• Journal of the Korean Chemical Society
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• v.22 no.3
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• pp.117-127
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• 1978

Slater type orbitals, located at two different points A and B, are expressed in a common coordinate system by expanding the spherical harmonics and the radial part of these orbitals in terms of the reference point A. Master formulas for two center overlap integrals are derived, using the general expansion formulas of slater type atomic orbitals. Two center overlap integrals for $CH_4,\;H_2O,\;NH_3,\;C_2H_6\;and\;PH_3$molecules are evaluated, using master formulas for two center overlap integrals. The results are in agreement with those of two center overlap integrals of Mulliken.

• Journal of KIISE
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• v.42 no.10
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• pp.1185-1194
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• 2015

A spherical panoramic image does not conform to the pin-hole camera model, and, hence, it is not possible to utilize previous techniques consisting of plane-to-plane transformation. In this paper, we propose a new method to estimate the planar geometric transformation between the planar image and a spherical panoramic image. Our proposed method estimates the transformation parameters for latitude, longitude, rotation and scaling factors when the matching pairs between a spherical panoramic image and a planar image are given. A planar image is projected into a spherical panoramic image through two steps of nonlinear coordinate transformations, which makes it difficult to compute the geometric transformation. The advantage of using our method is that we can uncover each of the implicit factors as well as the overall transformation. The experiment results show that our proposed method can achieve estimation errors of around 1% and is not affected by deformation factors, such as the latitude and rotation.

• Journal of the Korean Chemical Society
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• v.23 no.3
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• pp.125-131
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• 1979

A method for calculation of two center overlap integrals for a pair of Slater type orbitals was developed by Mulliken et al. In this method the spherical polar coordinates for a pair of Slater type orbitals located at two different points are required to be transformed into a spheroidal coordinate set for calculation of two center overlap integrals. A new method, the expansion method for spherical harmonics, in which Slater type orbitals, located at two different points, are expressed in a common coordinate system has been applied for computation of two center overlap integrals. The new method for computation of two center overlap integrals is required to translate Slater type orbitals centered at two different points into the reference point for computation of two center overlap integrals. This work has been expanded the expansion method for spherical harmonics for computation of two center overlap integrals to $|3s{\g}$, $|5s{\g}$ and $|5s{\g}$. Master formulas for two center overlap integrals are derived for these orbitals, using the general expansion formulas. The numerical values of the two center overlap integrals evaluated for a hypothetical NO molecule are in agreement with those of the previous works.

• Journal of Korea Game Society
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• v.8 no.3
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• pp.69-76
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• 2008

This paper presents a novel rendering algorithm based on sperical coordinate representation of the object. The vertices of the object are transformed into the sperical coordinate system, and we construct additional maps: the centroid and index of the triangle, the memory access table. While OpenGL rendering pipeline touches all vertices of an object, the proposed method takes account of the only visible vertices by examining the visible triangles of the object. Simulation results demonstrated that the proposed method achieve an efficient rendering performace.

• International Journal of Aeronautical and Space Sciences
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• v.13 no.4
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• pp.484-490
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• 2012

This paper is devoted to investigate the feasibility of using a medium power ground-based laser to produce a torque on LEO satellites of various shapes. The laser intensity delivered to a satellite is calculated using a simple model of laser propagation in which a standard atmospheric condition and linear atmospheric interaction mechanism is assumed. The laser force is formulated using a geocentric equatorial system in which the Earth is an oblate spheroid. The torque is formulated for a cylindrical satellite, spherical satellites and for satellites of complex shape. The torque algorithm is implemented for some sun synchronous low Earth orbit cubesats. Based on satellites perigee height, the results demonstrate that laser torque affecting on a cubesat has a maximum value in the order of $10^{-9}$ which is comparable with that of solar radiation. However, it has a minimum value in the order of $10^{-10}$ which is comparable with that of gravity gradient. Moreover, the results clarify the dependency of the laser torque on the orbital eccentricity. As the orbit becomes more circular it will experience less torque. So, we can conclude that the ground based laser torque has a significant contribution on the low Earth orbit cubesats. It can be adjusted to obtain the required control torque and it can be used as an active attitude control system for cubesats.

