2006-2009 Jean-Marie Favreau
Decomposing surfaces into quadrangle regions is a relevant issue both from a theoretical and an applicative point of view, and specific approaches have been described and applied in several domains. Control over the tiling topology and tile size and number is important as these factors highly influence the applicability, performance and use of the resulting quadrangulation. In this work, we describe an original approach to tile a surface with large quadrangles, satisfying combinatorial, geometrical and topological constraints. The large tiles resulting from our cutting process can be easily fitted by NURBS because of the properties of this decomposition. The topological control is managed through the critical points of a scalar function defined on the surface, and the cutting paths are not necesserily following the original mesh edges. These two specificities ensure that our approach is highly adjustable, and can include manual or automatic adjustements by modifying the scalar function. Results are presented, assessed and tested w.r.t. robustness and stability.