#curvature

Let’s take a closer look at the midterm jury assignment for our “Field & Matter”- themed Computation-based Basic Design 2 studio, which I conducted last year alongside Serkan Uysal, İpek Kuran, and Sinan Logie. I shared the studio’s final project, Earthbound, in a previous post. In this post, we will focus on our process-oriented midterm project named Spacebound. Topography as a Data Field In this first major phase of the “Field & Matter” studio, we examined how moving and stationary…

The development of geometry began by measuring the world as discrete objects. Moving beyond measuring nature, it evolved into reasoning, calculation, and mathematics. Platonic solids were one of the most elegant and beautiful ideas reached by geometry. Pondering why there are only five of them was a tribute to collective human intelligence. Earlier in this blog, we modeled polyhedra, like the Platonic solids, using geometric construction methods. This process was like solving a puzzle. To construct a point whose distances…

This is the last of the site analysis tools we previously used in the midterm project of first-year architecture education. As you may recall, we previously introduced a tool that generates topographies based on specific parameters. Afterward, we examined two tools that perform slope and flow analyses on these topographies. Today, we are presenting a tool that analyzes curvature. This topic actually constitutes one of the interesting intersection points between architectural design and differential geometry. Curvature is not something architects…

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…

Curvature can be roughly described as how much a curve is “turning” at point a P. We place two “very” close tangents and measure the difference between them. The closer these tangents are, the more precise our approximation would be. An osculating circle is a tangent circle that has the same curvature as the curve at point P. The larger the circle, the more “flat” the curve is. An infinitely large osculating circle means the curve is linear at point…

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…

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,…

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.