Curve interpolation based on Catmull-Clark subdivision scheme (Q1425343)

The authors propose an algorithm for interpolating cubic \(B\)-splines curves with Catmull-Clark subdivision surfaces, where it is necessary only to guarantee the symmetry of polygons on both sides of the control polygon edges of interpolated curves. The process is convergent and the limit surface is \(C^2\) everywhere except for a finite number of points. Sharp creases can also be modeled on the limit subdivision surface by duplicating the vertices of the tagged edges of the initial mesh.