Polar Embedded Catmull-Clark Subdivision Surface

In this paper, a new subdivision scheme for Polar embedded Catmull-Clark mesh structure is presented. The ripple effect commonly found at high-valence extraordinary points of a CCS surface is improved by replacing high-valence CCS extraordinary faces with triangular Polar faces. The new scheme is valence independent and is stationary. By using the same subdivision mask on both the quadrilateral part and the triangular part, artifacts that have been noticed before (mismatching subdivision masks, exponentially increased Valence at Polar extraordinary points by the recursive subdivision process) are resolved. Test results show that with the new scheme, one can generate very high quality, curvature continuous subdivision surfaces on the triangular part. Combined with current CCS G2 schemes, one can generate high quality subdivision surfaces appropriate for most engineering applications on any Polar embedded Catmull-Clark control meshes.