During the visit, several potential research directions have been analyzed in the context of the activities of AIM@SHAPE’s Task 6.2 (Geometry processing for the semantics). Besides the scientific aspects, research areas have been evaluated also considering the added-value provided by an active collaboration between the two institutions.

In this sense, thorough discussions made the two partners conclude that IMATI’s expertise on greedy mesh simplification could be fruitfully combined with INRIA’s expertise on surface approximation. Open issues in the field of subdivision surface modeling have been explored, and it turned out that combining greedy approaches and surface approximation methods may help in achieving efficient solutions to the Reverse Subdivision problem, also referred to as subdivision surface fitting. This problem may be formalized as follows:

Given a mesh subdivision scheme and an input shape S given as a dense mesh, an implicit function or a parametric surface, we propose to explore the problem of automatically generating a coarse control mesh whose limit subdivision surface (with respect to the subdivision scheme) best approximates S. “Best” herein means to minimize a given error metric carefully chosen for the targeted application. Ultimately one seeks an approximation scheme flexible enough to take as input the error metric, as well as the type of mesh (triangular, quadrangular, mixed, or polygonal).

An efficient computational solution to the Reverse Subdivision problem is hard to define, and existing techniques are rather expensive in terms of computational costs and do not provide satisfactory guarantees on the quality of the approximation. On the other hand, finding efficient solutions is of broad interest, hence the Reverse Subdivision problem became part of AIM@SHAPE’s Joint Programme of Activity for the second 18 months.