• Journal of Korea Multimedia Society
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• v.22 no.4
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• pp.491-501
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• 2019

Variational methods, which cast deformation as an energy-minimization problem, are known to provide a good trade-off between practicality and speed. However, the time required to deform a fully detailed shape means that these methods are largely unsuitable for real-time applications. We simplify a 2D shape into a curve skeleton, which can be deformed much more rapidly than the original shape. The curve skeleton also provides a simplified control for the user, utilizing a small number of control handles. Our system deforms the curve skeleton using an energy-minimization method and then applies the resulting deformation to the original shape using linear blend skinning. This approach effectively reduces the size of the variational optimization problem while producing deformations of a similar quality to those obtained from full-scale nonlinear variational methods.

• Korean Journal of Computational Design and Engineering
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• v.11 no.1
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• pp.1-10
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• 2006

This paper addresses B-spline curve approximation of a set of ordered points to a specified toterance. The important issue in this problem is to reduce the number of control points while keeping the desired accuracy in the resulting B-spline curve. In this paper we propose a new method for error-bounded B-spline curve approximation based on adaptive selection of dominant points. The method first selects from the given points initial dominant points that govern the overall shape of the point set. It then computes a knot vector using the dominant points and performs B-spline curve fitting to all the given points. If the fitted B-spline curve cannot approximate the points within the tolerance, the method selects more points as dominant points and repeats the curve fitting process. The knots are determined in each step by averaging the parameters of the dominant points. The resulting curve is a piecewise B-spline curve of order (degree+1) p with $C^{(p-2)}$ continuity at each knot. The shape index of a point set is introduced to facilitate the dominant point selection during the iterative curve fitting process. Compared with previous methods for error-bounded B-spline curve approximation, the proposed method requires much less control points to approximate the given point set with the desired shape fidelity. Some experimental results demonstrate its usefulness and quality.

• Journal of Korean Neurosurgical Society
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• v.38 no.4
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• pp.255-258
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• 2005

Objective : Lumbar lordotic curve on L4 to S1 level is important in maintaining spinal sagittal alignment. Although there has been no definite report in lordotic value, loss of lumbar lordotic curve may lead to pathologic change especially in degenerative lumbar disease. This study examines the changes of lumbar lordotic curve after posterior lumbar interbody fusion with wedge shape cage. Methods : We studied 45patients who had undergone posterior lumbar interbody fusion with wedge shape cage and screw fixation due to degenerative lumbar disease. Preoperative and postoperative lateral radiographs were taken and one independent observer measured the change of lordotic curve and height of intervertebral space where cages were placed. Segmental lordotic curve angle was measured by Cobb method. Height of intervertebral space was measured by averaging the sum of anterior, posterior, and midpoint interbody distance. Clinical outcome was assessed on Prolo scale at 1month of postoperative period. Results : Nineteen paired wedge shape cages were placed on L4-5 level and 6 paired same cages were inserted on L5-S1 level. Among them, 18patients showed increased segmental lordotic curve angle. Mean increased segmental lordotic curve angle after placing the wedge shape cages was $1.96^{\circ}$. Mean increased disc height was 3.21mm. No cases showed retropulsion of cage. The clinical success rate on Prolo's scale was 92.0%. Conclusion : Posterior lumbar interbody fusion with wedge shape cage provides increased lordotic curve, increased height of intervertebral space, and satisfactory clinical outcome in a short-term period.

• Journal of applied mathematics & informatics
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• v.35 no.1_2
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• pp.75-82
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• 2017

In this paper, we investigate the proper shape and location of the maximum curve of transcendental entire functions $e^{az^2+bz+c}$. We show that the alpha curve of $e^{az^2+bz+c}$ is a subset of a rectangular hyperbola, and the maximum curve is the connected set originating from the origin as a subset of the alpha curve.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10a
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• pp.12-15
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• 1996

In this paper, a new shape control law is derived as a result of introducing the parametric curve representation. This control alw is based on the estimation of the curve parameters corresponding to the target joint positions and the target tip position. Estimating target curve parameters makes it possible to find, easily, a simple shape control law by the Lyapunov design method.

