• 한국수학교육학회지시리즈B:순수및응용수학
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• 제5권2호
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• pp.87-93
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• 1998

Mejia and Minda proved that if a hyperbolic simply connected region $\Omega$ is k-convex, then (equation omitted), $z \in \Omega$. We show that this inequality actually characterizes k-convex regions.

• 한국정밀공학회지
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• 제25권7호
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• pp.103-110
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• 2008

This paper presents a new approach of recognizing a 3D object using a single camera, based on the extended convex hull of its silhouette. It aims at minimizing the DB size and simplifying the processes for matching and feature extraction. For this purpose, two concepts are introduced: extended convex hull and measurable region. Extended convex hull consists of convex curved edges as well as convex polygons. Measurable region is the cluster of the viewing vectors of a camera represented as the points on the orientation sphere from which a specific set of surfaces can be measured. A measurable region is represented by the extended convex hull of the silhouette which can be obtained by viewing the object from the center of the measurable region. Each silhouette is represented by a relation graph where a node describes an edge using its type, length, reality, and components. Experimental results are included to show that the proposed algorithm works efficiently even when the objects are overlapped and partially occluded. The time complexity for searching the object model in the database is O(N) where N is the number of silhouette models.

• 한국정보통신학회논문지
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• 제18권8호
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• pp.1931-1940
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• 2014

x본 논문에서는 키넥트(Kinect) 시스템에서 획득한 깊이 영상으로부터 convex-hull을 이용한 기하학적 특징 기반의 손 모양 인식 기법을 제안한다. 키넥트 시스템은 깊이 영상과 사용자의 골격 정보를 제공하는 카메라로 손 영역 검출에 유용하게 활용할 수 있다. 제안하는 기법에서는 키넥트로 획득한 깊이 영상에서 손 영역을 검출하고, 이 손 영역의 convex-hull을 구한다. 손 모양에 따라서 변하는 convex-hull에서 잡음으로 생긴 경계점 및 인식에 불필요한 경계점을 일련의 기법을 통해 제거한다. 추려진 경계점을 통해 재구성된 convex-hull을 특정 다각형으로 판단하고, 이 다각형의 내각의 합을 이용하여 손 모양을 인식하게 된다. 실험을 통해 제안하는 기법이 인식하고자 하는 모델에 대하여 높은 인식률을 보여준다는 것을 확인하였고, 단순히 특정 방향으로 고정된 손 모양뿐만 아니라 같은 모양이나 방향이 틀어진 손 모양에 대해서도 우수한 인식 성능을 확인하였다.

• 제어로봇시스템학회논문지
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• 제15권1호
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• pp.99-104
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• 2009

This article describes the analysis of stable grasping for multi-fingered robot. An analysis method of stable grasping, which is based on the three-dimensional acceleration convex polytope, is proposed. This method is derived from combining dynamic equations governing object motion and robot motion, force relationship and acceleration relationship between robot fingers and object's gravity center through contact condition, and constraint equations for satisfying no-slip conditions at every contact points. After mapping no-slip condition to torque space, we derived intersected region of given torque bounds and the mapped region in torque space so that the intersected region in torque space guarantees no excessive torque as well as no-slip at the contact points. The intersected region in torque space is mapped to an acceleration convex polytope corresponding to the maximum acceleration boundaries which can be exerted by the robot fingers under the given individual bounds of each joints torque and without causing slip at the contacts. As will be shown through the analysis and examples, the stable grasping depends on the joint driving torque limits, the posture and the mass of robot fingers, the configuration and the mass of an object, the grasp position, the friction coefficients between the object surface and finger end-effectors.

• 대한수학회지
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• 제36권6호
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• pp.1169-1180
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• 1999

Two-point comparison theorems between hyperbolic and euclidean geometry for convex regions in the complex plane are known([5], [6]). We give new geometric proofs of sharp two-point comparison theorems for convex regions.

