• Transactions of the Korean Society of Mechanical Engineers A
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• v.34 no.8
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• pp.1007-1013
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• 2010

A new local refinement scheme for spline finite element method has been proposed; this scheme involves the use of hierarchical B-spline. NURBS has been widely used in CAD; however, the local refinement of NURBS is difficult due to its tensor-product property. In this study, we attempted to use hierarchical B-splines as local refinement strategy in spline FEM. The regions of high gradients are overlapped by hierarchically-created local meshes. Knot vectors and control points in local meshes are extracted from global meshes, and they are refined using specific schemes. Proper compatibility conditions are imposed between global and local meshes. The effectiveness of the proposed method is verified on the basis of numerical results. Further, it is shown that by using a proposed local refinement scheme, the accuracy of the solution can be improved and it could be higher than that of the solution of a conventional spline FEM with relatively lower degrees of freedom.

• Journal of the Korea Computer Graphics Society
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• v.16 no.4
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• pp.41-50
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• 2010

We present a new technique for multilevel editing of hierarchical B-spline curves. At each level, control points of a displacement function are expressed in the rotation minimizing frames (RMFs) [1] which are computed on nodal points of the curve at previous level. When the curve is edited at previous level, the corresponding RMFs are updated and the control points of the displacement function at current level are applied to the new RMFs, which maintains the relative details of the curve at current level to those of previous level. We demonstrate the effectiveness and robustness of the proposed technique using several experimental results.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.39 no.12
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• pp.1124-1132
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• 2011

This paper deals with smooth path generation using B-spline for fixed-wing unmanned aerial vehicles manuevering in 2D environment. Hexagonal cell representation is employed to model the 2D environment, which features increased connectivity among cells over square cell representation. Subsequently, hexagonal cell representation enables smoother path generation based on a discrete sequence of path from the path planner. In addition, we present an on-line path smoothing algorithm incorporating B-spline path templates. The path templates are computed off-line by taking into account all possible path sequences within finite horizon. During on-line implementation, the B-spline curves from the templates are stitched together repeatedly to come up with a reference trajectory for UAVs. This method is an effective way of generating smooth path with reduced on-line computation requirement, hence it can be implemented on a small low-cost autopilot that has limited computational resources.

• Journal of the Korea Computer Graphics Society
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• v.22 no.5
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• pp.1-16
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• 2016

In this paper, we propose and efficient curve reconstruction method based on the classical least-square fitting scheme. Specifically, given planar sample points equipped with normals, we reconstruct the objective curve as the zero set of a hierarchical implicit ZP(Zwart-Powell)-spline that can recover large holes of dataset without loosing the fine details. As regularizers, we adopted two: a Tikhonov regularizer to reduce the singularity of the linear system and a discrete Laplacian operator to smooth out the isocurves. Benchmark tests with quantitative measurements are done and our method shows much better quality than polynomial methods. Compared with the hierarchical bi-quadratic spline for datasets with holes, our method results in compatible quality but with less than 90% computational overhead.

• International Journal of CAD/CAM
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• v.7 no.1
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• pp.1-10
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• 2007

The compression of CAD models is a key technology for realizing Internet-based collaborative product development because big model sizes often prohibit us to achieve a rapid product information transmission. Although there exist some algorithms for compressing discrete CAD models, original precise CAD models are focused on in this paper. Here, the characteristics of hierarchical structures in CAD models and the distribution of their redundant data are exploited for developing a novel data encoding method. In the method, different encoding rules are applied to different types of data. Geometric data is a major concern for reducing model sizes. For geometric data, the control points of B-spline curves and surfaces are compressed with the second-order predictions in a local coordinate system. Based on analysis to the distortion induced by quantization, an efficient method for computation of the distortion is provided. The results indicate that the data size of CAD models can be decreased efficiently after compressed with the proposed method.

• Journal of Korea Multimedia Society
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• v.11 no.6
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• pp.869-874
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• 2008

The work of creating character motion needs the higher professional technology and sense and the creating work of realistic and natural motion possess the most part of production term. In this paper we introduce the easy and convenient 3D animation authoring tool which makes the motion based on whole-body inverse kinematics and motion editing function. The proposed 3D animation authoring tool uses the forward kinematics using quaternion and whole-body inverse kinematics to determine the rotation and displacement of skeleton. Also, it provides the motion editing function using multi-level B-spline with quasi-interpolant. By using the proposed tool, we can make 3D animation easily and conveniently.

• Steel and Composite Structures
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• v.26 no.2
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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.