• 대한수학회논문집
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• 제31권2호
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• pp.395-414
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• 2016

In this work, we study on subdivision schemes reproducing polynomials and build a symmetric subdivision scheme reproducing polynomials of a certain predetermined degree, which is a slight variant of the family of Deslauries-Dubic interpolatory ones. Related to polynomial reproduction, a necessary and sufficient condition for a subdivision scheme to reproduce polynomials of degree L was recently established under the assumption of non-singularity of subdivision schemes. In case of stepwise polynomial reproduction, we give a characterization for a subdivision scheme to reproduce stepwise all polynomials of degree ${\leq}L$ without the assumption of non-singularity. This characterization shows that we can investigate the polynomial reproduction property only by checking the odd and even masks of the subdivision scheme. The minimal-support condition being relaxed, we present explicitly a general formula for the mask of (2n + 4)-point symmetric subdivision scheme with two parameters that reproduces all polynomials of degree ${\leq}2n+1$. The uniqueness of such a symmetric subdivision scheme is proved, provided the two parameters are given arbitrarily. By varying the values of the parameters, this scheme is shown to become various other well known subdivision schemes, ranging from interpolatory to approximating.

• 대한수학회보
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• 제46권1호
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• pp.183-198
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• 2009

In this paper, we derive a characterization of orthonormal balanced multiwavelets of order p in terms of the continuous moments of the multiscaling function $\phi$. As a result, the continuous moments satisfy the discrete polynomial preserving properties of order p (or degree p - 1) for orthonormal balanced multiwavelets. We derive polynomial reproduction formula of degree p - 1 in terms of continuous moments for orthonormal balanced multiwavelets of order p. Balancing of order p implies that the series of scaling functions with the discrete-time monomials as expansion coefficients is a polynomial of degree p - 1. We derive an algorithm for computing the polynomial of degree p - 1.

• Journal of applied mathematics & informatics
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• 제29권3_4호
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• pp.713-719
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• 2011

The problem of approximation from a set of scattered data arises in a wide range of applied mathematics and scientific applications. In this study, we present a quasi-interpolatory approximation scheme for scattered data approximation problem, which reproduces a certain space of polynomials. The proposed scheme is local in the sense that for an evaluation point, the contribution of a data value to the approximating value is decreasing rapidly as the distance between two data points is increasing.

• East Asian mathematical journal
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• 제38권3호
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• pp.365-377
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• 2022

In this paper, we present a new class of interpolatory Hermite subdivision schemes of order 2 reproducing polynomials. Each member in this class, denoted by H_n for n ≥ 1, preserves polynomials of degree up to 4n + 1 admitting the approximation order of 4n + 2. Furthermore, it has free parameters which provide flexibility in designing curves/surfaces. H₁, the simplest and the most attractive scheme in this class, achieves C⁴ smoothness with the parameters in certain ranges, and its performance is demonstrated with numerical examples.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2003년도 ICCAS
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• pp.215-219
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• 2003

In this paper, we generate a trajectory minimized the energy gait of a biped robot for walking a staircase using genetic algorithms and apply to the computed torque controller for the stable dynamic biped locomotion. In the saggital plane, a 6 degree of freedom biped robot that model consists of seven links is used. In order to minimize the total energy efficiency, the Real-Coded Genetic Algorithm (RCGA) is used. Operators of genetic algorithms are composed of a reproduction, crossover and mutation. In order to approximate the walking gait, the each joint angle is defined as a 4-th order polynomial of which coefficients are chromosomes. Constraints are divided into equality and inequality. Firstly, equality constraints consist of position conditions at the end of stride period and each joint angle and angular velocity condition for periodic walking. On the other hand, inequality constraints include the knee joint conditions, the zero moment point conditions for the x-direction and the tip conditions of swing leg during the period of a stride for walking a staircase.

• International Journal of CAD/CAM
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• 제6권1호
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• pp.149-156
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• 2006

This paper presents a novel approach for constructing a piecewise triangular cubic polynomial surface with $C^1$ continuity around a common corner vertex. A $C^1$ continuity condition between two cubic triangular patches is first derived using mixed directional derivatives. An approach for constructing a surface with $C^1$ continuity around a corner is then developed. Our approach is easy and fast with the virtue of cubic reproduction, local shape controllability, $C^2$ continuous at the corner vertex. Some experimental results are presented to show the applicability and flexibility of the approach.