• Proceedings of the KSRS Conference
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• 2002.10a
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• pp.242-242
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• 2002

The Earth's magnetic field acquired from KOMPSAT-1's TAM (Three-Axis Magnetometer) between June 19th and 21st 2000 was analyzed. The TAM, one of the KOMPSAT-1's Attitude and Orbit Control Subsystems, plays an important role in determining and controlling the satellite's attitude. This also can provide new insight on the Earth's magnetic field. By transforming the satellite coordinate from ECI to ECEF, spherical coordinate of total magnetic field was achieved. These data were grouped into dusk (ascending) and dawn (descending) data sets, based on their local magnetic times. This partitioning is essential for performing 1-D WCA (Wavenumber Correlation Analysis). Also, this enhances the perception of external fields in the Kompsat-1's TAM magnetic maps that were compiled according to different local. The dusk and dawn data are processed independently and then merged to produce a total field magnetic anomaly map. To extract static and dynamic components, the 1-D and 2-D WCAs were applied to the sub-parallel neighboring tracks and dawn-dusk data sets. The static components were compared with the IGRF, the global spherical harmonic magnetic field model. The static and dynamic components were analyzed in terms of corefield, external, and crustal signals based on their origins.

• 전자공학회논문지 IE
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• v.46 no.3
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• pp.19-25
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• 2009

In this paper, I suggested the character recognition methods which are used the centroid method and included the spherical transform from the rectangle coordination for the character recognition system and obtained the results of the above 78.14% average differential ratio for the character features. The character feature extraction system using the spherical transform method is suggested in this paper, and the possibilities of the method which is get the invariant feature for the character transition using the centroid are suggested through the differential ratio results.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.38 no.9
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• pp.1029-1036
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• 2014

Several types of automatic 3D scanners are available for use in the 3D scanning industry, e.g., an automatic 3D scanner that uses a robot arm and one that uses an automatic rotary table. Specifically, these scanners are used to obtain a 3D shape using automatic assisting devices. Most of these scanners are required to perform numerous operations, such as merging, aligning, trimming, and filling holes. We are interested in developing an automatic 3D shape collection device using a spherical-coordinate-based guiding system. Then, the aim of the present study is to design an automatic guiding system that can automatically collect 3D shape data. We develop a 3D model of this system and measuring data which are collected by a personal computer. An optimal design of this system and the geometrical accuracy of the measured data are both evaluated using 3D modeling software. The developed system is then applied to an object having a highly complex shape and manifold sections. Our simulation results demonstrate that the developed system collects higher-quality 3D data than the conventional method.

• Journal of the Korean Society for Precision Engineering
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• v.12 no.5
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• pp.46-56
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• 1995

As demands on the precision bevel gears are increased in the related industry, the exact kinematical investigations of a pair of spherical involute bevel gears are required for the computer aided design. The exact angular velocity ratio based on the characteristics of the spherical involute tooth is derived and verified from the relationship between rotational angles. Elementary kinematics of the gearsets is investigated by applying the transformation of the coordinate systems. The tooth contact lines based on logarithmic tooth-wise curve are examines in three dimentional space. Contact ratio is formulated and simulated according to the system parameters such as shaft angles, pressure angle, and spiral angles. The condition of teeth interference is dervied and the critical numbers of gear teeth are calculated. The whole surface geometry of a spiral bevel gearsets are discretized and visualized by a computer graphic tool.

• Geomechanics and Engineering
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• v.25 no.4
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• pp.283-294
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• 2021

This paper presents a rigorous solution for spherical cavity expansion in unsaturated soils under constant suction condition. The hydraulic behavior that describes the saturation-suction relationship is modeled by a void ratio-dependent soil-water characteristic curve, which allows the hydraulic behavior to fully couple with the mechanical behavior that is described by an extended critical state soil model for unsaturated soil through the specific volume. Considering the boundary condition and introducing an auxiliary coordinate, the problem is formulated to a system of first-order differential equations with three principal stress components and suction as basic unknowns, which is solved as an initial value problem. Parameter analyses are conducted to investigate the effects of suction and the overconsolidation ratio on the overall expansion responses, including the pressure-expansion response, the distribution of the stress components around the cavity, and the stress path of the soil during cavity expansion. The results reveal that the expansion pressures and the distribution of the stress components in unsaturated soils are generally higher than those in saturated soils due to the existence of suction.