Surface design using locally interpolating subdivision schemes

Non-uniform multivariate subdivision schemes art constructed, which generate limit functions interpolating some of the initial control points. Our schemes differ from the known interpolatory subdivision schemes, in that only some of the original control paints are interpolated, and not the control points in every level. These new schemes are combinations of a non-interpolatory schemes with different local schemer near some of the original control points. They generate smooth surfaces interpolating given points, using stencils of small support. Next, it is shown how to modify known subdivision schemer so that the limit surfaces generated by them interpolate given normal vectors at given interpolation points. (C) 2000 Academic Press.