The use of polygonal meshes, especially triangle meshes, is manifold but a lot of algorithms require the mesh to be structured in a certain way and cannot be applied to an arbitrarily shaped mesh. The process of replacing an arbitrary mesh by a structured one is called remeshing. Triangle meshes with subdivision connectivity are an important class of structured meshes and have been studied thoroughly in the past. In this paper we concentrate on another class of regular meshes instead and present a method for replacing an arbitrary triangle mesh by a regular quadrilateral mesh. These kind of meshes can later be used for a very simple and efficient surface reconstruction method with tensor product Bspline surfaces.