• Proceedings of the Korea Information Processing Society Conference
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• 2010.11a
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• pp.1839-1842
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• 2010

등각사상은 함수론의 기본적인 문제로 2차원 Laplace방정식이 나타나는 열전도, 정전(靜電) potential, 유체의 문제에 이용되는 등 공학이나 물리학에서 그 응용분야가 넓다. 수치등각사상의 목적은 보다 빠르고, 보다 정확하며, 보다 적용범위가 넓은 계산법을 연구하는데 있다. 단위원 내부로부터 Jordan 영역 내부로의 등각사상을 구하는 문제는 비선형 방정식인 Theodorsen 방정식을 푸는 것으로 귀결된다. Theodorsen 방정식에 관해서는 여러 가지 수치해법이 제안되어 있는데 본 논문에서는 그 중 SOR 법인 Niethammer와 Newton법인 Vertgeim의 방법을 다루어 비교, 분석하였다. 이 2가지 방법을 실제 계산기상에 실현시켜 수치실험을 하여 그 유효성을 비교, 분석한 결과 난이도가 낮은 문제에서는 Niethammer의 방법이 난이도가 높은 문제에서는 Vertgeim이 제안한 방법이 유효함을 알게 되었다.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.13 no.2
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• pp.170-175
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• 2002

The cut-off frequencies of higher order modes in a symmetrical stripline are calculated using the variational finite element method combined with the conformal mapping. The conformal mapping is used to Improve the modeling of the infinite transverse extents of a stripline. And then the finite element method is employed to solve the variational equation in the transformed finite region. Comparisons with numerical results found in the literature validate the presented method.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2009.10a
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• pp.821-824
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• 2009

Conformal mapping is useful to solve problems in physics, engineering and so on. This paper is to discuss the numerical conformal mapping from the unit disk onto Jordan region, which can be solved by Theodorsen equation. Wegmann's method has been known as the most efficient one for the Theodorsen equation. However, we found divergence through numerical experiments by the iterative method of Wegmann. The divergence occurs especially when some degree of difficulty is high. We analyze the cause of divergence and propose an improved method by applying a low frequency pass filter to Wegmann's method. By this proposed method we can get a stable convergence for all the problems which was unstable with the Wegmann's method.

• The KIPS Transactions:PartA
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• v.14A no.1 s.105
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• pp.73-76
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• 2007

The determination of the conformal maps from the unit disk onto a Jordan region has been completed by solving the Theodorsen equation which is an nonlinear equation for the boundary correspondence function. Wegmann's method has been well known for the efficient mothed among the many suggestions for the Theodorsen equation. We proposed an improved method for convergence by applying a low-frequency pass filter to the Wegmann's method and theoretically proved convergence of improved iteration[1, 2]. And we proposed an effective method which makes it possible to estimate an error even if the real value is nut acquired[3]. In this paper, we propose an automatic algorithm for numerical conformal mapping bared on this error analysis in our early study. By this algorithm numerical conformal mapping is determined automatically according to the given domain of problem and the required accuracy. The discrete numbers and parameters of the low-frequency filter were acquired only by experience. This algorithm, however, is able to determine the discrete numbers and parameters of the low-frequency filter automatically in accordance with the given region This results from analyzing the function, which may decide the shape of the given domain under the assumption that the degree of the problem depends of the transformation of a given domain, as seen in the Fourier Transform. This proposed algorithm is also ploved by numerical experience.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.13 no.3
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• pp.451-457
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• 2009

Most of objects in computer graphics may be represented by a form of mesh. The exact computation of vertex normal vectors is essential for user to apply a variety of geometric operations to the mesh and get more realistic rendering results. Most of the previous algorithms used a weight which resembles a local geometric property of a vertex of a mesh such as the interior angle, the area, and so on. In this paper, we propose an efficient algorithm for computing the normal vector of a vertex in meshes. Our method uses the conformal mapping which resembles synthetically the local geometric properties, and the mean value coordinates which may smoothly represent a relationship with the adjacent vertices. It may be confirmed by experiment that the normal vector of our algorithm is more exact than that of the previous methods.

• Journal of the Institute of Electronics Engineers of Korea CI
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• v.38 no.1
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• pp.7-18
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• 2001

In this paper, we present a new method to generate obstacle-free path by using conformal mapping, when avatar navigates in virtual environment. First, we show that the proposed method generates a path to keep away from a circular obstacle. Then, we show that the method can be extended to an elliptical obstacle and multiple obstacles. For real applications, we combine the proposed local method with a global navigation method using sub-target to generate a global obstacle-free path by which avatar navigates naturally in virtual environment.

• The KIPS Transactions:PartA
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• v.8A no.4
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• pp.503-508
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• 2001

Conformal mapping is useful to solve problems in heat conduction, electrostatic potential and fluid flow involving Laplace's equation in two independent variables. Determinations of conformal maps from the unit disk onto a Jordan region eventually requires solving the Theodorsen equation which is in general nonlinear with respect to the boundary correspondence function. H bner's method which has been well known for the efficient method among the many suggestions for the Theodorsen equation, was improved in early study[1, 2]. In this paper Wegmann's method is treated that is more efficient in computation cost rather than H bner's. But we found that a question which is divergent in some difficult problems by numerical experiment of Wegmann's iteration. We analyze theoretically the cause of divergence and propose an improved method by applying a low frequency filter to the Wegmann's method. Numerical experiments by our improved method show convergence for all divergent problems by Wegmann's method.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.27 no.2
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• pp.281-288
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• 2009

In the paper, we try to develop the methodology for updating road networks of large-scale digital maps by using construction drawing data. For the purpose, it is pre-requite step to merge road networks detached in CAD drawing data. As such, tie points are identified in neighboring drawings and used for solving the parameters of 2D conformal transformation between drawings. Then, the merged road network in CAD data is transformed to the coordinate system of digital maps. In the process, IPs in the drawings are considered as control information and 2D affine transformation is selected for coordinate transformation. Through the experiments with real dataset, we can identify that the developed method is valid and generally applicable.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.23 no.6 s.165
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• pp.988-1000
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• 1999

An experimental study is presented for the effect of number of terms of a pewee series type stress function on stress analysis around a hole in tensile loaded plate. The hybrid method coupling photoelastsic data inputs and complex variable formulations involving conformal mappings and analytical continuity is used to calculate tangential stress on the boundary of the hole in uniaxially loaded, finite width tensile plate. In order to measure isochromatic data accurately, actual photoelastic fringe patterns are two times multiplied and sharpened by digital image processing. For qualitative comparison, actual fringes are compared with calculated ones. For quantitative comparison, percentage errors and standard deviations with respect to percentage errors are caculated for all measured points by changing the number of terms of stress function. The experimental results indicate that stress concentration factors analyzed by the hybrid method are accurate within three percent compared with ones obtained by theoretical and finite element analysis.

• Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
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• v.24 no.6
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• pp.35-42
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• 2010

We use conformal mapping method to derive the analytical expressions for calculating electrostatic fields and electric potentials surrounding the conductor-backed coupled coplanar waveguide(CBCCPW) structure. Using the derived expressions, the electrostatic fields and potentials are computed at various points of the CBCCPW's geometry and the field and potential distributions are analyzed. The proposed method provides a faster and simpler calculation of the field distributions than the full-wave analysis method because no iterations are required. This method can be widely applied to the analysis of microwave integrated circuits using coupled line, such as coupler, filter, and microstrip antenna.