• 대한수학회논문집
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• 제37권3호
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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.

• 대한원격탐사학회지
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• 제27권4호
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• pp.495-506
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• 2011

천리안 위성의 궤도상 시험이 위성발사 직후인 2010년 7월부터 2011년 1월까지 약 7개월에 걸쳐 성공적으로 수행되었으며, 과학탑재체인 기상 및 해양탑재체 자료는 2011년 4월부터 공식적으로 배포되고 있다. 이 논문에서는 천리안위성의 궤도상 시험 중 핵심적인 요소인 탑재체 자료의 보정 과정 중 최종 단계인 기하보정의 궤도상 테스트 내용에 중점을 두고 있다. 천리안위성 기하보정 알고리즘의 구조와 내용을 간략하게 소개하였으며, 위성발사 후 행해진 기하보정시스템의 기능 및 검증 테스트의 단계별 과정들과 그 결과를 분석 정리하였다. 실시간 위성자료 전처리 시스템을 통해 확보한 자료들을 이용한 천리안 기하보정알고리즘의 최종 성능테스트는 요구 조건을 만족하는 우수한 정확도를 보여 주었다.

• Journal of applied mathematics & informatics
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• 제7권3호
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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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• 제22권2호
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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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• 제22권6호
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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.

• 한국전산구조공학회논문집
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• 제17권2호
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• pp.105-117
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• 2004

각 산업분야의 엔지니어들은 각종 정보기술을 이용하여 통합환경을 구축해 오고 있다. 통합환경 구축을 위한 핵심기술은 표준화된 정보를 기반으로 한 데이터베이스이다. 본 연구에서는 이와 같은 요구사항에 대처하고 각종업무에서 발생하는 전자정보를 통합하기 위한 일환으로 강교량의 설계정보를 포함하는 데이터베이스를 구축하였다. 데이터베이스 구축과정에서 데이터 구조로 사용된 데이터모델은 국제 표준 즉, ISO/STEP(STandard for the Exchange of Product model data)을 기반으로 강교량의 설계정보를 표현할 수 있도록 기하부분과 비기하부분으로 분류되었다. 기하부분의 정보는 기존정보의 재사용이 가능하도록 3차원 솔리드모델로 표현하고, 비기하부분의 정보는 표준 데이터모델 개발 방법론에 의거해 분석된 정보요구사항을 표현하였다. 개발된 데이터모델의 검증을 위해서, 본 연구에서는 EXPRESS Engine을 이용하여 모델의 구문을 검토하였으며, 한남대교의 설계 데이터를 데이터베이스에 저장하여 개발된 모델의 타당성을 입증하였다

• 한국CDE학회논문집
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• 제5권4호
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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.

• 한국생산제조학회지
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• 제21권2호
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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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• 제28권1호
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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.

• 한국측량학회지
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• 제25권6_1호
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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.