多重調和関数を用いたモーフィング

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  • Morphing Using Polyharmonic Function

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In this paper, we discuss morphing using a polyharmonic function. A method for creating implicit surfaces is described using a polyharmonic function (radial basis function) to form complex solid models from scattered surface points. The conventional method of constructing CSG model use simple solid primitives. In the presented method, many quite complex solid primitives can be used, because only surface points are used for boundary representation. The presented methods contain the conventional Boolean operations on solids and new Boolean operations for points. This method uses Poisson's equations and a polyharmonic function, which is a type of thin plate function. Thin-plate solution has several problems. The first problem is that O (n2) computations are required to solve the system of equations. The second problem is that a small change in even one constraint affects the entire resulting interpolated surface, because every known point affects the result. However, thin-plate interpolation is often used in computer vision, because surface patch is not necessary. In order to investigate the efficiency of this method, several examples are given.

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