• Journal of the Korean Mathematical Society
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• v.44 no.6
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• pp.1373-1381
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• 2007

In this paper, we establish an equivalence form of the Brunn-Minkowski inequality for volume differences. As an application, we obtain a general and strengthened form of the dual $Kneser-S\ddot{u}ss$ inequality.

• Journal of the Korean Mathematical Society
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• v.43 no.3
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• pp.593-607
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• 2006

In this paper, we study the properties of the dual harmonic quermassintegrals systematically and establish some inequalities for the dual harmonic quermassintegrals, such as the Minkowski inequality, the Brunn-Minkowski inequality, the Blaschke-Santalo inequality and the Bieberbach inequality.

• Bulletin of the Korean Mathematical Society
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• v.52 no.2
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• pp.453-465
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• 2015

In this paper we establish general Minkowski inequality, Aleksandrov-Fenchel inequality and Brunn-Minkowski inequality for polars of mixed complex projection bodies.

• The Journal of Korea Robotics Society
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• v.17 no.3
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• pp.359-364
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• 2022

This study presents a nonlinear model predictive control (NMPC)-based obstacle avoidance and whole-body motion planning method for the mobile manipulators. For the whole-body motion control, the mobile manipulator with an omnidirectional mobile base was modeled as a nine degrees-of-freedom (DoFs) serial open chain with the PPR (base) plus 6R (arm) joints, and a swept sphere volume (SSV) was applied to define a convex hull for collision avoidance. The proposed receding horizon control scheme can generate a trajectory to track the end-effector pose while avoiding the self-collision and obstacle in the task space. The proposed method could be calculated using an interior-point (IP) method solver with 100[ms] sampling time and ten samples of horizon size, and the validation of the method was conducted in the environment of Pybullet simulation.

• The Journal of Korea Institute of Information, Electronics, and Communication Technology
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• v.10 no.6
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• pp.545-551
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• 2017

It is very important to effectively obtain the information related to the human body shape for user-centered design. The human body shape is a huge combination of various irregular curves and is typically obtained by a 3-D Scanner. 3-D scanners show high reliability; however, they are expnsive equipment with limited mobility. 3-D models of irregular-shaped curves were created by a photogrammetric approach and the errors between the original curve and the models were evaluated. 3-D models were created based on 160, 80, 40, 20, 10, and 5 marking points evenly located on the original curve. In the case of convex curve, low levels of residuals were observed in the models from 160, 80, 40, and 20 marking points (0.13% max). In the combination of convex and concave curves, relatively low levels of residuals were observed in the models from 160, 80, and 40 marking points (0.29%). It is possible to conclude that marking points should be placed at every 5% of overall length of a convex curve and at every 2.5% of overall length of a curve with convex and concave curve in order to maintain low levels of errors. A photogrammetric approach can be used as an alternative for the 3-D scanners with advantages of low cost and mobility.

• Transactions of the Korean Society of Mechanical Engineers
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• v.14 no.1
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• pp.189-196
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• 1990

In the present study, a new method of generating boundary-fitted coordinates systems controlled by control function is introduced. Application of the method to a three-dimensional simply-connected region is the demonstrated. The numerical grid generation has following feat ures, (a) The generated boundary fitted coordinates is well concentrated in near wall region and satisfied orthogonality, (b) The grid control function is fully automatic and well controlled in sharp convex boundary.

• Bulletin of the Korean Mathematical Society
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• v.47 no.5
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• pp.1011-1023
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• 2010

In this paper we define the $L_p$-mixed curvature function of a convex body. We develop a formula connection the support function of $L_p$-mixed projection body with Fourier transform of the $L_p$-mixed curvature function. Using this formula we solve an analog of the Shephard projection problem for $L_p$-mixed projection bodies.

• Animal Systematics, Evolution and Diversity
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• v.31 no.4
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• pp.277-283
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• 2015

Two pleurostomatid ciliates, Loxophyllum perihoplophorum Buddenbrock, 1920 and L. rostratum Cohn, 1866, were collected from the coastal waters of the East Sea, Korea. Their morphologies are described based on live observation and protargol staining, and morphometrics are provided. Loxophyllum perihoplophorum is characterized by the following features: 200-650 μm long in vivo; body slender leaf-shaped, flexible and contractile, with thin and wide extrusome-belted zone; 2 macronuclear nodules (Ma) and 1 micronucleus (Mi); 7-9 contractile vacuoles (CV) positioned along dorsal margin; extrusomes (Ex) evenly distributed along edge of entire body, with about 10 dorsal warts (Wa); 9-11 left (LSK) and 19-22 right somatic kineties (RSK), 4-5 furrows (Fu) on left side. Loxophyllum rostratum is about 100-130 μm long in vivo; body oblate leaf-shaped, contractile, convex ventral side and S-shaped dorsal side, beak-like anterior end; 2 Ma and 1 Mi; 1 CV terminally located; Ex distributed along edge of entire body, with about 9-10 dorsal Wa; 7-8 LSK and 15-19 RSK, ca. 5 Fu on left body side. In addition, sequences of small subunit ribosomal DNA were determined from these two Loxophyllum species and compared with the known Loxophyllum sequences.

• 한국HCI학회:학술대회논문집
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• 2007.02c
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• pp.326-333
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• 2007

To simulate solid dynamics,a we must com-pute the mass, the center of mass, and the products of inertia about the axes of the body of interest. These mass property computations must be continuously re-peated for certain simulations with rigid bodies or as the shape of the body changes. We introduce a GPU-friendly algorithm to approximate the mass properties for an arbitrarily shaped body. Our algorithm converts the necessary volume integrals into surface integrals on a projected plane. It then maps the plane into a frame-buffer in order to perform the surface integrals rapidly on the GPU. To deal with non-convex shapes, we use a depth-peeling algorithm. Our approach is image-based; hence, it is not restricted by the mathematical or geometric representation of the body, which means that it can efficiently compute the mass properties of any object that can be rendered on the graphics hardware. We compare the speed and accuracy of our algorithm with an analytic algorithm, and demonstrate it in a hydrostatic buoyancy simulation for real-time applications, such as interactive games.

• Fashion & Textile Research Journal
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• v.12 no.4
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• pp.467-476
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• 2010

The purpose of this study was to develop a plausible methodology based on experimental data how to set up darts and split lines on 3D parametric body dressed with tight-fit garment. The results were as following: Through the process of making convex hull, the concave parts were straightened to make a convex hull, especially in the center part of bust, under breast part and scapular part. To figure out the optimum positions of darts and split lines, the inflection points of curve ratio were searched along the horizontal polylines of waist and bust. This procedures produced reliable results with low deviation. Using Rapidform, CATIA and Unigraphics, six patches of bodice patterns were drawn and aligned. Paired t-test results showed the outline and area between 3D surface and 2D were not significantly different, meaning this method could be adaptable when flattening 3D surfaces. The amount of waist dart measured on the pattern showed that the highest portion was allocated on 2nd dart(back), followed by 1st dart(back), 1st dart(front), 2nd dart(front)/side dart, and center back dart. A series of findings suggested that curve ration inflection point could be used as a guide to set up darts and split line on 3D parametric model with low deviation.