• Journal of Korea Multimedia Society
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• v.19 no.11
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• pp.1900-1908
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• 2016

Recent times have seen the introduction of modeling technologies using implicit surface and marching cubes algorithm in the field of computer graphics. Implicit surface modeling is used to express characters or fluid. This study presents a calculation method for the density of curve skeletal primitives using parametric curve and implements an implicit surface modeling tool by utilizing Maya API. Skeletal primitives can be assembled and utilized in character modeling using the implemented modeling tool. Results could be obtained more effectively compared to existing particle-based methods.

• Bulletin of the Korean Mathematical Society
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• v.44 no.1
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• pp.13-29
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• 2007

In this paper, we first present a method for finding the implicit equation of the curve given by rational parametric equations. The method is based on the computation of $Gr\"{o}bner$ bases. Then, another method for implicitization of curve and surface is given. In the case of rational curves, the method proceeds via giving the implicit polynomial f with indeterminate coefficients, substituting the rational expressions for the given curve and surface into the implicit polynomial to yield a rational expression $\frac{g}{h}$ in the parameters. Equating coefficients of g in terms of parameters to 0 to get a system of linear equations in the indeterminate coefficients of polynomial f, and finally solving the linear system, we get all the coefficients of f, and thus we obtain the corresponding implicit equation. In the case of polynomial surfaces, we can similarly as in the case of rational curves obtain its implicit equation. This method is based on characteristic set theory. Some examples will show that our methods are efficient.

• Journal of the Korean Society for Precision Engineering
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• v.22 no.3 s.168
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• pp.107-114
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• 2005

A new approach which combines implicit surface scheme and point projection method is presented in order to fill the arbitrarily shaped holes in the polygon model. In the method a trimmed surface which has an outer boundary curve is generated by using the implicit surface scheme and normal projection of point onto the base surface. The base surface is constructed by creating smooth implicit surface from the incomplete polygon model through which the surface should pass. In this paper an implicit surface is defined by a radial basis function, a continuous scalar-valued function over the domain $R^3$. The base surface is the set of all points at which this scalar function takes on the value zero and is created by placing zero-valued constraints at the vertices of the polygon model. In order to show the validity of the present study, various hole fillings are carried out for the complex polygon model of arbitrary topology.

• Journal of the Korean Society for Precision Engineering
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• v.23 no.9 s.186
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• pp.190-199
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• 2006

A new approach which combines implicit surface scheme and recursive subdivision method is suggested in order to fill the holes with complex shapes in the polygon model. In the method, a base surface is constructed by creating smooth implicit surface from the points selected in the neighborhood of holes. In order to assure C$^1$ continuity between the newly generated surface and the original polygon model, offset points of same number as the selected points are used as the augmented constraint conditions in the calculation of implicit surface. In this paper the well-known recursive subdivision method is used in order to generate the triangular net with good quality using the hole boundary curve and generated base implicit surface. An efficient anisotropic smoothing algorithm is introduced to eliminate the unwanted noise data and improve the quality of polygon model. The effectiveness and validity of the proposed method are demonstrated by performing numerical experiments for the various types of holes and polygon model.

• Journal of the Korea Computer Graphics Society
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• v.2 no.1
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• pp.31-38
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• 1996

Many efforts for finding smooth curves and surfaces satisfying given constraints have been made, and interpolation and approximation theories with the help of computers have played an important role in this endeavour. Most research in curve and surface modeling has been largely dominated by the theory of parametric representations. While they have been successfully used in representing physical objects, parametric surfaces are confronted with some problems when objects are represented and manipulated in geometric modeling systems. In recent year, increasing attention has been paid to implicit algebraic surfaces since they are often more effective than parametric surfaces are. In this paper, we summarize the geometric properties and computational processes of objects represented using implicit algebraic functions and explain of the implementation of design tools which can design curves and surfaces of revolution. These surfaces of revolution are played an importance role in effective areas such as CAD and CAM.

• Transactions of Materials Processing
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• v.9 no.6
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• pp.590-597
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• 2000

A finite element formulation lot the simulation of axisymmetric sheet hydroforming is proposed, and an implicit program is coded. In order to describe normal anisotropy of steel sheet, Hill's non-quadratic yield function (Hill, 1979) is employed. Frictional contacts among sheet surface, rigid tool surface, and flexible hydrostatic pressure are considered using mesh normal vectors based on finite element of the sheet. Applied hydraulic pressure is also considered as a function of forming rate and time and treated as an external loading. The complete set of the governing relations comprising equilibrium and interfacial equations is approximately linearized for Newton-Raphson algorithm. In order to verify the validity of the developed finite element formulation, the axisymmetric bulge test is simulated. Simulation results are compared with other FEM results and experimental measurements and showed good agreements. In axisymmetric hydroforming processes of a disk cover, formability changes are observed according to the hydraulic pressure curve changes.

• Applied Biological Chemistry
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• v.43 no.2
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• pp.116-123
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• 2000

A numerical model of three-dimensional soil water distribution for drip irrigation management under cropped conditions was developed using Richards equation in Cartesian coordinates. The model accounts for both seasonal and diurnal changes in evaporation and transpiration, and the growth of plant root and the shape of root zone. Solutions were numerically approximated using the Crank-Nicolson implicit finite difference technique on the block-centered grid system and the Gauss-Seidel elimination in tandem. The model was tested under several conditions to allow the flow rates and configurations of drip emitters vary. In general, simulation results agreed well with experimental results and were as follows. The velocity of soil-water flow decreased drastically with distance from the drip source, and the rate of expansion of the wetted zone decreased rapidly during irrigation. The wetting front of wetted zone from a surface drip emitter traveled farther in vertical direction than in horizontal direction. Under this experimental weather condition, water use efficiency of a drip-irrigated apple field was greatest for 4-drip-emitter system buried at 25 cm, resulting from 10% increase in transpiration but 20% reduction in soil evaporation compared to those for surface 1-drip emitter system. Soil moisture retention curve obtained using disk tension infiltrometer showed significant difference from the curve obtained with pressure plate extractor.