Planar Quadrilateral : Grasshopper Workshop @ Tamkang University
This workshop is invited by professor Chen-Cheng Chen from the architecture department of Tamkang University. It focuses on the particular geometry of planar quadrilateral(PQ) mesh. PQ mesh draws interests from architects in recent years because of its constructability. There are many advantages using PQ over triangulation when discretizing a freeform surface. For more information on PQ mesh and descretization, see paper A parametric strategy for free-form glass structures using quadrilateral planar facets by Glymph at el. and Discrete Surfaces for Architectural Design by Pottmann et al.
The paper by Glymph at el. introduces several methods to construct a PQ mesh. One is called “translation surface” and the other “scale-translation surface.” These method generates discrete versions of the freeform surfaces using PQ strips. While in the translation surface method, the strips are discrete versions of conic developable surfaces; in scale-translation surface, the strips are discrete versions of conic developable surfaces. If we increase the division points on the section curve, the strip will eventually become a developable surface. Here is the procedure to build a scale-translation surface in grasshopper.
There are two things worth noting in the definition. First, the graph mapper controls the scaling of section curve along the rail. Second, the relative component matches the four vertices of a quad face.
If the model is going to be fabricated with planar material, tabs might need to be added to the faces for construction. See the details in the installation by Skylar Tibbits for reference. Also, the geometry needs to be flattened for cutting. In the definition, Clusters are used to improve the re-usability of components. A Cluster is a collection of components that are packed into a single component. Because of the datatree management issue, clusters will sometimes produce undesired results when connected by multiple inputs. Currently, it is not as robust as comparable features in GenerativeComponents or CATIA. However, using clusters is still a good practice that makes your canvas less chaotic.
Download the definition file here.