• Journal of applied mathematics & informatics
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• v.7 no.3
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• pp.983-994
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• 2000

We consider the problem of determining the circle of best fit to a set of data points in the plane. In [1] and [2] several algorithms already have been given for fitting a circle in least squares sense of minimizing the geometric distances to the given data points. In this paper we present another new descent algorithm which computes a parametric represented circle in order to minimize the sum of the squares of the distances to the given points. For any choice of starting values our algorithm has the advantage of ensuring convergence to a local minimum. Numerical examples are given.

• Journal of Korean Society for Geospatial Information Science
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• v.19 no.1
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• pp.97-103
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• 2011

LiDAR system has become a popular tool for generating 3D surface data such as Digital Surface Model. Extraction of valuable information, such as digital building models, from LiDAR data has been an attractive research subject. This research addresses to extract planar patches from LiDAR data. Planar patches are important primitives consisting of man-made objects such as buildings. In order to determine the best fitted planes, this research proposed a method to reduce/eliminate the impact of the outliers and the intersection areas of two planes. After finishing plane fitting, planar patches are segmented by pseudo color values which are calculated by determined three plane parameters for each LiDAR point. In addition, a segmentation procedure is conducted using the pseudo color values to find planar patches. This paper evaluates the feasibility of the proposed method using both airborne and terrestrial LiDAR data.

• Geophysics and Geophysical Exploration
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• v.19 no.1
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• pp.1-10
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• 2016

The hypocenter distribution of microseismic events generated by hydraulic fracturing for shale gas development provides essential information for understanding characteristics of fracture network. In this study, we evaluate how inaccurate velocity models influence the inversion results of two widely used location programs, hypoellipse and hypoDD, which are developed based on an iterative linear inversion. We assume that 98 stations are densely located inside the circle with a radius of 4 km and 5 artificial hypocenter sets (S0 ~ S4) are located from the center of the network to the south with 1 km interval. Each hypocenter set contains 25 events placed on the plane. To quantify accuracies of the inversion results, we defined 6 parameters: difference between average hypocenters of assumed and inverted locations, $d_1$; ratio of assumed and inverted areas estimated by hypocenters, r; difference between dip of the reference plane and the best fitting plane for determined hypocenters, ${\theta}$; difference between strike of the reference plane and the best fitting plane for determined hypocenters, ${\phi}$; root-mean-square distance between hypocenters and the best fitting plane, $d_2$; root-mean-square error in horizontal direction on the best fitting plane, $d_3$. Synthetic travel times are calculated for the reference model having 1D layered structure and the inaccurate velocity model for the inversion is constructed by using normal distribution with standard deviations of 0.1, 0.2, and 0.3 km/s, respectively, with respect to the reference model. The parameters $d_1$, r, ${\theta}$, and $d_2$ show positive correlation with the level of velocity perturbations, but the others are not sensitive to the perturbations except S4, which is located at the outer boundary of the network. In cases of S0, S1, S2, and S3, hypoellipse and hypoDD provide similar results for $d_1$. However, for other parameters, hypoDD shows much better results and errors of locations can be reduced by about several meters regardless of the level of perturbations. In light of the purpose to understand the characteristics of hydraulic fracturing, $1{\sigma}$ error of velocity structure should be under 0.2 km/s in hypoellipse and 0.3 km/s in hypoDD.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.46 no.6
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• pp.43-57
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• 2009

Integrating 3D data acquired in multiple views is one of the most important techniques in 3D modeling. However, the existing integration methods are sensitive to registration errors and surface scanning noise. In this paper, we propose a integration algorithm using the local surface topology. We first find all boundary vertex pairs satisfying a prescribed geometric condition in the areas between neighboring surfaces, and then separates areas to several regions by using boundary vertex pairs. We next compute best fitting planes suitable to each regions through PCA(Principal Component Analysis). They are used to produce triangles that be inserted into empty areas between neighboring surfaces. Since each regions between neighboring surfaces can be integrated by using local surface topology, a proposed method is robust to registration errors and surface scanning noise. We also propose a method integrating of textures by using parameterization technique. We first transforms integrated surface into initial viewpoints of each surfaces. We then project each textures to transformed integrated surface. They will be then assigned into parameter domain for integrated surface and be integrated according to the seaming lines for surfaces. Experimental results show that the proposed method is efficient to face modeling.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.18 no.2
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• pp.135-141
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• 2000

This study aims to analyze stone's surface roughness measurement accuracy of a high resolution DCS 420 digital camera by digital close-range photogrammetric technique. For this purpose, the surface roughness measurement system was constructed by means of microsoft visual basic 6.0 in windows. As the analysis results of measurement accuracy of digital camera using this system, the roughness error of the normal distance between the best fitting reference surface obtained by least square method and sample points in the ideal plane or surface did not exceed $\pm$0.1 mm

• 한국방재학회:학술대회논문집
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• 2008.02a
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• pp.249-252
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• 2008

The solutions are expressed in terms of a double integral transformation over wavenumber and frequency. The complete solution is considered in such a full wave theory approach. This method can handle a larger number of plane layers. Therefore, the result of FK method is very similar to real data. Using the models that were modified in velocity and Q value with depth by iterative process from a model (Kang and Park, 2006) and considered as one of the best models in Korean Peninsula, the synthetic data are simulated for explosions and earthquakes of North Korea. This study notes that the wave shape of the synthetic data is very dependent on Q value, velocities, and thickness of sedimentary layers. Comparing between the real and the synthetic, fitting well in arrival time of first arrival and wave shape causes us to arrive at an indication that the model is very close representation of upper crustal structure and simulations are well done in amplitude fitting and in identification of phases of local and regional waves.

