  A novel algorithm that produces a quad layout based on imposed set of
singularities is proposed. In this paper, we either use singularities that
appear naturally, e.g., by minimizing Ginzburg-Landau energy, or use as an
input user-defined singularity pattern, possibly with high valence
singularities that do not appear naturally in cross-field computations. The
first contribution of the paper is the development of a formulation that allows
computing a cross-field from a given set of singularities through the
resolution of two linear PDEs. A specific mesh refinement is applied at the
vicinity of singularities to accommodate the large gradients of cross
directions that appear in the vicinity of singularities of high valence. The
second contribution of the paper is a correction scheme that repairs limit
cycles and/or non-quadrilateral patches. Finally, a high quality
block-structured quad mesh is generated from the quad layout and per-partition
parameterization.
