A heuristic offsetting scheme for Catmull-Clark subdivision surfaces

In rapid prototyping, a hollowed prototype is preferred and significantly reduces the building time and material consumption in contrast to a solid model. Most rapid prototyping obtains solid thin shell by gradually adding or solidifying materials layer by layer. This is a non-trivial problem to offset a solid which involves finding all self-intersections and filling gaps after raw offsetting. While Catmull-Clark subdivision (CCS) surfaces are widely used in solid modeling, the hollow solid/thin shell problems are not well addressed yet. In this paper, we explore earlier methods of obtaining thin shell CCS solid and present a new thin solid approach. With this new scheme, one can efficiently avoid creases and handle gaps. The new scheme is heuristic, but inner surface is parametric, so computation of the inner surface is simplified. And with offsetting Bezier crust applied, the inner surface maintains the mesh structure and continuity of the outer surface. The obtained thin shell solid is C² continuous everywhere, except at extraordinary points, where it is C¹ continuous.