• Journal of KIISE:Computer Systems and Theory
• /
• v.36 no.5
• /
• pp.404-411
• /
• 2009

We introduce in this paper a new method for smooth foldover-free warping of images, based on the vector field deformation technique proposed by Von Funck et al. It allows users to specify the constraints in two different ways: positional constraints to constrain the position of a point in the image and gradient constraints to constrain the orientation and scaling of some parts of the image. From the user-specified constraints, it computes in the image domain a C1-continuous velocity vector field, along which each pixel progressively moves from its original position to the target. The target positions of the pixels are obtained by solving a set of partial derivative equations with the 4th order Runge-Kutta method. We show how our method can be useful for texture mapping with hard constraints. We start with an unconstrained planar embedding of a target mesh using a previously known method (Least Squares Conformal Map). Then, in order to obtain a texture map that satisfies the given constraints, we use the proposed warping method to align the features of the texture image with those on the unconstrained embedding. Compared to previous work, our method generates a smoother texture mapping, offers higher level of control for defining the constraints, and is simpler to implement.

• 한국전산유체공학회:학술대회논문집
• /
• 2000.05a
• /
• pp.99-106
• /
• 2000

A method of two and three dimensional orthogonal grid generation with control of spacing by using the covariant Laplace equation is Presented. An important feature of the methodology is its ability to control effectively the grid spacing especially near the boundaries still maintaining good orthogonality in whole field. The method is based on the concept of decomposition of the global transformation into consecutive transformation of an approximate conformal mapping and au auxiliary orthogonal mapping to have linear and uncoupled equations. Control of cell spacing is based on the concept of reference arc length, and orthogonal correction is performed in the auxiliary domain. It is concluded that the methodology can successfully generate well controlled orthogonal grids around bodies of 2 and 3 dimensional configurations.

• Journal of computational fluids engineering
• /
• v.5 no.1
• /
• pp.14-21
• /
• 2000

A method of two and three dimensional orthogonal grid generation with control of spacing by using the covariant Laplace equation is presented. An important feature of the methodology is its ability to control effectively the grid spacing especially near the boundaries still maintaining good orthogonality in whole field. The method is based on the concept of decomposition of the global transformation into consecutive transformation of an approximate conformal mapping and an auxiliary orthogonal mapping to have linear and uncoupled equations. Control of cell spacing is based on the concept of reference arc length, and orthogonal correction is peformed in the auxiliary domain. It is concluded that the methodology can successfully generate well controlled orthogonal grids around bodies of 2 and 3 dimensional configurations.

• Bulletin of the Korean Mathematical Society
• /
• v.52 no.6
• /
• pp.1925-1935
• /
• 2015

In this paper, we study right half-plane harmonic mappings $f_0$ and f, where $f_0$ is fIxed and f is such that its dilatation of a conformal automorphism of the unit disk. We obtain a sufficient condition for the convolution of such mappings to be convex in the direction of the real axis. The result of the paper is a generalization of the result of by Li and Ponnusamy [11], which itself originates from a problem posed by Dorff et al. in [7].

• Proceedings of the KIEE Conference
• /
• 1998.07a
• /
• pp.67-69
• /
• 1998

In order to design or predict the performance of a cylindrical electrostatic motor it is necessary to analyze the torque generated by such a structure. In this paper a simple but sufficiently accurate analytical model is developed for use in design. Conformal mapping are used to model the capacitance and torque of the motor as a function of the rotor position, using a quasi-static, two-dimension approximation, the effect of an insulating dielectric layer on the stator or rotor is also evaluated.

• Journal of the Institute of Electronics Engineers of Korea SD
• /
• v.39 no.7
• /
• pp.26-36
• /
• 2002

Mach-Zehnder type traveling-wave optical modulators with 3-section and 5-section phase reversal were designed and fabricated on z-cut $LiNbO_3$ substrates. Optical waveguides were designed by means of the FDM(Finite Difference Method). Design of CPW traveling-wave electrodes were performed by the SOR(Successive Over Relaxation) in the active region and by the CMM(Conformal Mapping) in the input/output section. The optical response R(${\omega}$ calculated based on the measured S-parameters showed the bandwidth of 15GHz centered at 25GHz for the 3-section, and the bandwidth of 22GHz at 45GHz for the 5-section.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.34 no.9
• /
• pp.1287-1292
• /
• 2010

In this paper, a hybrid technique is presented. First, the isochromatic fringe data of a given set of points are calculated by the finite element method and are used as input data in complex variable formulations. Then the numerical model of the specimen with a central inclined crack is transformed from the physical plane to the complex plane by conformal mapping. The stress field is analyzed and the mixed-mode stress intensity factors are calculated for this complex plane. The stress intensity factors are calculated by the finite element method as well as by a theoretical method and compared with each other. In order to conveniently compare these values with each other, both actual and regenerated photoelastic fringe patterns are multiplied by a factor of two and sharpened by digital image processing.

• Journal of the Korean Society for Precision Engineering
• /
• v.25 no.10
• /
• pp.84-91
• /
• 2008

Due to the complexity of the engineering problems, it is difficult to obtain directly the stress field around the crack tip by theoretical derivation. In the paper, the hybrid method is employed to calculate full-field stress around the crack tip in uni-axially leaded finite width tensile plate, using the displacement data of given points calculated by finite element method as input data. The method uses complex variable formulations involving conformal mappings and analytical continuity. In order to accurately compare calculated fringes with experimental ones, both actual and reconstructed photoelastic fringe patterns are two times multiplied and sharpened by digital image processing. Reconstructed fringes by hybrid method are quite comparable to actual fringes. The experimental results indicate that Mode I stress intensity factor analyzed by the hybrid method are accurate within a few percent compared with ones obtained by empirical equation and finite element analysis.

• Korean Journal of Optics and Photonics
• /
• v.29 no.3
• /
• pp.104-109
• /
• 2018

We explain the basic principle of transformation optics, and introduce several design techniques for transformation cavities that can maintain the characteristics of whispering gallery modes (WGMs) even if the cavity is strongly deformed from a circular shape. As a method of obtaining various transformation cavities under a specific conformal mapping, we suggest a method of parallel movement of the initial cavity domain, and a method of rotating the ellipse as a cavity domain. The internal wave pattern and the far-field output characteristics of several designed resonant modes are numerically calculated. From these results, it is confirmed that a variety of GRIN resonators are possible for a given conformal coordinate transformation.

• Journal of the Korean Institute of Telematics and Electronics
• /
• v.27 no.10
• /
• pp.68-77
• /
• 1990

In this paper, a neural patten recognition method for the automatic circuit diagram reading system is proposed. The proposed procedure to recognize a deformed logic symbols is composed of three stages: feature detection, log mapping, and pattern classification. In the feature detection stage, a modified competitive learning algorithm where each pattern has the inhibition weight as well as the activation weight is developed. The global information of hand-written logic symbols is obtained by the feature detection neural network having both the inhibition and activation weights. The obtained global data is then transformed into a log space by the conformal mapping where according to the Schwartz's theory about the human visual signal process-ing, the degree of rotation and the scale change are mapped into the translation change. Logic symbols are finally classified by a three layer perceptron trained by the error back propagation algorithm. The computer simulation demonstrates that the proposed multistage neural network system can recognize well the deformed patterns of hand-written logic circuit diagrams.