I was reading this publication: https://core.ac.uk/download/pdf/38060738.pdf
And would like to ask if a planar quad mesh, whose faces have inscribed circles, has all the time principal curvature in u-v directions of such quad mesh ?
The reason for asking this, is that mesh would be planar after creating triangulation (3) , making dual (4) and then intersecting current polygon plane with neighbor ones(5).
Interesting, I’d have to think about it some more.
I notice there are multiple choices for the location of the planes (depending on how you form the dual - barycentric, circumcentric etc), and their normals (since the polygons in step 4 aren’t planar, there are various ways to define a single normal for each one).
I suspect as well that this method might not guarantee the planar hexagons aren’t ever self intersecting, though it looks from your image like it is working well here.