• 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.

• International Journal of Precision Engineering and Manufacturing
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• v.8 no.1
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• pp.3-10
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• 2007

A new approach based on implicit surface interpolation combined with domain decomposition is proposed for filling complex-shaped holes in a large polygon model, A surface was constructed by creating a smooth implicit surface from an incomplete polygon model through which the actual surface would pass. The implicit surface was defined by a radial basis function, which is a continuous scalar-value function over the domain $R^{3}$. The generated surface consisted of the set of all points at which this scalar function is zero. It was created by placing zero-valued constraints at the vertices of the polygon model. The well-known domain decomposition method was used to treat the large polygon model. The global domain of interest was divided into smaller domains in which the problem could be solved locally. The LU decomposition method was used to solve the set of small local problems; the local solutions were then combined using weighting coefficients to obtain a global solution. The validity of this new approach was demonstrated by using it to fill various holes in large and complex polygon models with arbitrary topologies.

• Korean Journal of Computational Design and Engineering
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• v.12 no.3
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• pp.220-232
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• 2007

Current geometric modeling and analysis are commonly based on B-Rep modeling and a finite elements method respectively. Furthermore, it is difficult to represent an object whose material property is heterogeneous using the B-Rep method because the B-Rep is basically used for homogeneous models. In addition, meshes are required to analyze a property of a model when the finite elements method is applied. However, the process of generating meshes from B-Rep is cumbersome and sometimes difficult especially when the model is deformed as time goes by because the topology of deforming meshes are changed. To overcome those problems in modeling and analysis including homogeneous and heterogeneous materials, we suggest a unified modeling and analysis method based on implicit representation of the model using R-function which is suggested by Rvachev. For implicit modeling of an object a distance field is approximated and blended for a complex object. Using the implicit function mesh-free analysis is possible where meshes are not necessary. Generally mesh-free analysis requires heavy computational cost compared to a finite elements method. To improve the computing time of function evaluation, we utilize GPU programming. Finally, we give an example of a simple pipe design problem and show modeling and analysis process using our unified modeling and analysis method.

• Journal of the Korean Society for Precision Engineering
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• v.24 no.11
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• pp.144-153
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• 2007

In order to generate the input data for rapid prototyping, a new approach which is based on the implicit surface interpolation method is presented. In the method a surface is reconstructed by creating smooth implicit surface from unorganized cloud of points through which the surface should pass. In the method an implicit surface is defined by the adaptive local shape functions including quadratic polynomial function, cubic polynomial function and RBF(Radial Basis Function). By the reconstruction of a surface, various types of error in raw STL file including degenerated triangles, undesirable holes with complex shapes and overlaps between triangles can be eliminated automatically. In order to get the slicing data for rapid prototyping an efficient intersection algorithm between implicit surface and plane is developed. For the direct usage for rapid prototyping, a robust transformation algorithm for the generation of complete STL data of solid type is also suggested.

• 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.

• Journal of applied mathematics & informatics
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• v.26 no.3_4
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• pp.591-603
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• 2008

We employ the notion of implicit functions to prove a general common fixed point theorem in fuzzy metric spaces besides adopting the idea of R-weak commutativity of type (P) in fuzzy setting. In process, several previously known results are deduced as special cases to our main result.

• 제어로봇시스템학회:학술대회논문집
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• 1992.10a
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• pp.686-691
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• 1992

Implicit guidance algorithm can deal with the trajectory error rapidly, but it has to save much data. If, however, the control variable is represented by a specific function form, a few parameters will suffice to define the control variable. In this paper, we study the method of updating the parameters of the control function for the reduction of trajectory errors. The method proposed here does not require much memory for guidance.

• Journal of the Korean Institute of Intelligent Systems
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• v.25 no.4
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• pp.412-417
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• 2015

Kinect sensor has two output data which are produced from red green blue (RGB) sensor and depth sensor, it is called color image and depth map, respectively. Although this device's prices are cheapest than the other devices for three-dimensional (3D) reconstruction, we need extra work for reconstruct a smooth 3D data and also have semantic meaning. It happened because the depth map, which has been produced from depth sensor usually have a coarse and empty value. Consequently, it can be make artifact and holes on the surface, when we reconstruct it to 3D directly. In this paper, we present a method for solving this problem by using implicit surface representation. The key idea for represent implicit surface is by using radial basis function (RBF) and to avoid the trivial solution that the implicit function is zero everywhere, we need to defined on-surface point and off-surface point. Based on our simulation results using captured face as an input, we can produce smooth 3D face and fill the holes on the 3D face surface, since RBF is good for interpolation and holes filling. Modified anisotropic diffusion is used to produced smoothed surface.

• Bulletin of the Korean Mathematical Society
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• v.40 no.2
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• pp.289-300
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• 2003

We prove a simplified version of the Nash-Moser implicit function theorem in weighted Banach spaces. We relax the conditions so that the linearized equation has an approximate inverse in different weighted Banach spaces in each recurrence step.

• Journal of the Korean Society for Precision Engineering
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• v.23 no.9 s.186
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• pp.200-207
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• 2006

In this paper a new approach which combines implicit surface scheme and NURBS surface interpolation method is proposed in order to generate a complete surface model from unorganized point cloud data. In the method a base surface was generated by creating smooth implicit surface from the input point cloud data through which the actual surface would pass. The implicit surface was defined by a combination of shape functions including quadratic polynomial function, cubic polynomial functions and radial basis function using adaptive domain decomposition method. In this paper voxel data which can be extracted easily from the base implicit surface were used in order to generate rectangular net with good quality using the normal projection and smoothing scheme. After generating the interior points and tangential vectors in each rectangular region considering the required accuracy, the NURBS surface were constructed by interpolating the rectangular array of points using boundary tangential vectors which assure C$^1$ continuity between rectangular patches. The validity and effectiveness of this new approach was demonstrated by performing numerical experiments for the various types of point cloud data.