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.
For the more advanced analysis, we are going to undertaking a 3D examination of the forces at play to optimize for compression only. See the following post:
For the more custom solution, dig through the following blog post to find the section on using Kangaroo to analyze compression only structures through catenary curves. We will be looking at something like this as a 2D analysis.
Vault based of aperiodic tiling