Improved method generating a free-form surface using integral equations Original Research Article

This paper illustrates a method of generating a free-form surface using the boundary integral equation with the polyharmonic function and the integrated polyharmonic function. This method requires the boundary geometry of a free-form surface and the lines or the points on the free-form surface. The height of the points on the free-form surface is calculated after solving the discretized boundary integral equation. In this paper, the integrated polyharmonic functions are derived. The surface, which is obtained using these functions, is effectively smooth even if lower-order functions are used. In order to investigate the effectiveness of this method, several examples are shown.