• International Journal of Internet, Broadcasting and Communication
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• v.11 no.1
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• pp.54-59
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• 2019

The parametrization of the surface plays an important role in the 3D computer graphics and computer vision. Especially, it is essential in 3D mesh editing that manipulates the position of 3D objects on a computer monitor. Because computer monitors are two-dimensional, while vertices of objects that actually want to change are in a three-dimensional virtual space. In this study, we propose a new type of parametrization method that takes advantage of the special properties of circles that are common to local parameterization. Experimental results show that our parameterization method is more efficient in terms of time and space than the standard parameterization method that was designed by Floater et al.

• International Journal of CAD/CAM
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• v.6 no.1
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• pp.59-64
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• 2006

A new method to obtain explicit re-parameterization that preserves the curve degree and parametric domain is presented in this paper. The re-parameterization brings a curve very close to the arc length parameterization under $L_2$ norm but with less segmentation. The re-parameterization functions we used are $C^1$ continuous piecewise rational linear functions, which provide more flexibility and can be easily identified by solving a quadratic equation. Based on the outstanding performance of Mobius transformation on modifying pieces with monotonic parametric speed, we first create a partition of the original curve, in which the parametric speed of each segment is of monotonic variation. The values of new parameters corresponding to the subdivision points are specified a priori as the ratio of its cumulative arc length and its total arc length. $C^1$ continuity conditions are imposed to each segment, thus, with respect to the new parameters, the objective function is linear and admits a closed-form optimization. Illustrative examples are also given to assess the performance of our new method.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.25 no.4
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• pp.196-220
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• 2021

This study formulates a new geometric parameterization scheme to effectively address numerical analysis subject to the variation of the fiber radius of a square unit cell. In particular, the proposed mesh-morphing approach may lead to a parameterized weak form whose bilinear and linear forms are affine in the geometric parameter of interest, i.e. the fiber radius. As a result, we may certify the reduced basis analysis of a square unit cell model for any parameters in a predetermined parameter domain with a rigorous a posteriori error bound. To demonstrate the utility of the proposed geometric parameterization, we consider a two-dimensional, steady-state heat conduction analysis dependent on two parameters: a fiber radius and a thermal conductivity. For rapid yet rigorous a posteriori error evaluation, we estimate a lower bound of a coercivity constant via the min-θ method as well as the successive constraint method. Compared to the corresponding finite element analysis, the constructed reduced basis analysis may yield nearly the same solution at a computational speed about 29 times faster on average. In conclusion, the proposed geometric parameterization scheme is conducive for accurate yet efficient reduced basis analysis.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.22 no.3
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• pp.259-265
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• 2009

This paper studies the Element Connectivity Parameterization Method(ECP method) for topology optimization considering dynamic compliance. The previous element density based topology optimization method interpolates Young's modulus with respect to design variables defined in each element for topology optimization. Despite its various applications, these element density based methods suffer from numerical instabilities for nonlinear structure and multiphysics systems. To resolve these instabilities, recently a new numerical method called the Element Connectivity Parameterization(ECP) Method was proposed. Unlike the existing design methods, the ECP method optimizes the connectivities among plane or solid elements and it shows some advantages in topology optimization for both nonlinear structure and multiphysics systems. In this study, the method was expanded for topology optimization for the dynamic compliance by developing a way to model the mass matrix in the framework of the ECP method.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.33 no.8
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• pp.779-785
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• 2009

This paper is concerned with a computational approach for topology optimization of geometrically nonlinear structures following specific load-displacement trajectories. In our previous works, attention was paid to stabilize topology optimization involving large displacement and a method called the element connectivity parameterization was developed. Here, we aimed to extend the element connectivity parameterization method to find an optimal geometrically nonlinear structure yielding a specific load-displacement trajectory. In contrast to designing a stiffest structure, the trajectory design problem requires special consideration in topology optimization formulation and solution procedure. Some numerical problems were considered to test the developed element connectivity parameterization based formulation.

