Karciauskas, KestutisPeters, JörgAndres, Bjoern and Campen, Marcel and Sedlmair, Michael2021-09-252021-09-252021978-3-03868-161-8https://doi.org/10.2312/vmv.20211371https://diglib.eg.org:443/handle/10.2312/vmv20211371Subdivision surfaces based on bi-quadratic splines have a control net, the DS-net, whose irregularities are n-sided facets. To date their limit shape is poor due to a small footprint of the refinement rules and the difficulty of controlling shape at the center irregularity. By contrast, a control net where vertices are surrounded by n quadrilateral faces, a CC-net, admits higher-quality subdivision and finite polynomial constructions. It would therefore be convenient to leverage these constructions to fill holes in a C1 bi-quadratic spline complex. In principle the switch in layout from a control net with central n-sided facet to one with a central irregular point is easy: just apply one step of Catmull-Clark refinement. The challenge, however, is to define the transition between the bi-quadratic bulk and the n-sided cap construction to be of sufficiently good shape to not destroy the advantage of higher-quality algorithms. This challenge is addressed here by explicit formulas for conversion from a DS-net to a CC-net.10.2312/vmv.2021137155-62