• The Pure and Applied Mathematics
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• v.5 no.2
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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.

• Journal of the Korean Society for Precision Engineering
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• v.25 no.7
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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.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.18 no.8
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• pp.1931-1940
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• 2014

In this paper, we propose a new hand shape recognition algorithm based on the geometric features using the convex-hull from the depth image acquired by Kinect system. Kinect is a camera providing a depth image and user's skeleton information and used for detecting hand region. In the proposed algorithm, hand region is detected in a depth image acquired by Kinect and convex-hull of the region is found. Boundary points caused by noise and unnecessary points for recognition are eliminated in the convex-hull that changes depending on hand shape. Hand shape is recognized by the sum of internal angle of a polygon that is matched with convex-hull reconstructed with selected boundary points. Through experiments, we confirm that proposed algorithm shows high recognition rate not only for five models but also those cases rotated.

• Journal of Institute of Control, Robotics and Systems
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• v.15 no.1
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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.

• Journal of the Korean Mathematical Society
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• v.36 no.6
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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.

• Bulletin of the Korean Mathematical Society
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• v.60 no.4
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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.

• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.2
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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

• Proceedings of the Korea Concrete Institute Conference
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• 2006.11a
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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.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2002.10a
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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.

• Journal of the Korea Concrete Institute
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• v.20 no.5
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• pp.627-634
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• 2008

This paper presents an optimum mixture design method for proportioning a concrete. In the proposed method, the search space is constrained as the domain defined by the minimal convex region of a database, instead of the available range of each component and the ratio composed of several components. The model for defining the search space which is expressed by the effective region is proposed. The effective region model evaluates whether a mix-proportion is effective on processing for optimization, yielding highly reliable results. Three concepts are adopted to realize the proposed methodology: A genetic algorithm for the optimization; an artificial neural network for predicting material properties; and a convex hull for evaluating the effective region. And then, it was applied to an optimization problem wherein the minimum cost should be obtained under a given strength requirement. Experimental test results show that the mix-proportion obtained from the proposed methodology using convex hulls is found to be more accurate and feasible than that obtained from a general optimum technique that does not consider this aspect.