Algorithms

This is about conforming distortions on surfaces and creating imperfect (say ugly) surfaces. I started with planar surfaces, however, I continued with spherical ones. There are interesting results when applying trigonometric functions to spherical surfaces. Example surface equations: Please be patient if animations are loading slowly. But they represent a way of creating free-form-looking surfaces, highly mathematical behind the scene. As you see, I used the UVW coordinate system of the sphere, subdivided into 20 pieces. W represents the amount…

This is probably the most simple definition on this site but I think it’s very useful. The timer is a special component of Grasshopper that is significant in terms of the real-time sketching paradigm. This basic use of a timer includes a 1-second update to a Vb script. Inside the script, the system date’s seconds are returned, so we see a real-time increasing number at output A. Beyond this point, It’s up to your imagination, how you can use that…

Truncated hexagonal tessellation (or named 3-12-12) is represented in hyperbolic space (as far as I understood it). The idea is simple if you don’t mix it with complex equations. Below is the 2-dimensional representation of hyperbolic projection. Paper space is defined by the thick line there. Projection is based on a two-sheet hyperboloid surface. Euclidean version of this tessellation is described here.

This is my second attempt on getting into non-euclidean representations of space. Althouth it seems easy at first sight, this represents a close point of theory between mathematics and contemporary computational design geometry. As always, architects tend to use mathematical terms such as “non-euclidean geometries” but as far as I saw, most of them have no idea about what it is. So, I’m trying to learn and understand this connection by experiencing small parts of it, sailing at the edges…

This is my first attempt at representing a non-euclidean space. There are several representations of a non-euclidean space in euclidean means such as Beltrami-Klein or Klein, Poincare, Poincare half-plane, and Weierstrass. Here, I tried to understand Poincare’s approach. Random straight lines are drawn on a hypothetical hyperbolic space using a simulation of Poincare’s famous disk representation. Although there is a precise description of the disk and its construction, I used a ready-made arc component of Grasshopper3d, showing start and end points along…

Using SPM Vector Components developed by two talented people, Daniel Hambleton and Chris Walsh (website here), I’ve studied ways of displaying dynamic diagrams of form. I’ve modified an example file and found myself in a surprising formal exploration. It’s like watching the clouds, giving them meaning like a sheep, a flower, a baby… This needs SPM tools to be installed first and includes a timer component. To run the simulation, double-click on the lower toggle (set it to false) and run the timer…

I’ve worked a little more about the Solar Position definition I’ve started here. The definition uses Danel da Rocha’s beautiful solar position script and utilizes it with other components. It creates visual output for any given surface, divided into quads (with side faces of course) and coloring according to their orientation to the sun. This time I added an occlusion part to calculate the surface’s own shadow. Now, the solar calculation takes surfaces as obstacles and dispatches the occluded faces…

Here I am testing the nesting. RhinoNest is a plug-in for Rhino and a set of components for Grasshopper. I tested it using my old interlocking fabrication definition (here) and (here). I downloaded RhinoNest from this website and installed it. However, I sounded a little complicated at first sight. Then I found a sample definition (here) and modified it a little bit to meet my purposes. First of all, I added orientation components (grey group below) to align all sections to the WorldXY…

I have come across several high school topics I was afraid of. While I was searching for a geodesic dome definition in Grasshopper, it was quite surprising that I found an easier way of modeling an approximation of icosahedron, the famous platonic solid. Icosahedron was a research topic of this website at various posts before (here, here, and here). In order to generate geodesic spheres, first I had to solve icosahedron. My first experiment was partially successful. I knew icosahedron’s…

Yesterday, Kağan asked me about the isovist component in Grasshopper and how it works. In fact, it is a long story, I said because once upon a time, I was curious about Space Syntax theory as my old friend Ela Çil introduced it. So, here is an original definition of Michael Benedikt: “The environment is defined as a collection of visible actual surfaces in space. An isovist is the set of all points visible from a given vantage point in…