• 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.8 s.185
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• pp.89-99
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• 2006

In this paper a new shape reconstruction method that allows us to construct surface models from very large sets of points is presented. In this method the global domain of interest is divided into smaller domains where the problem can be solved locally. These local solutions of subdivided domains are blended together according to weighting coefficients to obtain a global solution using partition of unity function. The suggested approach gives us considerable flexibility in the choice of local shape functions which depend on the local shape complexity and desired accuracy. At each domain, a quadratic polynomial function is created that fits the points in the domain. If the approximation is not accurate enough, other higher order functions including cubic polynomial function and RBF(Radial Basis Function) are used. This adaptive selection of local shape functions offers robust and efficient solution to a great variety of shape reconstruction problems.

• 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.