approximators, we have obtained a plant parametrization which permits the construction of an adaptive observer. The particular property of this parametrization is that the dynamic order of the filters in this design does not depend on the number of parameters in the plant parametrization. This appears to be a beneficial property especially because the number of such parameters tends to be very high for universial approximator based designs.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2003년도 학술회의 논문집 정보 및 제어부문 A
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• pp.331-334
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• 2003

In this paper, using B-splines as universial approximators, we have obtained a plant parametrization which permits the construction of an adaptive observer. The particular property of this parametrization is that the dynamic order of the filters in this design does not depend on the number of parameters in the plant parametrization. This appears to be a beneficial property especially because the number of such parameters tends to be very high for universial approximator based designs.

• 한국컴퓨터정보학회논문지
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• 제10권1호
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• pp.35-44
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• 2005

서로 다른 기하학적 모델링 시스템을 사용하는 곡선 및 곡면의 자료 교환에서, 시스템이 지원하는 B-spline 곡선 및 곡면의 최대 차수에 제한이 있을 때, 주어진 허용 오차 범위 내에서 낮은 차수로의 차수 감소가 필요하다 본 논문에서는 근사 변환의 한 방법인 B-spline 곡선의 차수 감소 방법을 적용한 실험적 결과를 제공한다. B-spline 곡선의 근사변환에서 기존의 $B\acute{e}zier$ 곡선의 차수감소 방법들을 차수 감소 과정에 적용하고. 그 방법들을 비교 분석한다 knot 제거 알고리즘도 자료 감소를 위하여 차수 감소과정에 적용한다

• Journal of information and communication convergence engineering
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• 제9권4호
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• pp.424-427
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• 2011

The paper is devoted to problem of spline approximation. A new method of nodes location for curves and surfaces computer construction by means of B-splines, of Reyabenko's splines and results of simulink-modeling is presented. The advantages of this paper is that we comprise the basic spline with classical polynomials both on accuracy, as well as degree of paralleling calculations are also show's.

• 대한기계학회논문집A
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• 제33권2호
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• pp.127-134
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• 2009

T-splines are recently proposed geometric modeling tools. A T-spline surface is a NURBS surface with T-junctions and is defined by a control grid called T-mesh. Local refinement can be performed very easily for T-splines while it is limited for B-splines or NURBS. Using T-splines, patches with unmatched boundaries can be combined easily without special technique. In this study, the analysis methodology using T-splines is proposed. In this methodology, T-splines are used both for description of geometries and for approximation of solution spaces. Two-dimensional linear elastic and dynamic problems will be solved by employing the proposed T-spline finite element method, and the effectiveness of the current analysis methodology will be verified.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제3권1호
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• pp.81-98
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• 1999

In spite of the well developed theory and the practical use of the univariate B-spline, the theory of multivariate B-spline is very new and waits its practical use. We compare in this article the multivariate B-spline approximation with the polynomial approximation for the surface fitting. The graphical and numerical comparisons show that the multivariate B-spline approximation gives much better fitting than the polynomial one, especially for the surfaces which vary very rapidly.

• Steel and Composite Structures
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• 제26권2호
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• pp.171-182
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• 2018

This paper presents an isogeometric discretization of Kirchhoff-Love thin shells using truncated hierarchical B-splines (THB-splines). It is demonstrated that the underlying basis functions are ideally appropriate for adaptive refinement of the so-called thin shell structures in the framework of isogeometric analysis. The proposed approach provides sufficient flexibility for refining basis functions independent of their order. The main advantage of local THB-spline evaluation is that it provides higher degree analysis on tight meshes of arbitrary geometry which makes it well suited for discretizing the Kirchhoff-Love shell formulation. Numerical results show the versatility and high accuracy of the present method. This study is a part of the efforts by the authors to bridge the gap between CAD and CAE.