• 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.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.

• Proceedings of the Korean Information Science Society Conference
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• 2003.10b
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• pp.694-696
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• 2003

본 논문은 회화적 렌더링(painterly rendering)을 위한 다양한 크기를 갖는 곡선 브러시 스트로크(brush stroke)의 생성에 관한 알고리즘과 그 구현 방법을 다루고 있다. 논문에서 제시하는 알고리즘은 한 장의 영상을 입력으로 하여. 화가가 손으로 그린 듯한 느낌을 주는 결과 영상을 만들어 낸다. 결과 영상은 브러시의 크기에 따라 몇 개의 계층(layer)으로 구성되며 각 계층들은 일련의 스플라인 커브(spline curve)로 모델링된 곡선 브러시 스트로크들로 이루어진다. 또한 결과 영상의 회화적 느낌을 강조하기 위하여 입력 영상의 색상을 변환하는 과정을 포함하고 있다.

• 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.