Interpolating meshes of boundary intersecting curves by subdivision surfaces

Given a polyhedral network with a set of tagged control polygons, a subdivision surface that smoothly interpolates the curves of these control polygons can be generated. The idea consists of constructing a set of polygonal complexes, one for each tagged control polygon, on the original or its subdivided network. This paper descibes how to construct such complexes to interpolate meshes of curves intersecting at the boundary of a surface, such as a boundary curve intersecting an interior curve or another one. The method can also be used to generate subdivision surfaces through arbitrary meshes of curves with C-0 (creases) or C-1 continuity across the interpolated curves.