# WIP: Cross field solver

Quadrilateral mesh generation using a cross/guiding field. For more details on the methodology, see `Marcon, J., Kopriva, D. A., Sherwin, S. J., & Peiró, J. (2019). A high resolution PDE approach to quadrilateral mesh generation. Journal of Computational Physics, 399C, 108918. https://doi.org/10.1016/j.jcp.2019.108918`

. The process has 4 main steps:

- Generation in NekMesh of a triangular mesh as base for the cross/guiding field solution. At the same time, we export the list of geometry vertices, needed later to trace streamlines.
- Solution of the cross/guiding field equations. This is done using a modified Laplace solve (in the ADR solver), which overwrites the BC based on the geometrical orientation of the boundaries.
- Processing of the field in FieldConvert, comprising 6 steps: import of geometry vertices; location of interior singularities; calculation of the valence of all vertices and singularities; tracing of streamlines; optional manipulation/merging of streamlines; export of streamlines.
- Generation of the quad mesh in NekMesh, compising 5 steps: re-import of the initial geometry; import of streamlines and splining; split of the geometry using the streamlines; trivial meshing of the multi-surface geometry using 1 quad each; optional splitting of the quad mesh using the isoparametric approach. These 4 steps are reflected in 4 regression tests in the appropriate parts of the code.