• Honam Mathematical Journal
• /
• v.27 no.3
• /
• pp.465-476
• /
• 2005

In this article, we solve some kinds of non-compact Douglas-Plateau problem for two convex curves in parallel planes.

• Journal of applied mathematics & informatics
• /
• v.23 no.1_2
• /
• pp.397-410
• /
• 2007

Visualization of 2D and 3D data, which arises from some scientific phenomena, physical model or mathematical formula, in the form of curve or surface view is one of the important topics in Computer Graphics. The problem gets critically important when data possesses some inherent shape feature. For example, it may have positive feature in one instance and monotone in the other. This paper is concerned with the solution of similar problems when data has convex shape and its visualization is required to have similar inherent features to that of data. A rational cubic function [5] has been used for the review of visualization of 2D data. After that it has been generalized for the visualization of 3D data. Moreover, simple sufficient constraints are made on the free parameters in the description of rational bicubic functions to visualize the 3D convex data in the view of convex surfaces.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.16 no.2
• /
• pp.302-312
• /
• 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 KSME Conference
• /
• 2001.06d
• /
• pp.447-452
• /
• 2001

Quenching phenomena of hemispherical downward facing convex surfaces with narrow gaps have been investigated experimentally. Experiments employed test sections having 1 and 2 mm in gap thickness and 1 atm in system pressure. From interpretations of the temperature and the heat flux history, it was found that the flooding inside the gap was restricted by CCFL phenomena and quenching process was propagated from lower to upper region of the internal copper shell. The ratio of the maximum heat fluxes at 1 mm to 2mm in gap thickness was the almost same that obtained by steady state experiments. The quenching scenario of the hemispherical downward facing surface with narrow gap has been suggested.

• Journal of the Korean Society for Precision Engineering
• /
• v.17 no.2
• /
• pp.73-79
• /
• 2000

The part-surface of mold or stamping-dies consists of a compound surface which consists of lots of composite surfaces, and may have various types of feature shapes including convex sharp edge (CSE). Those CSE features should be considered with care in machining the surface, which necessitates extraction of CSE curves on a compound surface. This work can be done rather easily for a solid model which has a complete topology information. In case of the compound surface without topology information, however, such CSE curves must be gathered through some geometrical calculations paying much computation time. In the paper, extracting CSE curves by the construction of a CSE region-map which can reduce time, and detecting various common edge types are presented.

• Journal of the Korean Mathematical Society
• /
• v.33 no.4
• /
• pp.1139-1171
• /
• 1996

The purpose of our research is to understand geometric and topological aspects of real projective structures on surfaces. A real projective surface is a differentiable surface with an atlas of charts to $RP^2$ such that transition functions are restrictions of projective automorphisms of $RP^2$. Since such an atlas lifts projective geometry on $RP^2$ to the surface locally and consistently, one can study the global projective geometry of surfaces.

• 제어로봇시스템학회:학술대회논문집
• /
• 2005.06a
• /
• pp.314-319
• /
• 2005

When a robot navigates in the real environment, it frequently meets various environments that can be expressed by simple geometrical shapes such as fiat floor, uneven floor, floor with obstacles, slopes, concave or convex corners, etc. Among them, the convex corner composed of two plain surfaces is the most difficult one for the robot to negotiate. In this paper, we propose a gait planning algorithm to help the robot overcome the convex environment. The trajectory of the body is derived from the maximum distance between the edge boundary of the corner and the bottom of the robot when it travels in the convex environment. Additionally, we find the relation between kinematical structure of the robot and its ability of avoiding collision. The relation is realized by considering the workspace and the best posture of the robot in the convex structure. To provide necessary information for the algorithm, we use an IR sensor attached in the leg of the robot to perceive the convex environment. The validity of the gait planning algorithm is verified through simulations and the performance is demonstrated using a quadruped walking robot, called "MRWALLSPECT III"( Multifunctional Robot for WALL inSPECTion version 3).

• Journal for History of Mathematics
• /
• v.20 no.4
• /
• pp.49-60
• /
• 2007

In this article, the concept of rigidity of smooth surfaces in the three dimensional Euclidean space which naturally arises in elementary geometry is introduced, and the natural process of the development of rigidity theory for compact surfaces and its generalizations are investigated.

• Korean Journal of Optics and Photonics
• /
• v.4 no.4
• /
• pp.390-396
• /
• 1993

When a one-dimensional telecentric paraxial holographic kinoform is used as a Fourier transform lens, we analyzed three surface-relief structures, i.e., plano-convex, convex-plano and biconvex shapes, employing exact raytracing method based on Snell's law. For the kinoform of E/8 and focal length of 15 mm, the number of zones, the thickness, and the slope of parabolic surfaces are varied by changing the refractive indicies of kinoform material and surrounding medium. It is found that biconvex shape gives the best results in general, although off-axis performance degrades in all cases as the slope of parabolic surfaces increases.

• Journal of the Korean Society for Precision Engineering
• /
• v.25 no.7
• /
• pp.103-110
• /
• 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.