• 대한수학회보
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• 제60권4호
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• pp.905-913
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• 2023

Suppose that M is a strictly convex hypersurface in the (n + 1)-dimensional Euclidean space 𝔼ⁿ⁺¹ with the origin o in its convex side and with the outward unit normal N. For a fixed point p ∈ M and a positive constant t, we put 𝚽_t the hyperplane parallel to the tangent hyperplane 𝚽 at p and passing through the point q = p - tN(p). We consider the region cut from M by the parallel hyperplane 𝚽_t, and denote by I_p(t) the (n + 1)-dimensional volume of the convex hull of the region and the origin o. Then Schneider's characterization theorem for ellipsoids states that among centrally symmetric, strictly convex and closed surfaces in the 3-dimensional Euclidean space 𝔼³, the ellipsoids are the only ones satisfying I_p(t) = 𝜙(p)t, where 𝜙 is a function defined on M. Recently, the characterization theorem was extended to centrally symmetric, strictly convex and closed hypersurfaces in 𝔼ⁿ⁺¹ satisfying for a constant 𝛽, I_p(t) = 𝜙(p)t^𝛽. In this paper, we study the volume I_p(t) of a strictly convex and complete hypersurface in 𝔼ⁿ⁺¹ with the origin o in its convex side. As a result, first of all we extend the characterization theorem to strictly convex and closed (not necessarily centrally symmetric) hypersurfaces in 𝔼ⁿ⁺¹ satisfying I_p(t) = 𝜙(p)t^𝛽. After that we generalize the characterization theorem to strictly convex and complete (not necessarily closed) hypersurfaces in 𝔼ⁿ⁺¹ satisfying I_p(t) = 𝜙(p)t^𝛽.

• 대한기계학회논문집
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• 제16권2호
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• pp.302-312
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• 1992

Three dimensional velocity measurements of a 35.deg. inclined jet issuing into turbulent boundary layer on both concave and convex surfaces have been conducted. To investigate solely the effect of each curvature on the flow field, streamwise pressure variations are minimized by adjusting the shape of the opposite wall in the curved region. From the measured velocity components, streamwise mean vorticities are calculated to determine jet-crossflow interface. The results on convex surface show that the injected jet is separated from the wall and the bound vortex maintains its structure far downstream. On concave surface, the secondary flow in the jet cross-sections are enhanced and in some downstream region from the jet exit, the flow on the concave surface has been developed to Taylor-Gortler vortices

• 한국콘크리트학회:학술대회논문집
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• 한국콘크리트학회 2006년도 추계 학술발표회 논문집
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• pp.909-912
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• 2006

This paper examined the applicability of convex hull, which is defined as the minimal convex polygon including all points, to assessment model for effective region. In order to validate the applicability of the convex hull to assessment model for effective region, a genetic algorithm was adopted as a optimum technique, and an artificial neural network was adopted as a prediction model for material properties. The mix-proportion obtained from the proposed technique is more reasonable than that obtained from previous work.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2002년도 가을 학술발표회 논문집
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• pp.271-278
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• 2002

Structural optimization using improved higer-order convex approximation is proposed in this paper. The proposed method is a generalization of the convex approximation method. The order of the approximation function for each constraint is automatically adjusted in the optimization process. And also the order of each design variable is differently adjusted. This self-adjusted capability makes the approximate constraint values conservative enough to maintain the optimum design point of the approximate problem in feasible region. The efficiency of proposed algorithm, compared with conventional algorithm is successfully demonstrated in the Three-bar Truss example.

• 콘크리트학회논문집
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• 제20권5호
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• pp.627-634
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• 2008

이 연구에서는 한정된 데이터베이스를 바탕으로 콘크리트 물성 예측 모델을 만들어 최적 배합을 구할 때, 탐색 범위를 한정된 데이터베이스로 제안함으로써 보다 신뢰성 있는 콘크리트 배합을 제시할 수 있는 기법을 제안하였다. 제안한 기법은 각 구성 재료의 가능한 모든 영역을 포함하는 데이터베이스를 구축하지 않고 최적화 과정에서 탐색 범위를 한정된 데이터베이스로 제안함으로써 콘크리트 물성 예측 모델이 신뢰성을 확보할 수 있게 된다. 이 연구에서 이러한 영역을 유효영역으로 정의 하였다. 제안한 기법은 유전자 알고리즘, 인공신경회로망, 그리고 최소 볼록 집합을 이용하여 구현하였으며, 이 방법의 타당성을 검증하기 위하여 주어진 강도 조건을 만족하면서 최저의 가격으로 제조할 수 있는 배합을 찾는 최적화 문제에 적용하였으며 검증 실험을 수행하였다. 실험 결과 데이터베이스의 영역 특성을 반영하는 제안한 기법을 통하여 보다 정확하고 신뢰성 있는 최적 배합을 찾을 수 있음을 확인하였다.