If we treat the center line of our tiled plane as the geodesic on the surface – the part that is ‘straight’ in a higher dimensionality (3D) but ‘curved’ in the lower dimension representation (2D) then ‘straightening’ our centerline can be understood as ‘vaulting’ the geometry in a manner that is analogous to the medieval elevation of the plan, but in a non-Euclidean manner. We talked about this yesterday.
The new bit: How to script this as a method? What I realized last night is that if we keep the angles and side lengths of the Penrose tiles fixed, but allow the degree of curvature to change, we should be able to force an optimization of the plane that becomes three-dimensional. This is good as it is quite easy to change curvature degree in Rhino, and if everything else is constrained we would not need too crazy of a physics model (via Kangaroo) and genetic model (via Galapagos) for optimization purposes.