  We propose an end-to-end pipeline to robustly generate high-quality,
high-order and coarse quadrilateral meshes on CAD models. This kind of mesh
enables the use of high-order analysis techniques such as high-order finite
element methods or isogeometric analysis. An initial unstructured mesh is
generated; this mesh contains a low number of irregular vertices but these are
not necessarily aligned, causing a very dense quad layout. A T-mesh is built on
the mesh which allows to modify its topology by assigning new integer lengths
to the T-mesh arcs. The task of simplifying the quad layout can be formulated
as an Integer Linear Program which is solved efficiently using an adequate
solver. Finally, a high-order quad mesh is extracted from the optimized
topology. Validation on several CAD models shows that our approach is fast,
robust, strictly respects the CAD features, and achieves interesting results in
terms of coarseness and quality.
