Quadrilateral Mesh of Non-simply Connected Domain and Non-planar Surfaces From a Given Cross-Field

In this paper, we present a method for constructing a quad mesh from an initial cross-field given by the user. The idea of this approach is to provide a framework to process any cross-field in order to generate a quad mesh and thus benefit from the properties of the field in the resulting mesh. With this point of view, we handle the case of non-simply connected domains and we also address the notion of singular point placement on the edge, which allows us to handle geometries of arbitrary index. Finally, we give an extension of the method to non-planar surface manifolds.