• Smart Structures and Systems
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• v.5 no.3
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• pp.241-260
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• 2009

Shape control of flexible structures using piezoelectric materials has attracted much attention due to its wide applications in controllable systems such as space and aeronautical engineering. The major work in the field is to find a best control voltage or an optimal placement of the piezoelectric actuators in order to actuate the structure shape as close as possible to the desired one. The current research focus on the investigation of static shape control of intelligent shells using spatially distributed piezoelectric curve beam actuators. The finite element formulation of the piezoelectric model is briefly described. The piezoelectric curve beam element is then integrated into a collocated host shell element by using nodal displacement constraint equations. The linear least square method (LLSM) is employed to get the optimum voltage distributions in the control system so that the desired structure shape can be well matched. Furthermore, to find the optimal placement of the piezoelectric curve beam actuators, a genetic algorithm (GA) is introduced in the computation model as well as the consideration of the different objective functions. Numerical results are given to demonstrate the validity of the theoretical model and numerical algorithm developed.

• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• 2001.10a
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• pp.381-386
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• 2001

When a input image is extensively magnified on the computer system, it is almost impossible to replicate the original shape because of mismatched coordinates system. In order to resolve the problem, the shape of the magnified image has been reconfigured using the bilinear interpolation method, low pass special filtering interpolation method and B-spline interpolation method, Ferguson curve interpolation method based on the CAD/CAM curve interpolation algorithm. The computer simulation main result was that. Nearest neighbor interpolation method is simple in making the interpolation program but it is not capable to distinguish the original shape. Bilinear interpolation method has the merit to make the magnified shape smooth and soft but calculation time is longer than the other method. Low pass spatial filtering method and B-spline interpolation method has an effect to immerge the intense of the magnified shape but it is also difficult to distinguish the original shape. Ferguson curve interpolation method has sharping shape than B-spline interpolation method.

• The Transactions of the Korea Information Processing Society
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• v.6 no.3
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• pp.758-765
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• 1999

Shape-preserving property is the important method that controls the complex free form curve/surface. Interpolation method for the existed Shape-Preservation had problems that it has needed the minimization of a curvature-related functions for calculating single-valued data. Solving this problem, in this paper, it proposed to the algorithm of generalizing C piecewise parametric cubic that has shape-preserving property for both Single-value data and Multivalue data. When there are the arbitrary tangents and two data, including shape-preserving property, this proposed method gets piecewise parametric cubic polynomial by checking the relation between the shape-preserving property and then calculates efficiently the control points using that. Also, it controls the initial shape using curvature distribution on curve segments.

• Journal of Educational Research in Mathematics
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• v.22 no.1
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• pp.23-38
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• 2012

The purpose of this paper is to describe the true meaning of smooth curve and to let people understand the smooth curve by way of velocity. It is true that it is not easy for us to perceive smooth curve because when there are no cups in the curve and the shape of the curve looks smooth, we often perceive it is smooth curve. However, even when the shape of curve looks smooth, it happens that it is not smooth curve. When the particle moves on the curve, depending on the velocity, it can be smooth curve or not. That is, even though the shape looks smooth, when the velocity is discontinuous or it is 0, it is not smooth curve. Therefore, this paper shows that it is important to understand and to teach smooth curve by way of velocity. In other words, when parameter of path for the smooth curve is taught in the calculus of high school, it needs to be understood by way of velocity. Finally, this paper tries to suggest that we need to shift our paradigm in teaching of smooth curve from fixed curve to dynamic curve.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.21 no.2
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• pp.217-222
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• 1997

A simple finite element approach to predicting deformed shape and load-deflection curve of elastomers is presented in this paper. The method is based on several simplifications in deformation pattern and material behavior. The conventional updated Lagrangian approach is employed together with material data obtained by a simple tension test. The presented approach is verified through comparison of predicted results with experimental ones and applied successfully to shape design of various elastomers for shock, vibration and noise control. The advantage of the presented approach lies in easiness, simplicity and accuracy enough for engineering application.