• Journal of the Korean Society for Precision Engineering
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• v.23 no.1 s.178
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• pp.174-184
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• 2006

In order to fill the holes with complex shapes in the large polygon model, a new approach which is based on the implicit surface interpolation method combined with domain decomposition method is presented. In the present study, a surface is constructed by creating smooth implicit surface from the incomplete polygon model through which the surface should pass. In the method an implicit surface is defined by a radial basis function, a continuous scalar-valued function over the domain $R^3$ The generated 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 this paper the well-known domain decomposition method is used in order to treat the large polygon model. The global domain of interest is divided into smaller domains where the problem can be solved locally. LU decomposition method is used to solve a set of small local problems and their local solutions are combined together using the weighting coefficients to obtain a global solution. In order to show the validity of the present study, various hole fillings are carried out fur the large and complex polygon model of arbitrary topology.

• 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.

• Korean Journal of Computational Design and Engineering
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• v.13 no.3
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• pp.187-199
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• 2008

This paper describes a C++ class hierarchy of implicit objects for geometry modeling and processing. This class structure provides a software kernel for integrating many various models and methods found in current implicit modeling areas. The software kernel includes primitive objects playing a role of unit element in creating a complex shape, and operator objects used to construct more complex shape of implicit object formed with the primitive objects and other operators. In this paper, class descriptions of these objects are provided to better understand the details of the algorithm or implementation, and its instance examples to show the capabilities of the object classes for constructive shape geometry. In addition, solid modeling system shown as an application example demonstrates that the proposed implicit object classes allow us to carry out modern solid modeling techniques, which means they have the capabilities to extend to various applications.

• 한국전산유체공학회:학술대회논문집
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• 1999.11a
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• pp.17-22
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• 1999

Convergence characteristics and efficiency of three implicit approximate factorization schemes(ADI, DDADI and MAF) are examined using 2-Dimensional compressible upwind Navier-Stokes code. Second-order CSCM(Conservative Supra Characteristic Method) upwind flux difference splitting method with Fromm scheme is used for the right-hand side residual evaluation, while generally first-order upwind differencing is used for the implicit operator on the left-hand side. Convergence studies are performed using an example of the flow past a NACA0012 airfoil at steady transonic flow condition, i. e. Mach number 0.8 at $1.25^{\circ}$ angle of attack. The results were compared with other computational results in order to validate the current numerical analysis. The results from the implicit AF algorithms were compared well in low surface with the other computational results; however, not well in upper surface. It might be due to lack of the grid around the shock position. Because the algorithm minimizes the errors of the approximate decomposition, the improved convergence rate with MAF were observed.

• International Journal of CAD/CAM
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• v.8 no.1
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• pp.41-44
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• 2009

This paper describes an implementation of virtual teeth modeling for a haptic dental simulation. The system allows dental students to practice dental procedures with realistic tactual feelings. The system requires fast and stable haptic rendering and volume modeling techniques working on the virtual tooth. In our implementation, a volumetric implicit surface is used for intuitive shape modification without topological constraints and haptic rendering. The volumetric implicit surface is generated from input geometric model by using a closest point transformation algorithm. And for visual rendering, we apply an adaptive polygonization method to convert volumetric teeth model to geometric model. We improve our previous system using new octree design to save memory requirement while increase the performance and visual quality.

• Transactions of Materials Processing
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• v.16 no.7
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• pp.538-548
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• 2007

In this paper, a novel approach which enables rapid die surface modification for sheet metal forming process is proposed. In this method an implicit surface which interpolates a given set of control points and displacement constraints is generated to compute the displacements at arbitrary points located on die surface. The proposed method does not depend on the underlying surface representation type and is affected neither by its complexity nor by its quality. In addition, the domain decomposition method is introduced in order to treat large surface model. The global domain of interest is divided into smaller domains where the problem can be solved locally. And then the local solutions are combined together to obtain a global solution. In order to verify the validity and effectiveness of the proposed method, various surface modifications are carried out fur three kinds of die surface model including polygonal surface composed of triangular and rectangular meshes, polynomial surface and NURBS surface.

• Proceedings of the KSME Conference
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• 2003.04a
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• pp.2005-2011
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• 2003

Introducing the interfacial pressure jump terms based on the surface tension into the momentum equations of two-phase two-fluid model, the system of governing equations is turned mathematically into the hyperbolic system. The eigenvalues of the equation system become always real representing the void wave and the pressure wave propagation speeds as shown in the previous manuscript. To solve the interfacial pressure jump terms with void fraction gradients implicitly, the conventional semi-implicit method should be modified as an intermediate iteration method for void fraction at fractional time step. This advanced semi-implicit method (ASIM) then becomes stable without conventional additive terms. As a consequence, including the interfacial pressure jump terms with the advanced semi-implicit method, the numerical solutions of typical two-phase problems can be more stable and sound than those calculated exclusively by using any other terms like virtual mass, or artificial viscosity.

• The Journal of the Korea Contents Association
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• v.6 no.11
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• pp.135-144
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• 2006

Implicit surface model is convenient for modeling objects composed of complicated surfaces such as characters and liquids. Moreover, it can express various forms of surface using a relatively small amount of data. In addition, it can represent both the surface and the volume of objects. Therefore, the modeling technique can be applied efficiently to deformation of objects and 3D animation. However, the existing implicit primitives are parallel to the axis or symmetrical with respect to the axes. Thus it is not easy to use them in modeling objects with various forms of motions. In this paper, we propose an efficient animation method for modeling various poses of characters according to matching with motion capture data by adding the attribute of rotation to metacube which is one of the implicit primitives.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.29 no.5 s.236
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• pp.609-616
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• 2005

While the SIMPLE algorithm is most widely used for the simulations of flow phenomena that take place in the industrial equipments or the manufacturing processes, it is less adopted for the simulations of the free surface flow. Though the SIMPLE algorithm is free from the limitation of time step, the free surface behavior imposes the restriction on the time step. As a result, the explicit schemes are faster than the implicit scheme in terms of computation time when the same time step is applied to, since the implicit scheme includes the numerical method to solve the simultaneous equations in its procedure. If the computation time of SIMPLE algorithm can be reduced when it is applied to the unsteady free surface flow problems, the calculation can be carried out in the more stable way and, in the design process, the process variables can be controlled based on the more accurate data base. In this study, a modified SIMPLE algorithm is presented fur the free surface flow. The broken water column problem is adopted for the validation of the modified algorithm (MoSIMPLE) and for comparison to the conventional SIMPLE algorithm.

• Journal of the Korean Geotechnical Society
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• v.22 no.9
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• pp.45-59
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• 2006

The successful performance of any numerical geotechnical simulation depends on the accuracy and efficiency of the numerical implementation of constitutive model used to simulate the stress-strain (constitutive) response of the soil. The corner stone of the numerical implementation of constitutive models is the numerical integration of the incremental form of soil-plasticity constitutive equations over a discrete sequence of time steps. In this paper a well known two-surface soil plasticity model is implemented using a generalized implicit return mapping algorithm to arbitrary convex yield surfaces referred to as the Closest-Point-Projection method (CPPM). The two-surface model describes the nonlinear behavior of coarse-grained materials by incorporating a bounding surface concept together with isotropic and kinematic hardening as well as fabric formulation to account for the effect of fabric formation on the unloading response. In the course of investigating the performance of the CPPM integration method, it is proven that the algorithm is an accurate, robust, and efficient integration technique useful in finite element contexts. It is also shown that the algorithm produces a consistent tangent operator $\frac{d\sigma}{d\varepsilon}$ during the iterative process with quadratic convergence rate of the global iteration process.