# Gridshells without geometric torsion (torsion-free nodes)

Hi everyone,

I’m interested in the topic:

Hybridizing vertex and face normals to design torsion free structures: application to the X-mesh pavilion (see app.).
A torsion-free node, where central planes meet at the same axis (arrow).X_Mesh.pdf (1.1 MB)

Packing circles and spheres on surfaces (see app.)packing.pdf (7.4 MB)

Can someone help me to build an algorithm in Grasshopper with Kangaroo2 or with other components or upload a finished sample file (Grasshopper) here.

Dzintars

Here’s an example file of making a quad mesh conical and generating the torsion free offset structure

Many thanks Daniel,

Where it is shown, how to use Kangaroo components correctly.

Dzintars

I believe there is none, but you can find example files for different scenarios on Daniel’s Github.

On another note, planar quad or n-gon faces won’t guarantee that the “extruded” elements of the offset structure are also planar.

Furthermore, if you average the normals of a mesh vertex and its vertex neighbours (like in your diagram above), and use the normalised unit vector to offset the vertex in question, you’ll get an overall even mesh offset and the individual element nicely meet/connect at the vector. However, in most cases - especially with doubly-curved surfaces - the same elements won’t be torsion-free/planar.

Another method would be to “extrude” the mesh edges with averaged, normalised vectors, derived from the normals of their individual end points. This will always get you planar and torsion free elements, however a big downside is that the individual elements don’t exactly meet at common nodes anymore. And further processing of the elements will be necessary to extend the ones that don’t meet and trim others that intersect.

Now, you can use Kangaroo to for instance try to planarise extrusions from the first method! There even was a thread about this some time ago, but I couldn’t find it.
@DanielPiker, do you remember what it was called?

It’s true simply planarising the quad faces in general does not guarantee planar beams when you offset it.
However, this method does give you planar beams and torsion free nodes, as it makes the mesh conical (as described in http://www.geometrie.tugraz.at/wallner/focal.pdf).

@diff-arch - you don’t need to planarise the extrusions with this method, since once the mesh vertices meet the conical angle condition, the beams can be planar by construction.

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Thanks for your help (Daniel Piker and P1r4t3b0y).
Dzintars

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Is it possible to use Kangaroo2 with R5 and create a goal that does the same as the conicalise goal for triangular or quad meshes? Or does it require writing a custom goal?