Surface Component based on Gaussian Curvature

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.

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…

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.

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…

Today, there are pedagogical and practical challenges on the use of algorithms in architectural design, as computer puts not only a physical but also a cognitive layer between designer and the subject. Formulation of this cognitive layer is becoming important, regarding which model of computing is used to connect designer with the subject. Is it a “designerly” search, or design exploration in a visual programming environment? As most of the researchers admit that visual programming environments are very effective in generating variations,…