Surface Mapping

Some images of procedural exploration of mapping geometry to the surface.

Grasshopper Progress for Vaulting Hypothesis

Reconciling the Top & Bottom Layers with Triangles

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.

Model Measurements for Cutting

All Measurements are in inches


Mixer Tolerance about .4 in


Big slice:

x → 5.04

y → 10.236

z → 11.535


Small Slice:

x → 2.362

y → 9.843

z → 11.535


Roomba/Cutter Tolerance about .2 in


Purple and White:

x → 13.78

y → 3.779

z → 6.535


Spatula Tolerance about .3 in



x → 3.622

y → 10.945

z → 11.417



x → 2.99

y → 10.945

z → 11.417

Robot Arm Measurements for Cutting

(Thickness x Width x Length)

Bicep Top Half:  1″x 4.26″ x 12.41″

Bicep Bottom Half:  4.49″ x 4.27″ x 12″

Forearm Top Half:  2.19″ x 4.51″ x 10″

Forearm Bottom Half:  1.74″ x 4.51″ x 10.1″

Hand Top Half:  1.38″ x 4.09″ x 4.96″

Hand Bottom Half:  0.51″ x 4.09″ x 4.72″


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?