• Korean Journal of Computational Design and Engineering
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• v.5 no.4
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• pp.336-346
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• 2000

This paper presents a geometric method that can detect and compute all conic sections in the intersection of two tori. Conic sections contained in a torus must be circles. Thus, when two tori intersect in a conic section, the intersection curve must be a circle as well. Circles in a torus are classified into profile circles, cross-sectional circlet, and Yvone-Villarceau circles. Based on a geometric classification of these circles, we present a procedural method that can detect and construct all intersection circles between two tori. All computations can be carried out using simple geometric operations only: e.g., circle-circle intersections, circle-line intersections, vector additions, and inner products. Consequently, this simple structure makes our algorithm robust and efficient, which is an important advantage of our geometric approach over other conventional methods of surface intersection.

• International Journal of Reliability and Applications
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• v.9 no.1
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• pp.31-52
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• 2008

In this paper generalized version of the geometric distribution is introduced. This distribution can be considered as a two-parameter generalization of the discrete geometric distribution. The main statistical and reliability properties of this distribution are discussed. Two methods of estimation, namely maximum likelihood method and the method of moments are used to estimate the parameters of this distribution. Simulation is utilized to calculate these estimates and to study some of their properties. Also, asymptotic confidence limits are established for the maximum likelihood estimates. Finally, the appropriateness of this new distribution for a set of real data, compared with the geometric distribution, is shown by using the likelihood ratio test and the Kolmogorove-Smirnove test.

• Journal of Institute of Control, Robotics and Systems
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• v.16 no.5
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• pp.469-475
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• 2010

This paper presents a method of classifying discolored defects of metal pads using geometric texture for AFVI (Automated Final Vision Inspection) systems. In PCB manufacturing process, the metal pads on PCB can be oxidized and discolored partly due to various environmental factors. Nowadays the discolored defects are manually detected and rejected from the process. This paper proposes an efficient geometric texture feature, SUTF (Symmetry and Uniformity Texture Feature) based on the symmetric and uniform textural characteristics of the surface of circular metal pads for automating AFVI systems. In practical experiments with real samples acquired from a production line, 30 discolored images and 1232 roughness images are tested. The experimental results demonstrate that the proposed method using SUTFs provides better performance compared to Gabor feature with 0% FNR (False Negative Rate) and 1.46% FPR (False Positive Rate). The performance of the proposed method shows its applicability in the real manufacturing systems.

• ETRI Journal
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• v.44 no.5
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• pp.816-825
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• 2022

Nondestructive testing, which can monitor a product's interior without disassembly, is becoming increasingly essential for industrial inspection. Computed laminography (CL) is widely used in this application, as it can reconstruct a product, such as a printed circuit board, into a three-dimensional (3D) high-magnification image using X-rays. However, such high-magnification scanning environments can be affected by minute vibrations of the CL device, which can generate motion artifacts in the 3D reconstructed image. Since such vibrations are irregular, geometric corrections must be performed at every scan. In this paper, we propose a geometry calibration method that can correct the geometric information of CL scans based on the image without using geometry calibration phantoms. The proposed method compares the projection and digitally reconstructed radiography images to measure the geometric error. To validate the proposed method, we used both numerical phantom images at various magnifications and images obtained from real industrial CL equipment. The experiment results confirmed that sharpness and contrast-to-noise ratio (CNR) were improved.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1995.10a
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• pp.957-960
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• 1995

A new method is introduced for the parametrization in B-spline surface interpolation. THis method uses the basis function to assign the parameter values to the arbitrary set of geometric data. This method gives us several important advantages in geometric modeling.

• Structural Engineering and Mechanics
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• v.20 no.6
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• pp.609-630
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• 2005

A reliability analysis method is proposed in this paper through a combination of the advantages of the response surface method (RSM), finite element method (FEM), first order reliability method (FORM) and the importance sampling updating method. The accuracy and efficiency of the method is demonstrated through several numerical examples. Then the method is used to estimate the serviceability reliability of cable-stayed bridges. Effects of geometric nonlinearity, randomness in loading, material, and geometry are considered. The example cable-stayed bridge is the Second Nanjing Bridge with a main span length of 628 m built in China. The results show that the cable sag that is part of the geometric nonlinearities of cable-stayed bridges has a major effect on the reliability of cable-stayed bridge. Finally, the most influential random variables on the reliability of cable-stayed bridges are identified by using a sensitivity analysis.

• 제어로봇시스템학회:학술대회논문집
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• 1993.10a
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• pp.1227-1233
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• 1993

In this paper we present the differential geometric approach for the analysis and design of sliding modes in nonlinear variable structure feedback systems. We also design the robust controller for the nonlinear system using variable structure control theory on the basis of differential geometric methods and feedback linearization applying Min-Max control based on the Lyapunov second method. The robustness against parameter uncertainties for robot manipulators with flexible joint is considered. Simulation results are presented and show the advantage of the proposed nonlinear control method.

• Korean Journal of Mathematics
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• v.14 no.2
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• pp.281-289
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• 2006

We introduce the resistant length and examine its properties. We also consider the geometric applications of resistant length to the boundary behavior of analytic functions, conformal mappings and derive the theorem in connection with the cluster sets, purely geometric problems. The method of resistant length leads a simple proofs of theorems. So it shows us the usefulness of the method of resistant length.

• Journal of Korea Multimedia Society
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• v.15 no.9
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• pp.1102-1111
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• 2012

In this paper, we propose a robust watermarking method against geometric attack even though the watermarked image is partially damaged. This method consists of standard image normalization which transforms any image into a predefined standard image and embedding watermark in DCT domain of standard normalized image using spread spectrum technique. The proposed standard image normalization method has an improvement over existing image normalization method, so it is robust to partial damage and geometric attack. The watermark embedding method using spread spectrum technique also has a robustness to image losses such as blurring, sharpening and compressions. In addition, the proposed watermarking method does not need an original image to detect watermark, so it is useful to public watermarking applications. Several experimental results show that the proposed watermarking method is robust to partial damage and various attacks including geometric deformation.

• Journal of The Korean Astronomical Society
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• v.51 no.4
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• pp.111-117
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• 2018

A numerical method is proposed to calculate the response of detectors measuring particle energies from incident isotropic fluxes of electrons and positive ions. The isotropic flux is generated by injecting particles moving radially inward on a hypothetical, spherical surface encompassing the detectors. A geometric projection of the field-of-view from the detectors onto the spherical surface allows for the identification of initial positions and momenta corresponding to the clear field-of-view of the detectors. The contamination of detector responses by particles penetrating through, or scattering off, the structure is also similarly identified by tracing the initial positions and momenta of the detected particles. The relative contribution from the contaminating particles is calculated using GEANT4 to obtain the geometric factor of the instrument as a function of the energy. This calculation clearly shows that the geometric factor is a strong function of incident particle energies. The current investigation provides a simple and decisive method to analyze the instrument geometric factor, which is a complicated function of contributions from the anticipated field-of-view particles, together with penetrating or scattered particles.