Blending Based Chaikin type Subdivision Schemes for Nets of Curves

The paper presents a new subdivision scheme, which constructs a surface approximating a given net of 3D-curves. Similar to the well known Chaikin algorithm for points, having a refinement step based on piecewise linear interpolation of the control points followed by evaluation at 1/4 and 3/4 of the local parameter value, the refinement step in the proposed subdivision scheme is based on piecewise Coons patch interpolation followed by evaluation at 1/4 and 3/4 of the local parameters values in both directions, which results in a refined net of curves. We prove the convergence of the scheme to a continuous surface. The proof is based on the ”proximity” of the scheme to a new, convergent subdivision scheme for points. Some examples, illustrating the performance of our scheme, are given.