Quad Tiling on Double Curvature
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.
Cite this post
Related Posts
Quadrilateral Surface Tessellation
April 9, 2012
As far as I understood, it is impossible to physically construct double-curved surfaces from quadrilateral and planar faces. This definition tries to find an optimized alternative to this problem. Any surface, single or double curved, is divided into standard sub surfaces. But this time, those surfaces are treated as planar surfaces, therefore one corner is moved to meet this requirement. The output consists of only planar surfaces ready for fabrication. There are potential improvements to this definition such as finding…
Surface Components Basics
January 17, 2012
This is a basic formation of component-based design in a dataflow environment. A double-curved surface is subdivided and re-constructed using straight sections. Parametric model of a surface construction by variable components. The main data list of subsurfaces are distributed into four distinct lists, that will be used to construct lines out of double-curved quadrilateral faces. Such definitions could be further advanced by adding a precise fabrication detail.
Gaussian Curvature and Surface Paneling
January 24, 2019
As the design of free-form architectural surfaces becomes easier, questioning and foreseeing the feasibility of the construction of these surfaces becomes important. Such an inquiry requires sufficient knowledge of architectural geometry besides the knowledge of materials and structural systems. In this article, we present a preliminary example of a guide. It supports the design and production process of building surfaces with different geometric properties is presented. This guide aims to reveal the relationship between Gaussian curvature and surface paneling. It…
Points by Curvature
April 26, 2012
This is the basic form of a surface division, based on curvature. As each point on the surface has a curvature value, this might be used to dispatch those values and see the points at flat and curved parts of the surface. I used my favourite surface equation definition (here) as implemented equation of cos(x)+cos(y) in the animation below.
Monkey Saddle Surface
April 8, 2012
This is another popular “math surface” being rediscovered by designers nowadays, in 2012. Saddle surfaces, seen above as mentioned earlier (here) have a special type named “Monkey Saddle Surface”. This surface was a dramatic example of how Grasshopper can control equations and instantly show graphical results. The mathematical equations start with Z=… this makes it very easy for us to transform any x-y grid centers (a 2d data tree of 3d points) and add z values to them according to…