algorithmic modeling for Rhino

Hello everyone,

has someone a suggestion how to start with a reciprocal system on a freeform surface in grasshopper? Any suggestions are welcome.

Views: 32986


Replies to This Discussion


thought I can introduce a university project done on this topic in Kassel, germany.



Hi everyone,

Some really interesting stuff on this discussion. I am looking into reciprocal frames myself for a University project. In particular I am looking at Nexorades and exploring the rotational element from standard meshes to reciprocal frames. To achieve this each member is rotated along an axis normal to the surface. When this is done each member will be too short to reach its neighbours. I am having real trouble working out the final length of each member to ensure an overlap (the fact they don't touch is not yet relevant, I will solve that in future explorations). Essentially, the smaller pipes in the image below need to overlap by a fixed amount for whatever rotation of each member.

I have attached my file so far. I have tried tangential planes with intersection events, closest point calculations etc. but I keep coming back in circles. I am still fairly new to a lot of the software so apologies if I am missing something obvious. The definition does use a weaverbird 'polylines dodecahedron' and 'mesh edges' as a starting point for now and a kangaroo 'remove duplicate points'.

Thanks for any help anyone can give me and I look forward to seeing what everyone else is up to,



To clarify please see the notes scribbled in the latest definition


My file and approach:


Really Great work! is it possible to adapt your work on a Exagonal based subdivision like this?

Wow!!! I haven't bin here for a long time. Thank you so much for all these great inspirations to deal with this problem.
It seams to me, as Daniel said, it is really hard to get all the members straight and matching each other. I am trying hard to solve this problem, but I am not sure if this is possible just with grasshopper tools.
I will post it, if I get some thing.

Hello to all who are still interested in reciprocal frame systems.
I found by accident this Video:
It looks amazing!!

Really cool video, thanks for posting this. It seems they have solved the intersection points which everyone, myself included, seems to have struggled with in grasshopper to avoid overlapping or missing joints (what they call optimisation in the video)

I never posted where my explorations in grasshopper with reciprocal frames ended up going thanks to the help everyone provided on this thread. I am still working on it and will post some definitions and images when i have fixed a few bugs but if anyone is interested, the early development work can be found here:

And some images of later models can be found here (descriptions and development work to be posted at a later date):

great find Jerrimo,


Brilliant, thanks very much Jerrimo for posting this

Hi all,

In June we built this structure as part of the Structural Geometry workshop in Salerno run by Gennaro Senatore and myself:

Using techniques I hinted at earlier in this thread, with the line-line force in Kangaroo and Plankton for the mesh connectivity.

The approach is a bit different from the paper linked to above - instead of mapping a 2D pattern to a parametrization of the surface, we used the mesh connectivity directly - so it can handle arbitrary topologies and irregular vertices (the technique in the paper appears to be limited to genus 0, with a special symmetrical extension for spheres).

I'll post more info and pictures soon. Grazie to all the wonderful participants!






  • Add Photos
  • View All

© 2021   Created by Scott Davidson.   Powered by

Badges  |  Report an Issue  |  Terms of Service