• Atmosphere
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• v.23 no.1
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• pp.39-45
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• 2013

A parameterization for the scattering of longwave radiation by ice clouds has been developed based on spectral scattering property calculations with shapes and sizes of ice crystals. For this parameterization, the size distribution data by Fu (1996) and by Michell and Arnott (1994) are used. The shapes of ice crystal considered in this study are plate, solid column, hollow column, bullet-rosette, droxtal, aggregate, and spheroid. The properties of longwave scattering by ice crystals are presented as a function of the extinction coefficient, single-scattering albedo, and asymmetry factor. The heating rate and flux by the radiative parameterization model are calculated for wide range of ice crystal sizes, shapes, and optical thickness. The results are compared with the calculated results using a six-stream discrete ordinate scattering algorithm and Chou's method. The new method (with various habits and size distributions) provides a good simulation of the scattering properties and cooling rate in optically thin clouds (optical thickness < 5). Depending on the inclusion of scattering by ice clouds, the errors in the calculation of the cooling rates are significantly different.

• Journal of KIISE:Computer Systems and Theory
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• v.34 no.12
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• pp.641-655
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• 2007

Parameterization has been one of very important research subjects in several application areas including computer graphics. In the parameterization research, the problem of mapping 3D polygonal model to 2D plane has been studied frequently, but the previous methods often fail to handle complicated shapes of polygonal surfaces effectively as well as entail distortion between the 3D and 2D spaces. Several attempts have been made especially to reduce such distortion, but they often suffer from the problem when an arbitrary rectangular surface region on 3D model is locally parameterized. In this paper, we propose a new local parameterization scheme based on the projection level set method. This technique generates a series of equi-distanced curves on the surface region of interest, which are then used to generate effective local parameterization information. In this paper, we explain the new technique in detail and show its effectiveness by demonstrating experimental results.

• The Journal of the Korea Contents Association
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• v.10 no.4
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• pp.106-114
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• 2010

Mesh parameterization is the process of finding one-to-one mapping between an input mesh and a parametric domain. It has been considered as a fundamental tool for digital geometric processing which is required to develop several applications of digital geometries. In this paper, we propose a novel 3D volume parameterization by means that a harmonic mapping is established between a 3D volume mesh and a unit solid cube. To do that, we firstly partition the boundary of the given 3D volume mesh into the six different rectangular patches whose adjacencies are topologically identical to those of a surface cube. Based on the partitioning result, we compute the boundary condition as a precondition for computing a volume mesh parameterization. Finally, the volume mesh parameterization with a low-distortion can be accomplished by performing a harmonic mapping, which minimizes the harmonic energy, with satisfying the boundary condition. Experimental results show that our method is efficient enough to compute 3D volume mesh parameterization for several models, each of whose topology is identical to a solid sphere.

• Environmental Sciences Bulletin of The Korean Environmental Sciences Society
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• v.3 no.1
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• pp.41-56
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• 1999

Since UV-B radiation measuring networks have not been established, numerical models which calculate the flux from other readily available meteorological measurements may play an important role. That is, such a problem can be solved by using parameterization models such as two stream approximation, the delta-Eddington method, doubling method, and discrete ordinate method. However, most UV-B radiative transfer models have not been validated with measurements, because such models are not intended as practical computational schemes for providing surface estimates of UV-B radiation. The main concern so far has been to demonstrate model sensitivity for cloudless skies. In particular, few have been concerned with real cloud information. Clouds and aerosols have generally been incorporated as constituents of particular atmospheric layers with specified optical depths and scattering properties. The parameterization model presented here is a combination of a detailed radiative transfer algorithm for a coludless sky radiative process and a more approximate scheme to handle cloud effects. The model input data requires a daily measurement of the total ozone amount plus a daily record of the amount and type of cloud in the atmosphere. Measurements for an examination of the models at the Department of Atmospheric Sciences, Pusan National University have been takenfrom February, 1995. These models can be used to calculate present and future fluxes where measurements have not been taken, and construct climatologies for the period before ozone depletion began.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.48 no.3
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• pp.278-285
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• 1999

This paper utilizes the method of Q-parameterization control to design a controller which solves the problem of imbalance in magnetic bearing systems. There are two methods to solve this problem using feedback controal. The first method is to compensate for the imbalance forces by generating opposing forces on the bearing surface (imbalance compensation). The second method is to make the rotor rotate around its axis of inertia (automatic balancing);in this case no imbalance forces will be generated. In this paper we deal with only imbalance compensation. The free parameter of the Q-parameterization controller is chosen such that these goals are achieved. After the introduction of a model of the magnetic bearing system, we explain the Q-parameterization controller design of the magnetic bearing system with emphasis on the rejection of sinusoidal disturbance for imbalance compensation design. The design objectives are formulated as a linear equations in the controller free paramete Q. Finally, simulation and experimental results are presented and showed the robustness and effectiveness of the proposed controllers.