It is not possible to cover a double curvature surface with planar quads. Here is one method that overcomes quad tiling on double curvature by pulling one vertex of the quads to the plane defined by the other three. This method was used in architecture on several occasions such as the exterior facade of The Yas Hotel, designed by Asymptote Architecture in 2009. The same approach is also evident in the roof design covering the central courtyard of the Smithsonian Institute courtyard completed by Foster + Partners in 2007. In this Grasshopper implementation, I also experimented with a surface construction utilizing trigonometric functions.

This Grasshopper definition panels the surface of a trigonometric function with extended quad panels. It is an educational and exploratory code to learn Grasshopper and generate interesting designs with it. The inputs of the definition are the size and number of panels, the surface function, and a shifting parameter for animation purposes. The output of the code is the set of single surfaces in Rhinoceros. Therefore, it is ready for further investigation and modeling. You can modify this code to panel any given surface also. The code is using native Grasshopper components. Thus, no add-ons are necessary for it to work.

You can rebuild the definition by looking at the diagram and tutorial video. You can also visit this post to see an older version of the code that takes any surface objects. However, if you want to support my website by downloading my Grasshopper files; would you consider being my Patreon? Here is the link to my Patreon page including the Grasshopper files for the Quad Tiling on Double Curvature. Thank you.