2012 Volume 7 Pages 2406068
To generate a smooth implicit function that behaves naturally over an entire domain, a method to smoothly combine an implicit function f(x) with a global support function g(x) has been proposed. The proposed method can be applied to large scattered point data, since the implicit function f(x) is generated by a partition-of-unity-based method. The global support function g(x) is generated by a radial basis function-based method or by the least-squares method. To ensure a smooth combination of f(x) and g(x), an appropriate weight function is employed. In numerical experiments, the proposed method is applied to large point data. The results illustrate that the proposed method can generate a smooth implicit function F(x) with natural behavior over the entire domain. In addition, on the given points, the accuracy of F(x) is exactly the same as that of f(x). Furthermore, the computational cost for generation of F(x) is almost the same as that of f(x).
