• Journal of Computational Design and Engineering
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• 제1권2호
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• pp.116-127
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• 2014

This paper aims to review methods for computing orthogonal projection of points onto curves and surfaces, which are given in implicit or parametric form or as point clouds. Special emphasis is place on orthogonal projection onto conics along with reviews on orthogonal projection of points onto curves and surfaces in implicit and parametric form. Except for conics, computation methods are classified into two groups based on the core approaches: iterative and subdivision based. An extension of orthogonal projection of points to orthogonal projection of curves onto surfaces is briefly explored. Next, the discussion continues toward orthogonal projection of points onto point clouds, which spawns a different branch of algorithms in the context of orthogonal projection. The paper concludes with comments on guidance for an appropriate choice of methods for various applications.

• 한국CDE학회논문집
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• 제18권1호
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• pp.49-57
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• 2013

In this paper, orthogonal projection of a point onto a 2D planar curve is discussed. The problem is formulated as finding a point on a curve where the tangent of the curve is perpendicular to the vector connecting the point on the curve and a point in the space. Existing methods are compared and novel approaches to solve the problem are presented. The proposed methods are tested with examples.

• Communications for Statistical Applications and Methods
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• 제31권4호
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• pp.377-391
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• 2024

Accurate household projections are essential for sectors such as housing supply and tax policy planning, given the rapid social changes like declining birthrates, an aging population, and a rise in single-person households that impact household size and type. Korea introduced its first register-based census in 2015, transitioning from five-year general survey-based approach to an annual administrative data-based census. This change in census allows for more frequent and effective capturing the rapid demographic shifts and trends. However, this change in census has caused challenges in future projection by the existing household projection model due to the rapid dynamics. This paper proposes a new household projection method, the N-point Modified Exponential Model (MEM), that accurately reflects register-based census data and mitigates the impact of rapid demographic changes, in three types: the Weighted N-point MEM, the Regression-based N-point MEM, and the Rolling Weighted N+point MEM. Using register-based census data from 2016 to 2020 to forecast household headship rates by age, household size, and household type to 2051, the N-point modified exponential model outperformed the existing model in both long- and short-term forecast accuracy, suggesting its suitability as a future household projection model for Korea.

• 대한수학회논문집
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• 제27권2호
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• pp.279-296
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• 2012

In this paper, we define a generalized duality mapping, which is a generalization of the normalized duality mapping and using this, we extend the notion of a generalized projection and study their properties. Also we construct an approximating fixed point sequence using the generalized projection with the generalized duality mapping and prove its strong convergence.

• 대한수학회보
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• 제50권3호
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• pp.823-832
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• 2013

We present a new algorithm for solving a system of nonlinear equations with convex constraints which combines proximal point and projection methodologies. Compared with the existing projection methods for solving the problem, we use a different system of linear equations to obtain the proximal point; and moreover, at the step of getting next iterate, our projection way and projection region are also different. Based on the Armijo-type line search procedure, a new hyperplane is introduced. Using the separate property of hyperplane, the new algorithm is proved to be globally convergent under much weaker assumptions than monotone or more generally pseudomonotone. We study the convergence rate of the iterative sequence under very mild error bound conditions.

• East Asian mathematical journal
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• 제24권2호
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• pp.191-199
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• 2008

In this paper, we introduce and studied a system of nonlinear projection equations with perturbation in Hilbert spaces. By using the fixed point theorem, we prove an existence of solution for this system of nonlinear projection equations. We construct an algorithm for approximating the solution of the system of nonlinear projection equations with perturbation and show that the iterative sequence generated by the algorithm converges to the solution of the system of nonlinear projection equations with perturbation under some suitable conditions.

• 한국주거학회논문집
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• 제14권5호
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• pp.37-46
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• 2003

The quantitative analysis of view tells how surroundings and sky are showed, and requires understanding of visual perception and three dimensional information of buildings. The visual perception and the existing projection methods for view analysis are examined. The results of this study are as follows: The visual perception on the size is determined by the visual angle, which can be described as a solid angle. The analysis of view by planar projection can be narrow-sighted according to the size of the window and the location of the viewpoint, which will cause the obstacles in the normal direction of the window interfere the view. For the analysis of view by fisheye projection, the area around the focus point is calculated wider than other areas, and so the view ratio depends on the position of the focus point. When analyzing sky view by dividing the sky vault into the differential area, the distortion by projection can be minimized.