• Journal of applied mathematics & informatics
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• 제27권3_4호
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• pp.463-473
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• 2009

A family of quasi-interpolatory wavelet system was introduced in [10], extending and unifing the biorthogonal Coiffman wavelet system. The corresponding refinable functions and wavelets have vanishing moment of a certain order (say, L), which is a key property for data representation and approximation. One of main advantages of this wavelet systems is that we can get optimal smoothness in the sense of smoothing factors in the scaling filters. In this paper, we first discuss the biorthogonality condition of the quisi-interpolatory wavelet system. Then, we study the properties of the scaling and wavelet filters, related to the polynomial reproduction and the vanishing moment respectively, which in fact determines the approximation orders of biorthogonal projections. In addition, we discuss the approximation orders of the wavelet projections.

• Steel and Composite Structures
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• 제4권6호
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• pp.453-469
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• 2004

In this article, a genetic algorithm based optimum design method is presented for non-linear steel frames with semi-rigid connections. The design algorithm obtains the minimum weight frame by selecting suitable sections from a standard set of steel sections such as European wide flange beams (i.e., HE sections). A genetic algorithm is employed as optimization method which utilizes reproduction, crossover and mutation operators. Displacement and stress constraints of Turkish Building Code for Steel Structures (TS 648, 1980) are imposed on the frame. The algorithm requires a large number of non-linear analyses of frames. The analyses cover both the non-linear behaviour of beam-to-column connection and $P-{\Delta}$ effects of beam-column members. The Frye and Morris polynomial model is used for modelling of semi-rigid connections. Two design examples with various type of connections are presented to demonstrate the application of the algorithm. The semi-rigid connection modelling results in more economical solutions than rigid connection modelling, but it increases frame drift.

• 한국정밀공학회지
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• 제23권4호
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• pp.75-82
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• 2006

In this paper, we propose an optimal trajectory for biped robots to move up-and-down stairs using a genetic algorithm and a computed-torque control for biped robots to be dynamically stable. First, a Real-Coded Genetic Algorithm (RCGA) which of operators are composed of reproduction, crossover and mutation is used to minimize the total energy. Constraints are divided into equalities and inequalities: Equality constraints consist of a position condition at the start and end of a step period and repeatability conditions related to each joint angle and angular velocity. Inequality constraints include collision avoidance conditions of a swing leg at the face and edge of a stair, knee joint conditions with respect to the avoidance of the kinematic singularity, and the zero moment point condition with respect to the stability into the going direction. In order to approximate a gait, each joint angle trajectory is defined as a 4-th order polynomial of which coefficients are chromosomes. The effectiveness of the proposed optimal trajectory is shown in computer simulations with a 6-dof biped robot that consists of seven links in the sagittal plane. The trajectory is more efficient than that generated by the modified GCIPM. And various trajectories generated by the proposed GA method are analyzed in a viewpoint of the consumption energy: walking on even ground, ascending stairs, and descending stairs.

• 대한전자공학회논문지SP
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• 제49권4호
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• pp.40-48
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• 2012

본 논문은 추가적인 화이트 채널을 사용한 프로젝터와 사용하지 않은 프로젝터간의 매칭 실험을 통하여 색상이동 현상을 모델링하였고, 색상을 수정하는 방법을 제안하였다. 전체 색상 값에 대해 색상이동현상을 정량화하기 위하여, 동일한 밝기와 채도 값을 유지하여 24개의 색상 패치 값을 생성하여 이를 화이트를 추가한 상태와 추가하지 않은 상태에서 투영하였다. 다음으로 각각의 패치에 대해 화이트를 추가 하지 않은 상태와 동일한 색상으로 인지되도록 화이트를 추가한 상태의 색상 값을 변경하였다. 색상 매칭 실험을 통하여 얻은 색상 이동 값을 6개의 구간으로 나누어 4차 방정식을 이용하여 수식화하여 임의의 색상 값에 대한 색상 이동 값을 추정하였고, 색상 값을 수정하는 위하여 사용하였다. 실제로, 입력 RGB 영상은 각각의 픽셀에 대해 CIELAB LCH 색 공간으로 변경하여 각각의 픽셀의 색상 값을 계산하였다. 이 색상 값은 추정된 색상이동량을 이용하여 수정하게 된다. 최종적으로 결과 RGB 영상은 역 과정으로 변환하였다. 제안한 방법을 평가하기 위하여 여러 가지 테스트 영상을 이용하여 매칭 실험을 수행하였고 이를 z-scores를 이용하여 비교하였다.