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)
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.