• Journal of The Korean Astronomical Society
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• v.30 no.1
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• pp.95-106
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• 1997

We investigate the velocity distribution of dark matter in the disk of a galaxy like the Milky Way at the solar radius. Using N-body simulations with the total mass and z-component of angular momentum conserved, we calculate the response of a dissipationless dark matter galactic halo during the dissipational collapse of the baryonic matter in spiral galaxy formation. The initial distribution of dark matter and baryonic particles is assumed to be a homogeneous mixture based on a King model. The baryonic matter is assumed to contract, forming the final luminous components of the galaxy, namely the disk and, in some cases, a bulge and central point. Both slow and fast growth of the luminous components are considered. We find that the velocity distribution of dark matter particles in a reference frame rotating slowly about the galaxy center in the plane of the disk is similar to a Maxwellian, but it is somewhat boxier, being flatter at the peak and truncated in the tails of the distribution. We tabulate parameters for the best-fitting Maxwellian and modified-Maxwellian distributions. There is no significant difference between slow collapse and fast collapse for all these results. We were unable to detect any effect of disk formation on the z-dependence of the dark matter density distribution.

• Transactions of the Korean Society of Automotive Engineers
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• v.24 no.2
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• pp.242-254
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• 2016

This paper is the forth investigation on the evaluation methods of flow characteristics in a steady flow bench. In the previous works, it was concluded that the assumption of the solid rotation might cause serious problems and both of the eccentricity and the velocity profile distort the flow characteristics when using the ISM at 1.75B plane. Also particle image velocimetry (PIV) measurement at this position showed that the real velocity profile was far from the assumption of ISM evaluation. In this paper, the planar velocity profiles were measure from 1.75B to 6.00B position by PIV and the characteristics were examined according to the valve angles and lifts for further investigations about the effect of the position on the velocity profile. The results show that $26^{\circ}$ valve angle is always an unique exceptional case in all aspects. If the valve angle is $21^{\circ}$ and below, the planar velocity profiles according to the lift and the position are similar to each other, however, the tangential velocity curves along with the radial direction have common tendencies up to $16^{\circ}$ angle. Also the well arranged swirl behaviors are generally observed at the position above 3.00B and the velocity contour lines come closer to the concentric circle as the valve lift increases. In addition, the gradient of tangential velocity along with the radial direction from the swirl center becomes stable and constant as the position goes downstream. Concurrently the velocity gradient is larger to the eccentric direction of the center. In the meantime the tangential velocity curves along with the radial direction are irregular and various at 1.75B, however, they become regular and reach higher level as the evaluation position goes downstream. At this time the curves of 4.50B are the best fitted to the ideal one. On the other hand in an exceptional case, $26^{\circ}$, the velocity contours are very complicated over 6mm valve lift regardless the position and the gradient increases to the opposite direction of the eccentric center. Also, 6.00B is a best fitting position in the geometrical cylinder center base. With respect to the swirl center, the distribution range of centers for 1.75B is different to that for the other positions and the eccentricities of this plane are larger regardless the valve angle. After 1.75B, there is no certain tendency in the center position change according to the valve angle and lift. Additionally, the eccentricities are not sufficiently small to neglecting the effect on ISM measurement.

• Korean Journal of Materials Research
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• v.5 no.5
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• pp.598-605
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• 1995

Thin films of $YB_{2}Cu_{3}O_{7-d}$ were prepared on various substrated of MgO(100), $SrTiO_{3}$, and $LaAlO_{3}$ by using off-axis magentron sputtering methods and annealing in-situ. The prarameters of film fabrication processes had been optimized through a "follow the lcoal maxima" strategy to yield good quality films in therms of the critical temperature $T_{c}$ and the critical current density $J_{c}$. Optimizedproecsses employing a plane magndtron and an cylindrical magnetron yielded $T_{c}$>90K along with $J_{c}$$10^{6}$A/$\textrm{cm}^2$ at 77K and > 2${\times}$$10^{7}$A/$\textrm{cm}^2$ at 5K. The sampels, however, showed degradationinthe properties, after chemical etching for fabrication of microbridges with the line width of 2-10 mocrons. In particular, the value of $T_{c}$ for the microbridges of 2microns was as small as 80%. The degradation was strongly dependent on the line width through a formula : $T_{c}$(e)=$T_{c}$)b) [1-a exp(-1000 bL)} where $T_{c}$(e) and $T_{c}$ (b) are the values of $T_{c}$ in the absolute scale measured after and before chemical etching, respectively and L is the line width in mm. By utilizing a best fitting technique, the proper constant values of a and to b were found as exp(-1.2) and 0.22, respectively. This formula was very useful in estimatiing the upper limit of the device operationtemperature.