Interpolating Bézier spline surfaces with local control

This paper presents an approach to construct interpolating spline surfaces over a bivariate network of curves with rectangular patches. Patches of the interpolating spline surface are constructed by means of blending their boundaries with special polynomials. In order to ensure a necessary parametric continuity of the designed surface the polynomials of the corresponding degree are used. The constructed interpolating spline surfaces have local shape control. If the surface frame is determined by means of Bézier curves then patches of the interpolating spline surface are Bézier surfaces.