Some images of procedural exploration of mapping geometry to the surface.
Initial run of the 3D printed resin models, understanding the construction of the faceted surfaces in compression.
Trying to reconcile the top layer with projected geometry with the bottom layer. This is negotiated here with triangles. Then to determine the relationship they have with each other. After working with it for a little while… need to have the rhomboids on top and the kites and darts on bottom. There are too many pieces below for the number above currently.
If the centerline of our vault is a normal catenary curve then we could have the top surface as kites and darts and a lower surface as rhomboids. Then we use evolute to optimize the top and bottom surface to match as closely as possible to the centerline as representative of a normal catenary vault. If it bow ties inward to the center line, we have the beginning of the shape we need for the interconnecting parts.
So we find the set of vertices for the top and bottom surfaces, then we can examine them in sections through the vault, and optimize each back to the catenary curve allowing the curve to vary as it extrudes through the surface. Nice as it gives us a much simpler algorithm to test against (catenary curve) definition, yes?
Flatland… looking at two dimensions and manipulating in three
Script that generates options that take length of line and degree of curvature
Need to straighten out the center line
Probably looking at curves between degree two and degree five
Rhino works in derivative vectors rather than algebraic ones
Maintain lowest degree of curvature?
Shadow will look like the Penrose tiling
Defining our center line and determining whether we can have it be a foldable axis, like the crochet geometry
Container of lines, defined starting and end points
Select all end points, then select all points leftover at edges
Cull to make sure we’re selecting only what we need
Now we can ask what the length of a line is
Now we can do random +length to line
But now we have to change degree
Project back onto 2D surface
Check to make sure it looks like the Penrose
If it doesn’t, we need to fix some stuff
Galapagos will allow us to optimize a script with a genetic algorithm
So we’ll be able to implement this here to optimize our curvatures