A new cross subdivision scheme for surface design

In this paper, a new primal approximation -subdivision scheme for surface design, being named the cross scheme or C-scheme for short, is presented. The C²-continuity of the C-scheme is mathematically analyzed. The new scheme can be effectively applied to any 3D mesh of quadrilaterals. Extraordinary vertices and miscellaneous boundary scenarios are handled as well. Extensive implementation shows that it performs better than the classical Catmull-Clark subdivision scheme both at nearby vertices and along the non-vertical and non-horizontal directions.