Recursive subdivision schemes have become one of the most important paradigms to model 3D surfaces of arbitrary topology used in computer graphics applications. A number of researchers, both with a mathematical background and from the computer graphics community, have added - and still are adding - different algorithms and features to further improve their capabilities. This paper described a new modeling tool, providing the possibility to locally choose an interpolating variant of the conventionally approximating Catmull-Clark subdivision scheme. Our approach combines the advantages of approximating schemes with the precise control of interpolating schemes. Unlike other solutions that mostly narrow down to locally change the weighting factors of the subdivision scheme, we keep the underlying uniform scheme intact. Our method is based upon introducing additional control points on well-chosen locations, with optional interactive user control over the tangent plane (or surface normal) and the tension of the surface near the interpolating control points. Although this paper is concentrating on the Catmull-Clark scheme, the proposed techniques can be extended to other subdivision schemes.