2019 Download
Petras Vestartas, Nicolas Rogeau, Julien Gamerro, Yves Weinand
Modelling Workflow for Segmented Timber Shells using Wood-wood Connections
Design Modelling Symposium (DMS) Berlin 2019.
The planarization is probably the most basic one, when polygon faces are projected to average plane and then their vertices are combined together. This is run several times.
I used this method to planarize extruded mesh edges:
Other method involves tangent plane, when neighbour planes are intersected to computed planar polygon. Which is also constrained to particular geometries (mostly spheres, and negative curvature cases, so flat parts of geometry is always an issue):
I would suggest also to look at Kangaroo2 methods.
I am aware of the paper that you reference, but I doubt there is a close implementation in Rhino.
I believe it is also connected to remeshing and particular geometries. Just look at the naked edges of the geometry shown your figure, they are cut at the border. Meaning there is a surface parametrization to remesh underlying quad patches.
I think @DanielPiker mentioned that hexagons can be represented by two quads so two circles could be inscribed in this hexagon must be planar. There was a lot of discussion on the forum:
There is a general misconception about planarization, that you can put whatever tessellation and solver will give you a planar mesh. It is really connected to underlying curvature and subdivision and often 4 sided nurbs subdivision would not planarize well because the mesh cells are not oriented according to curvature as is described in the paper.
