• Communications of the Korean Mathematical Society
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• v.37 no.3
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• pp.915-938
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• 2022

We are interested in the problem of fitting a parabola to a set of data points in ℝ³. It can be usually solved by minimizing the geometric distances from the fitted parabola to the given data points. In this paper, a parabola fitting algorithm will be proposed in such a way that the sum of the squares of the geometric distances is minimized in ℝ³. Our algorithm is mainly based on the steepest descent technique which determines an adequate number λ such that h(λ) = Q(u - λ𝛁Q(u)) < Q(u). Some numerical examples are given to test our algorithm.

• Korean Journal of Remote Sensing
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• v.27 no.4
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• pp.495-506
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• 2011

COMS In-Orbit Tests(IOT), performed from July, 2010 to Jan, 2011, were successfully completed and the scientific data from MI and GOCI has been distributed officially from April, 2011. This paper focuses on the geometric calibration system tests conducted during the IOT. The geometric calibration process, which is one of the primary objectives of the IOT is the final step of COMS data pre-processing. The basic principles of the geometric calibration (or image navigation and registration, INR) algorithm for COMS are described and the functional and performance tests of COMS INR system were summarized according to the COMS IOT phases. Final performance testes were carried out using data sets acquired from the real-time COMS data pre-processing system. Geometric calibration accuracy of the COMS data showed excellent quality and met requirement specifications.

• 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 the Korean Data and Information Science Society
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• v.22 no.2
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• pp.353-360
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• 2011

We consider an asymmetric power transformed threshold GARCH(1.1) process and find sufficient conditions for the existence of a strictly stationary solution, geometric ergodicity and ${\beta}$-mixing property. Moments conditions are given. Box-Cox transformed threshold GARCH(1.1) is also considered as a special case.

• Journal of the Korean Data and Information Science Society
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• v.22 no.6
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• pp.1233-1240
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• 2011

An augmented asymmetric power GARCH(p, q) process is considered and conditions for stationarity, geometric ergodicity and ${\beta}$-mixing property with exponential decay rate are obtained.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.17 no.2
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• pp.105-117
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• 2004

In each industry field, many engineers have tried to develop integrated environments using information technology. The core technology in building integrated environments is the database based on standardized information. To meet the requirements, this study builds a database with detailed design information as a part of integrating digital information generated from every work of steel bridges. The data model used to build the database was developed based on the international standard, namely ISO/STEP. The data model is classified into geometric and non-geometric parts to represent the design information of steel bridges. The geometric parts are represented by a three dimensional solid model so that they may be able to reuse existing information. Also, the non-geometric parts represent information requirements that are analyzed by the development method of standard data model. To verify the data model, this study validates the syntax of the model on EXPRESS Engine and verifies the validation of the model by applying the design data of Hannam bridge to the database.

• Korean Journal of Computational Design and Engineering
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• v.5 no.4
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• pp.293-300
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• 2000

The non-manifold geometric modeling technique is to improve design process and to Integrate design, analysis, and manufacturing by handling mixture of wireframe model, surface model, and solid model in a single data structure. For the non-manifold geometric modeling, Euler operators and other high level modeling methods are necessary. Boolean operation is one of the representative modeling method for the non-manifold geometric modeling. This thesis studies Boolean operations of non-manifold model with the data structure of selective storage. The data structure of selective storage is improved non-manifold data structure in that existing non-manifold data structures using ordered topological representation method always store non-manifold information even if edges and vortices are in the manifold situation. To implement Boolean operations for non-manifold model, intersection algorithm for topological cells of three different dimensions, merging and selection algorithm for three dimensional model, and Open Inventor(tm), a 3D toolkit from SGI, are used.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.21 no.2
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• pp.208-213
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• 2012

In this paper, the radial error of a rotary table at five-axis machine tool is evaluated by utilizing ISO 230-2 and estimation method using double ball-bar. The geometric error of a rotary table is defined as position dependent geometric errors or position independent geometric errors according to their physical character. Then estimation method of geometric errors using double ball-bar is simply summarized including measurement path, parametric modeling and least squares approach. To estimate representative radial error, offset error, set-up error which affect to the double ball-bar data, mean value of measured data including CCW/CW-direction are used at estimation process. Radial errors are separated from measured data and used for evaluation with ISO 230-2. Finally, suggested evaluation method is applied to a rotary table at five-axis machine tool and its result is analyzed to improve the accuracy of the rotary table.

• East Asian mathematical journal
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• v.28 no.1
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• pp.13-23
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• 2012

In this paper, we present the geometric Hermite interpolation for planar Pythagorean-hodograph cubics for some general Hermite data.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.25 no.6_1
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• pp.545-555
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• 2007

3D buildings are the most prominent feature comprising urban scene. A few of mega-cities in the globe are virtually reconstructed in photo-realistic 3D models, which becomes accessible by the public through the state-of-the-art online mapping services. A lot of research efforts have been made to develop automatic reconstruction technique of large-scale 3D building models from remotely sensed data. However, existing methods still produce irregular building polygons due to errors induced partly by uncalibrated sensor system, scene complexity and partly inappropriate sensor resolution to observed object scales. Thus, a geometric regularization technique is urgently required to rectify such irregular building polygons that are quickly captured from low sensory data. This paper aims to develop a new method for regularizing noise building outlines extracted from airborne LiDAR data, and to evaluate its performance in comparison with existing methods. These include Douglas-Peucker's polyline simplication, total least-squared adjustment, model hypothesis-verification, and rule-based rectification. Based on Minimum Description Length (MDL) principal, a new objective function, Geometric Minimum Description Length (GMDL), to regularize geometric noises is introduced to enhance the repetition of identical line directionality, regular angle transition and to minimize the number of vertices used. After generating hypothetical regularized models, a global optimum of the geometric regularity is achieved by verifying the entire solution space. A comparative evaluation of the proposed geometric regulator is conducted using both simulated and real building vectors with various levels of noise. The results show that the GMDL outperforms the selected existing algorithms at the most of noise levels.