• 인터넷정보학회논문지
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• 제11권1호
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• pp.117-128
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• 2010

소모적이고 안전사고에 노출된 실탄 사격을 대체할 수 있는 사격 시뮬레이션 시스템과 관련된 연구가 활발히 진행되고 있다. 본 논문에서는 기존의 센서 기반 기술을 이용한 인식 방법을 사용하지 않고 영상처리기반 기술을 이용하여 탄착점을 추출하는 과정을 제시하였다. 이를 위해 모의총기의 총구에 부착된 카메라로부터 획득한 영상 분석을 통해 탄착점 위치를 찾아내고, 그 탄착점의 좌표 값과 과녁과의 매핑을 통한 최종 사격결과를 계산하여 제공할 수 있도록 한다. 이 시스템은 전송된 영상에서 영사영역을 구분하는 단계, 영사영역 내에서 탄착점 위치를 추출하는 단계, 탄착점 위치에 따른 사격결과를 계산하여 사용자에게 제공하는 단계로 나누어진다. 전송된 영상을 이진 영상으로 변환 후 영사영역의 꼭짓점의 위치를 찾고 그 안에 존재하는 탄착점을 추출한다. 구현된 탄착점 추출과정을 단계별로 제시하였으며 모의 사격 시스템을 위한 인터페이스에서 결과를 확인 할 수 있도록 하였다. 실험을 통해 영사영역의 꼭짓점 위치의 정확성을 확인하였으며 탄착점 추출 및 그에 따른 점수 환산결과를 확인할 수 있도록 하였다.

• 한국운동역학회지
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• 제17권2호
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• pp.157-166
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• 2007

This study was to compare the major kinematic factors between the success and failure group on performing the back somersault motion in floor exercise. Three gymnasts(height : $167.3{\pm}2.88cm$, age : $22.0{\pm}1.0years$, body weight : $64.4{\pm}2.3kg$) were participated in this study. The kinematic data was recorded at 60Hz with four digital video camera. Two successful motions and failure motions for each subject were selected for three dimensional analysis. 1. Success Trail It was appear that success trail was larger than failure group in projection velocity, but success trail was smaller than failure trail in projection angle. Also it was appear that success trail was longer than failure group in the time required. Hand segment velocity and maximum velocity in success trail were larger than those in failure trail, and this result was increasing the projection velocity and finally increasing the vertical height of center of mass. At the take-off(event 2), flection amount of hip and knee joint angle was contributed to the optimal condition for the take-off and at the peak point, hip and knee joint angle was maximum flexed for reducing the moment of inertia. Also in this point, upper extremities of success trail extended more than those of failure trail. in this base, success trail in upward phase(p3) 2. Failure Trail It was appear that failure trail was smaller than success trail in projection velocity, but failure trail was larger than success trail in projection angle. Also it was appear that failure trail was more short than success trail in the time required. Hand segment velocity and maximum velocity in failure trail were smaller than those in success trail, and this result was reducing the projection velocity and finally reducing the vertical high of center of mass. At the take-off(event 2), flection amount of hip and knee joint angle wasn't contributed to the optimal condition for the take-off and at the peak point, hip and knee joint angle wasn't maximum flexed for reducing the moment of inertia. Also in this point, upper extremities of failure trail didn't extended more than those of success trail.

• 대한수학회보
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• 제58권3호
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• pp.617-635
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• 2021

Let X be a smooth hypersurface X of degree d ≥ 4 in a projective space ℙⁿ⁺¹. We consider a projection of X from p ∈ ℙⁿ⁺¹ to a plane H ≅ ℙⁿ. This projection induces an extension of function fields ℂ(X)/ℂ(ℙⁿ). The point p is called a Galois point if the extension is Galois. In this paper, we will give necessary and sufficient conditions for X to have Galois points by using linear automorphisms.