Orbi - Symmetry Groups as parametric design tool

   

Logo of the Programs in Grasshopper
15 of 17 Ornament groups of the layer

Orbi is a plug-in for Grasshopper that generates patterns parametrically with symmetry groups.

Symmetry groups are elementary forms of repetition. Unfortunately, however, they appear almost exclusively in the curriculum of mathematicians.

 

Architects, designers and engineers are often not aware that there is more than point and mirror symmetry. They don´t know that there are very specific symmetries possible around a point, along a line or on a flat or spherically curved surface. And the astonishing fact that there are exactly 17 wallpapergroups, 14 spherical groups and 7 frieze groups is hardly known among many people professionally dealing with form. Orbi is supposed to change this and make symmetry groups accessible as a practical tool for designers using Rhino and Grasshopper.

 

Orbi allows to select a symmetry group and define any geometry as the fundamental region of a pattern. The fundamental region is the smallest part that is repeated in a pattern. In Orbi the shape of the fundamental region is displayed and used as drawing area for an input geometry.

he fundamental region can be freely arranged and oriented in space. Once the fundamental region and the symmetry group are defined, the corresponding pattern is generated automatically. Orbi offers clusters for symmetries of all rosette groups, frieze groups, wallpaper groups and spherical groups. Each cluster has the name of the symmetry group in Orbifold notation.

 

The Orbifold notation for symmetry groups goes back to William Thurston and John Conway and is probably the clearest and simplest taxonomy of symmetry groups. If you want to get a deeper insight into the Orbifold notation and symmetry groups, „The Symmetries of Things“ is a very clear and understandable introduction.

Orbi was created during a small course on folding with digital tools in the summer term 2020. Programming a symmetry group to create a folding pattern was an introductory exercise of the course. It turned out that symmetry groups are really useful and also fun. So a small group of interested people decided to build Orbi outside the curriculum. The goal was not only to build a useful new tool for their own design, but - from a more general perspective - to try to actively contribute as architects to the development of new and open digital drawing tools.

Here is the download-link for the manual.

user_manual_orbi_eng_v05

Here is the download-link for the application.

https://www.food4rhino.com/app/orbi

Flower of the passion fruit with 3,5 and 10 tenfold mirror symmetry, license CC-BY-NC-SA
Plate IX, Egyptian 06 from Owen Jones: The Grammar of Ornament, Day and Son, London 1856

Orbi is a plug-in for Grasshopper that generates patterns parametrically with symmetry groups.

Symmetry groups are elementary forms of repetition. Unfortunately, however, they appear almost exclusively in the curriculum of mathematicians. 

 

Architects, designers and engineers are often not aware that there is more than point and mirror symmetry. They don´t know that there are very specific symmetries possible  around a point, along a line or on a flat or spherically curved surface. And the astonishing fact that there are exactly 17 wallpapergroups, 14 spherical groups and 7 frieze groups is hardly known among many people professionally dealing with form. Orbi is supposed to change this and make symmetry groups accessible as a practical tool for designers using Rhino and Grasshopper.

 

Orbi allows to select a symmetry group and define any geometry as the fundamental region of a pattern. The fundamental region is the smallest part that is repeated in a pattern. 

In Orbi the shape of the fundamental region is displayed and used as drawing area for an input 

geometry. The fundamental region can be freely arranged and oriented in space. Once the fundamental region and the symmetry group are defined, the corresponding pattern is generated automatically. Orbi offers clusters for symmetries of all rosette groups, frieze groups, wallpaper groups and spherical groups. Each cluster has the name of the symmetry group in Orbifold notation. 

 

The Orbifold notation for symmetry groups goes back to William Thurston and John Conway and is probably the clearest and simplest taxonomy of symmetry groups. If you want to get a deeper insight into the Orbifold notation and symmetry groups, „The Symmetries of Things“ is a very clear and understandable introduction.

 

Orbi was created during a small course on folding with digital tools in the summer term 2020. Programming a symmetry group to create a folding pattern was an introductory exercise of the course. It turned out that symmetry groups are really useful and also fun. So a small group of interested people decided to build Orbi outside the curriculum. The goal was not only to build a useful new tool for their own design, but - from a more general perspective - to try to actively contribute as architects to the development of new and open digital drawing tools.