Blending based corner cutting subdivision scheme for nets of curves

We present a new subdivision scheme (BCC-algorithm) for constructing a surface from an initial net of 3D curves, by repeated refinements of nets of curves. This algorithm improves a subdivision scheme for nets of curves (BC-algorithm), proposed in a previous paper, which generalizes the well known Chaikin subdivision scheme refining control points. While the BC-algorithm generates continuous surfaces, the BCC-algorithm generates C¹ surfaces. This is achieved by a corner cutting step following each refinement step of the BC-algorithm. The analysis of convergence, smoothness and approximation order of the BCC-algorithm is based on its proximity to the tensor-product Chaikin scheme. A short discussion of boundary rules for the BCC-algorithm is also included. Several numerical examples, illustrating the operation of the BCC-algorithm, with and without boundary rules, are presented. In the examples the advantage of the BCC-algorithm over the tensor-product Chaikin algorithm is evident.