I'm interested in the subdivision of planar quadrilateral meshes (PQ-Meshes). Meshes consisting only of planar quadrilaterals, like discrete Voss surfaces and alike. I've been searching the web for any existing research/papers on the topic, but haven't been able to come up with anything?

If someone can provide some resources on this matter I would be more than happy. What approaches have been taken to subdivide PQ-Meshes while retaining planarity?