Rules Surfaces : D-Form Explorer in Grasshopper

Ruled Surfaces #1: D-Form Explorer (Grasshopper)

Here are some examples i am currently preparing for a set of lectures on Architectural Geometry to be held at TU Vienna starting in about two weeks. Since the main focus will lie on ruled surfaces, which are especially interesting for architectural applications when it comes to actually building a freeform design, these definitions will generate models based on these special surfaces.

First, we have a rather simple, but nevertheless very nice application. ‘D-Forms’ consist of two non-elastic surfaces-patches (e.g. paper) sharing the same perimeter. You can produce such objects by cutting out these patches from e.g. paper, starting to glue them together at arbitrarily chosen points along the two perimeters. The rest will follow automatically such that the shape will be closed. (Note that for the first image i just couldn’t resist to apply some filleting onto the edges 😉

In grasshopper, i select two closed bspline-curves, which serve as bases for two extrusions. These are then centered around the coordinate origin, after which they are assigned a boolean difference. To alter the result, you can change the height of one of the extrusions, as well as its rotation angle. Of course, it is also possible to alter the input curves.

In order to easily arrange nice results without leaving the context of grasshopper, i added two sliders allowing the user to shift their design to a free parking slot before baking it.

Using the ‘unroll surface’ command in rhino, the surfaces can be projected onto the base plane without distortion (since they are developable), after which you can cut them out and glue them together.

Have a look at Tony Wills’ webpage, who is the source of the D-Forms concept. Thanks to Georg Suter for some valuable feedback on this one !